JP5854346B2 - Transcriptome analysis method, disease determination method, computer program, storage medium, and analysis apparatus - Google Patents

Description

  The present invention relates to a principal component calculation method, a transcriptome analysis method, a gene, an aging determination method, a computer program, a storage medium, and an analysis apparatus, and more particularly to a principal component calculation method for calculating a principal component using experimental data, a transformer The present invention relates to a cryptogram analysis method, a gene, an aging determination method, a computer program, a storage medium, and an analysis apparatus.

Principal component analysis is a method of multivariate analysis that summarizes matrix data by compressing dimensions.
Referring to Non-Patent Document 1, principal component analysis originally originated from the consideration of the distance between a space and a matrix element by Pearson. On this basis, referring to Non-Patent Document 2, it is said that Hotelling has been summarized as a technique.
Referring to Non-Patent Documents 3 and 4, principal component analysis is widely used, and it is considered to be applied to analysis of transcriptome data having a particularly large dimension.
The transcriptome indicates the state of the expression level of total mRNA (messenger RNA, transcripts) in a cell under a predetermined condition. Organisms usually have the same genetic information (genome) within the same individual, but the transcriptome differs depending on the difference in tissue cells, differentiation status, age, response to extracellular stimuli, etc. .
The expression level of a plurality of mRNAs related to the transcriptome can be measured using a DNA array (microarray) or the like.

First, the principle of principal component analysis will be described with reference to FIG.
FIG. 13 is an explanatory diagram showing the principle of conventional principal component analysis. In the example of FIG. 13, the analysis target of 4 measurement items with 3 samples in 9 groups is calculated as a matrix X of 9 × 4 matrix.
In this calculation, the axis is obtained as a singular vector U or V using the singular value decomposition as the matrix X, and the principal component PC is obtained using these vectors.

  In principal component analysis, eigenvectors are found between items and between samples from multivariate data that has a large number of measurement items and samples and is linear or can be converted to linear. Multivariate data is efficiently summarized by evaluating the data using the vectors.

In many measurements, data can be represented by a matrix of sample s × measurement item g.
This matrix is both “a vector of elements for measurement items expressed in a dimension called samples” and “a vector of elements for samples expressed in a dimension called measurement items”.
Either way of thinking, the number of dimensions tends to be large, but these dimensions are not always orthogonal and do not efficiently represent the differences in elements.
In principal component analysis, a new axis representing the matrix dimension is set. These new axes are orthogonal to each other. The first axis is along the center of the element group, and the second axis is along the center of the residue not represented by the first axis.
In this way, each newly set axis efficiently approximates the data with fewer dimensions than the original matrix.

This operation will be described by singular value decomposition.
It is assumed that X is a data matrix standardized by centering with the average of the items, and X ′ is a transposed matrix of X. At this time,

X = U ・ L ^1/2・ V '

Here, U and V are unitary matrices describing singular vectors, V records an axis for samples, and U records an axis for items. L ^1/2 is a diagonal matrix, and the diagonal components are sorted in descending order of singular values. Further, V ′ represents a transposed matrix of V.
The sample principal component PCs and the item principal component PCg are defined by the following equations.

PCg = X · V

Similarly,

PCs = X'U

PCs is the main component of X ′.

As is clear from the definition of singular value decomposition, each principal component can reproduce X or X ′ before decomposition by taking the inner product with a unitary matrix.
Therefore, it can be seen that this is a rotation of X and X ′. Alternatively, it can be said that the orthogonal axis is newly set while the positional relationship of the elements of the original matrix remains unchanged.
Since these axes are orthogonal to each other and are selected from the direction that best represents the difference between the elements, the data can be represented with fewer dimensions than the original axes. This is the principle of data dimension compression.
Each main component depends on the number of samples and the number of genes. These values represent the total distance from the origin when the original element is projected onto each new axis. That is, if the principal component PCs of the sample, it is the sum of the distances of the items, and if it is the principal component PCg of the items, it is the sum of the distances of the samples. Of course, this value will change if the number of samples or items changes.
That is, referring to Non-Patent Document 4, the principal component is a relative value, and has meaning only in X.

Here, as an information processing apparatus that linearly analyzes or predicts the formation of a conventional transcriptome, referring to Patent Document 1, the model is used by approximating a transcriptome formation mechanism using a thermodynamic model. An information processing apparatus that performs transcriptome information processing is described (hereinafter referred to as Conventional Technology 1).
The information processing apparatus using the thermodynamic model of Prior Art 1 defines the concentration of each mRNA using an energy parameter that determines the synthesis rate of each mRNA and an energy parameter that determines the degradation rate of each mRNA, The energy parameter is defined using a local concentration of a factor that binds to RNA or DNA in a base sequence-specific manner and a specific coefficient of a base sequence that can be a target of the factor.
In the prior art 1, at least one of the mRNA concentration, the intracellular concentration of the factor, and the value of the specific coefficient of the base sequence is input to the thermodynamic model, and the remaining value is calculated and output as an unknown. .
According to the information processing apparatus using the thermodynamic model of the prior art 1, by expressing the interaction between the sequence and the protein factor objectively, it is possible to decode and transform the quantitative information of the genome at the transcriptome level. It is possible to reproduce the cryptogram and provide a platform for comparing the results of various experiments and measurements and for integrating knowledge.

JP 2006-236011 A

Pearson, K (1901), 'On Lines and Planes of Closest Fit to Systems of Points in Space', Physiologic Magazine, 2 (6), 559-72. Hotel Hotling, H.C. (1933), 'Analysis of a complex of statistical variables into principal components', Journal of Educational Psychology, 24 (7), 498-520. Jackson, J.M. Edward (1991), A User's Guide to Principal Components (New York: John Wiley & Sons, Inc). Shaw, Peter J .; A. (2003), Multivariate Statistics for the Environmental Sciences (London: Holder Arnold).

First, the information processing apparatus using the thermodynamic model of the prior art 1 needs to substitute the model with the mRNA concentration, the intracellular concentration of the factor, the specific coefficient of the base sequence, etc. into the model. It was difficult to apply to general-purpose microarray data, which is the data it has.
For this reason, it has been desired to analyze the transcriptome data obtained by measuring the amount of mRNA in a general microarray using the conventional principal component analysis suitable for analyzing data having a large dimension.
However, the conventional principal component analysis has a problem in applying to transcriptome data in the following points.

First, there is a problem that inspection items for recording as transcriptome data are often changed. In addition to this, there are many types of microarrays for examining transcriptomes that are available on the market, and there is a problem that the types increase with each update.
Furthermore, microarrays often differ in the types of genes they cover, and test items vary.
However, the conventional principal component analysis has a problem in that it does not support such changes in microarrays or changes in inspection items of microarray data.

The reason for this is that not all of the mRNA samples, test items, and gene types measured by the microarray have the same weight or importance.
In many cases, measurement using a microarray is repeatedly performed using a plurality of biological samples. In this case, the number of repetitions of the experiment is not necessarily the same. For this reason, all the samples in the matrix data are not equally independent and have the same weight.
However, the conventional principal component analysis does not cope with such a difference in weight, and there is a problem that there is no means for correcting it.

Also, in microarray experiments, it often happens that some variation is common between samples, regardless of the commonality of repeated experiments.
For example, in experiments, when multiple samples from different groups suffer from the same disease, the effects have been detected by principal component analysis.
For this reason, trends unrelated to these groups hindered the discovery of effective changes as the main component and also caused false positives.

Further, the conventional principal component analysis has a problem that it does not correspond to the group bias.
For example, when Principal Component Analysis is used for toxicology that analyzes the transcriptome corresponding to the drug response of cells, if many similar substances (drugs) are included in the data matrix, they are discovered by Principal Component Analysis. There is a problem that the direction of the axis to be overestimated those substance groups.

  In addition, the conventional principal component analysis did not deal with data such as medical examinations in which measurement items differ to some extent between hospitals, but there are many measurement items.

ここで、ｐ：実験群の番号であることを特徴とする。
本発明のトランスクリプトーム解析方法は、前記データ行列Ｘ_pを特異値分解すると、左特異ベクトルＵ_pと対角行列Ｌ^1/2および右特異ベクトルＶ_pの関係が下記式である

ことを特徴とする。
本発明のトランスクリプトーム解析方法は、前記主成分のうち、サンプル毎の主成分ＰＣ_sは、下記式である

ことを特徴とする。
本発明のトランスクリプトーム解析方法は、前記主成分のうち、遺伝子ごとの主成分ＰＣ_gは、下記式である

ことを特徴とする。
本発明の疾病判定方法は、解析装置を用いてデータ行列から主成分を算出する主成分算出方法であって、前記解析装置は、主成分を、その主成分の算出に用いたサンプル数又は測定項目数の平方根で除することでスケーリングし、前記解析装置は、スケーリングした前記主成分から、所定の閾値でサンプルを選択し、疾病群と対照群とを比較し、健康診断の測定項目についての前記データ行列から前記主成分を計算し、前記主成分を、前記主成分の算出に用いた前記データ行列の前記サンプル数の平方根、又は該主成分の算出に用いた前記データ行列の前記測定項目数の平方根で除することでスケーリングし、スケーリングした前記主成分から、前記所定の閾値で前記健康診断の測定項目が変化したことを判定して選択し、特異ベクトルで表される前記主成分の軸を求めるために、トレーニングデータを用い、前記トレーニングデータは、群の平均値からなる各群の代表値を用い、項目の基準値を設定して、該基準値で標準化され、前記基準値は、基準にするデータを特定して設定し、設定された基準にするデータは前記主成分の原点とし、前記主成分の軸は複数の測定値で共有しつつ、前記基準にするデータは各測定値で定め、前記トレーニングデータを用いて前記主成分の軸を定義し、前記主成分の軸を個々のサンプルのデータに適用することで、サンプルをクラス分けすることを特徴とする。
本発明のコンピュータプログラムは、前記トランスクリプトーム解析方法、又は前記疾病判定方法を実行することを特徴とする。
本発明の記憶媒体は、前記コンピュータプログラムを記憶した記憶媒体であることを特徴とする。
本発明の解析装置は、データ行列から主成分を計算する主成分演算部と、前記主成分を、前記主成分の算出に用いた前記データ行列のサンプル数の平方根、又は該主成分の算出に用いた前記データ行列の測定項目数の平方根で除することでスケーリングする主成分スケーリング部と、サンプルの選択と測定項目の選択をし、トレーニングデータを作成するトレーニングデータ作成部とを備え、スケーリングした前記主成分から、所定の閾値でサンプルを選択し、前記主成分演算部は、トランスクリプトーム又は健康診断の測定項目についての前記データ行列から前記主成分を計算し、前記スケーリング部は、前記主成分を、前記主成分の算出に用いた前記データ行列の前記サンプル数の平方根、又は該主成分の算出に用いた前記データ行列の前記測定項目数の平方根で除することでスケーリングし、スケーリングした前記主成分から、前記所定の閾値で前記トランスクリプトームに係る発現量又は前記健康診断の測定項目が変化したことを判定して選択し、前記トレーニングデータ作成部は、前記トレーニングデータとして、群の平均値からなる各群の代表値を用い、項目の基準値を設定して、該基準値で標準化し、前記基準値は、基準にするデータを特定して設定し、設定された基準にするデータは前記主成分の原点とし、前記主成分の軸は複数の測定値で共有しつつ、前記基準にするデータは各測定値で定め、前記トレーニングデータを用いて前記主成分の軸を定義し、前記主成分の軸を個々のサンプルのデータに適用することで、サンプルをクラス分けすることを特徴とする。 The transcriptome analysis method of the present invention is a transcriptome analysis method for calculating a principal component from a data matrix using an analysis device and analyzing the transcriptome, wherein the analysis device includes the principal component as its main component. Scale by dividing by the number of samples used to calculate the component or the square root of the number of measurement items, the analysis device selects a sample with a predetermined threshold from the scaled principal components, and the expression related to the transcriptome The principal component is calculated from the data matrix of change in quantity, and the principal component is the square root of the number of samples of the data matrix used for calculating the principal component, or the data matrix used for calculating the principal component. Scaled by dividing by the square root of the number of measurement items, and from the scaled principal component, the expression level changed at the predetermined threshold Is used to determine the axis of the principal component represented by a singular vector, training data is used, and the training data uses a representative value of each group consisting of an average value of the group, A reference value is set and standardized by the reference value. The reference value specifies and sets data to be used as a reference. The set reference data is the origin of the principal component and the axis of the principal component. Is shared by multiple measured values, while the reference data is defined by each measured value, the principal component axis is defined using the training data, and the principal component axis is applied to the data of individual samples By doing so, the samples are classified.
In the transcriptome analysis method of the present invention, the representative value of the training data is selected by selecting a sample and a measurement item by confirming a significant difference between groups in advance by analysis of variance and narrowing down the measurement item. It is characterized by defining.
In the transcriptome analysis method of the present invention, the change in the expression level is any of the amount of RNA, the amount of translated protein, the activity of the translated protein, and the amount of metabolite produced by protein metabolism. It is characterized by including these.
The transcriptome analysis method of the present invention is characterized in that the predetermined threshold is a threshold that allows false positives on both sides with a probability of 0.001 by comparing the scaled principal component with a normal distribution.
The transcriptome analysis method of the present invention is characterized by determining that the expression level has changed by comparing two or more scaled principal components.
In the transcriptome analysis method of the present invention, the training data is created by selecting the measurement item of the data matrix, and the data of the unselected item is replaced with zero to maintain the size of the original matrix. It is characterized by that.
The transcriptome analysis method of the present invention is characterized in that the missing data is replaced with zero when calculating the principal component.
The transcriptome analysis method of the present invention is characterized in that the principal component is calculated by applying an axis obtained from the training data to the data matrix.
The transcriptome analysis method of the present invention is characterized in that an axis obtained from the training data is used as a weight for data evaluation.
The transcriptome analysis method of the present invention uses selected data other than the data average as a reference when obtaining an axis from training data.
The transcriptome analysis method of the present invention uses selected data other than the data average as a reference when calculating the principal component.
The transcriptome analysis method of the present invention uses the data matrix X _s and the data matrix X _p that are re-standardized by performing centering according to the following formula when calculating the principal component:

Here, p is the number of the experimental group.
In the transcriptome analysis method of the present invention, when the data matrix X _p is subjected to singular value decomposition, the relationship between the left singular vector U _p , the diagonal matrix L ^1/2 and the right singular vector V _p is expressed by the following equation.

It is characterized by that.
In the transcriptome analysis method of the present invention, the principal component PC _s for each sample among the principal components is represented by the following formula:

It is characterized by that.
Transcriptome analysis method of the present invention, among the main component, the main component PC _g per gene is the following formula

It is characterized by that.
The disease determination method of the present invention is a principal component calculation method for calculating a principal component from a data matrix using an analysis device, wherein the analysis device uses the principal component as a sample number or measurement for calculating the principal component. The analysis apparatus performs scaling by dividing by the square root of the number of items, and the analysis device selects a sample with a predetermined threshold from the scaled principal components, compares the disease group with the control group, The principal component is calculated from the data matrix, and the principal component is the square root of the number of samples of the data matrix used for calculating the principal component, or the measurement item of the data matrix used for calculating the principal component. scaled by dividing by the number of the square root, the said main component scaled, measurement items of the health examination is selected by determining that it has changed by the predetermined threshold value, the table in singular vectors Training data is used to determine the axes of the principal components, and the training data is standardized by setting the reference value of the item using the representative value of each group consisting of the average value of the group and the reference value. The reference value is set by specifying the data to be used as a reference, the set reference data is the origin of the principal component, and the axis of the principal component is shared by a plurality of measured values, The data to be determined is determined by each measurement value, the axis of the principal component is defined using the training data, and the sample is classified by applying the axis of the principal component to the data of each sample. To do.
Computer program of the present invention is characterized by performing said transcriptome analysis method, or the disease determination method.
The storage medium of the present invention is a storage medium storing the computer program.
The analysis apparatus according to the present invention includes a principal component calculation unit that calculates a principal component from a data matrix, and a square root of the number of samples of the data matrix used to calculate the principal component, or the principal component. A principal component scaling unit that scales by dividing by the square root of the number of measurement items in the data matrix used, and a training data creation unit that creates training data by selecting samples and selecting measurement items A sample is selected from the principal components at a predetermined threshold, the principal component calculation unit calculates the principal components from the data matrix for a measurement item of a transcriptome or a health check, and the scaling unit includes the main component The component is the square root of the number of samples of the data matrix used to calculate the principal component, or the data matrix used to calculate the principal component. Selected serial measurements scaled by dividing by the number of items of the square root, the said main component scaled, determination is made that the expression amount or the measurement item of the medical examination according to the transcriptome at the predetermined threshold value is changed The training data creation unit uses a representative value of each group consisting of an average value of the group as the training data, sets a reference value for the item, standardizes the reference value, and the reference value is a reference value The data used as the reference is set as the origin of the principal component, and the axis of the principal component is shared by a plurality of measurement values, while the data used as the reference is determined by each measurement value. Defining the principal component axis using the training data, and applying the principal component axis to the data of each sample to classify the samples.

  According to the present invention, the orthogonal axis is found not from the data to be analyzed but from the training data, and by performing the scaling, the inspection item is changed, there is a difference in weight, and many similar substance groups are included. It is possible to provide a principal component calculation method for accurately analyzing conventional matrix data.

It is a block diagram which shows the control structure of the analyzer 10 which concerns on the 1st Embodiment of this invention. It is a conceptual diagram about the method of isolate | separating the discovery and setting of the axis | shaft which concerns on the 1st Embodiment of this invention from the application. It is a flowchart of the principal component analysis process for transcriptome based on the 1st Embodiment of this invention. In Example 1 which concerns on the 1st Embodiment of this invention, it is a figure which shows the example which determined the axis | shaft from all the data, and the example which determined the axis | shaft from training data. In Example 2 which concerns on the 1st Embodiment of this invention, it is a figure which shows the example of observation which gave bias to the sample which discovers an axis | shaft, and the example without bias. It is a figure which shows the example of the biplot which displayed sPCs and sPCg coaxially about the data of Example 1 which concerns on the 1st Embodiment of this invention. It is a plot figure which shows the result of the principal component analysis used for the gene list preparation which concerns on the 2nd Embodiment of this invention. It is a figure which shows the example of the search result of the ortholog which concerns on the 2nd Embodiment of this invention. It is a figure which shows the example which selected 10 genes from the list | wrist which concerns on the 2nd Embodiment of this invention, and computed the aging degree of each sample. It is a figure which shows the parameter calculated by normalization in Example 3 which concerns on the 2nd Embodiment of this invention. In Example 4 which concerns on the 2nd Embodiment of this invention, it is a graph histogram which shows the frequency distribution of sPC1g. It is a QQ plot which shows the difference of sPC1g and normal distribution based on the 2nd Embodiment of this invention. It is a conceptual diagram explaining the method of the conventional principal component analysis.

<First Embodiment>
[Control Configuration of Analysis Device 10]
First, with reference to FIG. 1, the control configuration of the analysis apparatus 10 (transcriptome analysis apparatus) according to the first embodiment of the present invention will be described.
The analysis apparatus 10 is a computing apparatus such as a PC / AT compatible machine or a general-purpose machine, and an OS such as Linux (registered trademark) or Windows (registered trademark) is installed therein.
The main components of the analysis apparatus 10 include a control unit 100 that is a control / arithmetic unit such as a CPU (Central Processing Unit) and a GPU (Graphics Processing Unit), a RAM (Random Access Memory), and a ROM (Read Only Memory). I / O from a storage unit 110 that is a storage device such as a HDD, a hard disk drive (HDD), a flash memory, or a solid state drive (SSD), and a pointing device such as a keyboard or a mouse, a touch panel, or a microarray analyzer. An input unit 130 including an O interface, a display unit 140 such as a liquid crystal display, an organic EL display, a printer that performs printing, and 1000Base-T And a network output unit 150 is a LAN board or a wireless LAN board or the like of case.
The analysis device 10 is executed by the control unit 100 using various programs mainly stored in the storage unit 110 and data including a database, etc., so that the transcriptome according to the first embodiment of the present invention is executed. The analysis method can be realized using hardware resources.

The storage unit 110 stores a computer program and data for realizing the transcriptome analysis method according to the first embodiment of the present invention. The transcriptome analysis method according to the first embodiment of the present invention can be executed using the program and data in the storage unit 110.
The program and data include a training data creation unit 210, a singular vector calculation unit 220, a principal component calculation unit 230, a principal component scaling unit 240, and a database 250.

  The training data creation unit 210 is a part for creating training data by selecting a sample and selecting a measurement item, further determining a reference item value.

  The singular vector calculation unit 220 is a part that obtains and stores a singular vector or a part thereof by performing singular value decomposition or eigen value decomposition on the training data.

  The principal component calculation unit 230 is a part that reads the above-described singular vector or part thereof, processes the standardized data created from the reference and sample data, and obtains the principal component.

  The principal component scaling unit 240 is a part that scales the principal components obtained by principal component analysis.

The database 250 is a part that stores databases such as SQL and various data.
The database 251 mainly stores microarray data 251, training data 252, axis data 253, and principal component data 254.

The microarray data 251 is a part for storing general microarray data as matrix data or the like for comparing groups in each experiment.
For example, the measurement data of Affymetrix Murine Genome U74 Version 2 Array manufactured by Affymetrix can be used as the microarray data 251.
Further, the microarray data 251 stores measurement data supplemented with missing data such as missing matrix elements as matrix data. By applying (evaluating) this matrix data to the orthogonal axis of the principal component analysis obtained from the training data 252, the analysis result by the principal component analysis is obtained.
The microarray data 251 can also store representative values described later.

The training data 252 is training data for finding the principal component by eliminating the bias of the measured value and finding the axis when performing the principal component analysis.
This training data is stored as matrix data _Xt .

The axis data 253 is data for storing values of orthogonal axes found from matrix data in the principal component analysis. The axis data 253 is scaled and held as will be described later.
As the axis data 253, stores matrix data X _t is a unitary matrix mark the singular vectors or the like obtained from U _t and V _t, L _t ^1/2, etc. is a diagonal matrix obtained from the matrix data X _t.

The principal component data 254 is data for storing principal components obtained by applying the matrix data of the microarray data 251 to the axis data 253.
As the principal component data 254, a principal component PCg and a principal component PCs orthogonal thereto are stored.
Further, sPCg which is a principal component obtained by scaling PCg and sPCs which is a principal component obtained by scaling PCs are stored.

[Principal component analysis for transcriptome]
Next, a transcriptome principal component analysis process for executing the transcriptome principal component analysis method according to the first embodiment of the present invention will be described with reference to FIGS.
The transcriptome data used in the present embodiment can correspond not only to the expression level of mRNA but also to transcriptome data in a wide range of fields such as protein increase / decrease and protein activity.

As described above, principal component analysis is a method of summarizing data by finding several orthogonal axes from matrix data and analyzing the data along the axes.
This principal component analysis can efficiently and objectively summarize data having a particularly large dimension, but the result is a relative value that has meaning only in the data and has no generality. Further, if there is a bias in the samples constituting the matrix data, the bias is reflected in the result.

For this reason, in the principal component analysis method for transcriptome according to the first embodiment of the present invention, axis discovery and application (evaluation) are separated.
In finding the axis, the orthogonal axis of principal component analysis is found from the training data, not the data to be analyzed. On this basis, the actual microarray experimental data is applied to the discovered axis to determine the principal component.
Thus, by finding the axis from the training data, it is possible to eliminate sample bias.
In addition, by separating the discovery and application of the axis, it is possible to share the axis widely, so that the effect that the analysis result becomes general can be obtained.
Furthermore, the analysis value can be expressed as an absolute value by scaling the principal component.

Here, an outline of the principal component analysis method for transcriptome according to the first embodiment of the present invention will be described with reference to FIG.
FIG. 2 is a conceptual diagram of a principal component analysis method for transcriptome that separates the discovery and setting of axes from the application in the present embodiment.
In the principal component analysis method for transcriptome according to the present embodiment, training data is used when determining an axis. In the example of FIG. 2, the representative value of each group is used.
In the example of FIG. 2, item 2 is not selected and the data is replaced with 0.
Furthermore, in the principal component analysis method for transcriptome according to the first embodiment of the present invention, the axis is obtained as a singular vector by singular value decomposition, and the principal component PC is obtained using these vectors. That is, in order to find the axis of principal component analysis, instead of using all of the matrix X, a part of X or a smaller matrix X _t (training data) derived from X is used and the axis is used. And analyze.
Regarding the scaling, in the example of FIG. 2, the number of items and the number of samples are 3, so scaling is performed by dividing by the square root of 3.
By configuring in this way, it is possible to analyze microarray data, which is difficult to analyze by conventional principal component analysis processing, by extending and generalizing principal component analysis.
Details of the transcriptome principal component analysis process according to the first embodiment of the present invention will be described below with reference to the flowchart of FIG.
These processes are realized by the control unit 100 executing the program and data in the storage unit 110.

In step S101, the control unit 100 performs an initialization process.
Specifically, the control unit 100 refers to the microarray data 251 in the database 250 of the storage unit 110 and performs processing to replace this with 0 (zero) or the like when there is deletion data.
The control unit 100 secures storage areas such as training data 252, axis data 253, and principal component data 254, and performs processing for initializing various programs.

(Handling of missing data)
Specifically, the handling of deletion data in this initialization process will be described.
For example, in a specific experiment using a microarray, complete microarray data may not be obtained due to engineering trouble, signal trouble, etc., such as dust and foreign matter on the microarray. That is, any item may not be measurable, and in this case, it is stored as a partial deletion of the microarray data.
Here, when the axis and data are measured separately as in the conventional principal component analysis, such deletion of data may be important. For example, deletion of one data makes it impossible to calculate the principal component of one sample.
For this reason, in the transcriptome principal component analysis processing according to the first embodiment of the present invention, the deleted data is replaced with zeros to compensate for the deleted data.
Replacing the missing data with zero is a measure based on a so-called fail-safe idea. By replacing the missing data with zero, the principal component is somewhat closer to zero. This is because the element replaced from the total distance disappears.
However, since the main component does not move away, the sPCg as the item value or the sPCs as the sample value is preferable because the absolute value does not increase due to the deletion data. It is.

Next, in step S <b> 102, the control unit 100 performs a training data determination process using the training data creation unit 210.
In this training data determination process, the control unit 100 performs measurement item selection, reference value setting, representative value selection, item selection, item reference value setting, standardization with reference values, and the like.

First, the control unit 100 selects a sample and a measurement item and creates training data.
At this time, the control unit 100 can summarize and set the sample information using an average or the like.

(Selection of sample and measurement item)
First, the control unit 100 confirms a significant difference between groups by an analysis of variance in advance, narrows down measurement items, selects samples and measurement items, and sets them in a matrix X _{t of} training data. Thereby, the representative value can be determined.
By selecting such samples and measurement items and limiting them to measurement items that have significant differences between groups, the possibility of false positive errors can be reduced.
Similarly, the control unit 100 excludes items outside the measurement limit. At this time, instead of deleting the items excluded from the target, by replacing all the values of the corresponding elements with zero, analysis can be performed while maintaining the matrix type.
This makes it possible to share axes in transcriptome data.

(Structure of training data)
Regarding the structure of the training data in the processing as described above, it is desirable to make the structure of the training data used for finding the axes uniform in order to eliminate the bias of the data and measurement values. For example, if a drug in one field is measured multiple times and compared to drugs in other fields, the frequency should be adjusted for each drug field.
In addition, when repeated measurement is performed, each sample is not independent. If the data of the place repeatedly measured is replaced with the sample average value, the influence of individual differences is reduced.
By creating such training data, it is possible to make the possibility of erroneously detecting the fluctuation “because of some cause coincidentally across groups” much smaller than the conventional principal component analysis.

Next, in step S <b> 103, the control unit 100 performs axis setting / discovery processing using the singular vector calculation unit 220.
Specifically, the control unit 100 performs singular value decomposition, eigenvalue decomposition, and the like to obtain a singular vector.
For example, when singular value decomposition is used, the control unit 100 performs singular value decomposition on a matrix X _t of data including selected samples and measurement items, and obtains a singular vector by the following equation.

X _t = U _t · L _t ^1/2 · V _t '

Here, V _t is data relating to the axis for the sample, and U _t is data relating to the axis for the item.

Next, in step S <b> 104, the control unit 100 performs an axis storage process using the singular vector calculation unit 220.
Specifically, the control unit 100 stores, in the axis data 253, singular vectors obtained by different value decomposition, eigenvalue decomposition, or the like.

Next, in step S <b> 105, the control unit 100 performs an axis reading process using the principal component calculation unit 230.
Specifically, the control unit 100 reads the axis data 253 that is pressed in step S104 described above, and arranges the data in a RAM or the like for calculating the principal component.

Next, in step S <b> 106, the control unit 100 performs a data reading process using the principal component calculation unit 230.
Specifically, the control unit 100 sets a reference value of an item from the above-described training data, and standardizes (normalizes) the reference value.

(Setting of standard data)
The control unit 100 identifies data based on the reference value of the item and sets it as training data.
At this time, the control unit 100 can select an average value of all data as reference data.
As a matter of course, the control unit 100 can also select data that is not an average value of all data for the reference data.
The set reference data is the origin of the principal component. That is, it should be used when certain criteria and control experiments are considered.
Furthermore, the reference data can be set by the user of the analysis apparatus 10 or the data provider using the input unit 130 for each experimental environment, for example.
It can be expected that the difference in the environment is corrected by using the data set as the standard.
That is, it is preferable that the axis is shared by a plurality of measurement values, and the reference data is determined by each measurement value.

Next, in step S <b> 107, the control unit 100 uses the principal component calculation unit 230 to perform principal component calculation processing.
Specifically, the control unit 100 applies the axis data 253 created using the training data described above to the matrix data of the microarray data 251. More specifically, as described with reference to FIG. 2, the control unit 100 obtains the main components PCs and PCg by the following formulas:

PCg = X _t '· U _t
PCs = X · V _t

The control unit 100 stores the obtained PCg and PCs in the principal component data 254.

Next, in step S <b> 108, the control unit 100 performs a scaling process using the principal component scaling unit 240.
Here, in order to perform a principal component analysis using the axis determined by the training data matrix X _t is a generalization of the main component, ie it is necessary to be changed item or sample is compared with that value.
By comparing the values, it is possible to confirm the validity of selection of items and sample groups when creating training data.
In order to realize this generalization, scaling of the principal component values described below is performed.

The controller 100 performs scaling by dividing the value of the principal component by the square root of the number of substantial items or samples used in the calculation. This is deduced from the fact that the sum of squares of the elements of the singular vector is 1 and the number of elements of the principal component.
For example, if the number of elements of X is quadrupled, the expected value of each element of the vector is halved. For this reason, the expected value of the main component is expected to be 4/2 = 2 times. In this case, by dividing the main component by route (4) = 2, it is possible to have the same scale as the first X main component.
In this way, by dividing by the square root of the number of items or samples, the main component can be treated as an average value of the items or samples. Therefore, an effect that comparison is possible regardless of the number of elements is obtained.
As a specific scaling method, for the main component PCg, when the number of samples is n_sample, the control unit 100 obtains sPCg by the following equation using the unitary matrix U _t described above:

sPCg = PCg / (n_sample ^1/2 )
= X _t '· U _t / (n_sample ^1/2 )

The value of sPCg is the average value of the contribution of one sample included in the main component of the item.

Similarly, when the value of the number of items selected in the same way is n_gene, the control unit 100 obtains sPCs, which is a contribution average value of one item included in the sample value:

sPCs = X · V _t / (n_gene ^1/2 )

Even if the values of sPCg and sPCs are obtained from different numbers of samples and items, they can be compared because they are represented as contributions per one.
The control unit 100 also stores the obtained sPCg and sPCs values in the principal component data 254.
Thus, the transcriptome principal component analysis process according to the first embodiment of the present invention is completed.

With the above configuration, the following effects can be obtained.
First, it is difficult to apply the information processing apparatus of the prior art 1 to general-purpose microarray data having a large dimension.
However, in the conventional principal component analysis, which is suitable for analyzing data with a large dimension, the inspection items are changed, there are differences in weights, and many similar substance groups are included. There was a problem that the transcriptome data used in the experiment could not be analyzed accurately.
On the other hand, the analysis apparatus 10 according to the first embodiment of the present invention finds the principal component analysis axis from the training data, not the data to be analyzed, and performs scaling so that the transcriptome data is obtained. Can be analyzed.

Further, the analysis apparatus 10 according to the first embodiment of the present invention performs principal component analysis by separating axis discovery and setting from application.
This makes it possible to share the axis between different analysts and laboratories and between measurements with different measurement items.

Furthermore, the analysis apparatus 10 according to the first embodiment of the present invention can perform the same analysis between different analysts and laboratories by sharing the axis. for that reason. The analysis results are not closed in a certain combination of data. That is, it becomes possible to compare an analysis result with the analysis result of other experimental data objectively.
Moreover, the analysis apparatus 10 according to the first embodiment of the present invention does not have a relative value by scaling.
The analysis apparatus 10 according to the first embodiment of the present invention can give generality to the main component by these processes.
For this reason, it is also possible to classify the material by applying the existing axis to the unknown material.

  Furthermore, the analysis apparatus 10 according to the first embodiment of the present invention can use the training data to make the analysis more robust with respect to the bias of the sample and the group, and can obtain a result according to the purpose of the experiment. .

Further, in the conventional principal component analysis, if the matrix is given, except for the sign of the principal component determined by chance, the principal component is obtained almost uniformly. That is, only the definition of distance has been left to the user who is an analyst in the conventional principal component analysis. The definition of distance varied with the choice of how to standardize the matrix, and there were no options after this standardization. For this reason, the analysis result of the conventional principal component analysis guarantees a certain sense of objectivity.
However, if the conventional principal component analysis is applied to data in which the number of items or the number of samples has changed in order to correspond to the transcriptome data, the scale of the principal component, which is the sum of the distances, changes. There was a problem that the values could not be compared.
On the other hand, the analysis apparatus 10 according to the first embodiment of the present invention also uses training data, and therefore, qualitatively differs from the conventional principal component analysis method. That is, if arbitraryness is given to which data matrix the axis is examined from, an option of “which item is selected and which sample is selected (how to represent the representative value)” is generated.
This seems to impair objectivity at first glance. However, the analysis apparatus 10 according to the first embodiment of the present invention can provide a comparability between the results of different selections by making the principal component values absolute values by scaling.
Therefore, it can be kept so that it can be examined which option is more appropriate.

  Hereinafter, analysis processing using specific microarray experimental data is performed using the analysis apparatus 10 according to the first embodiment of the present invention, and how the results change will be described.

[Example 1]
First, with reference to FIG. 4, the example used for the analysis of the time course experiment regarding the pregnancy and the delivery of a mouse mammary gland is shown. In this experiment, data of Series GSE 8191 in the GBI database of NCBI (URL <http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE8191>, “Key stages in magnitude” development. ") was used. Specifically, 40 chips from Series GSM202666 to GSM202705 (in consecutive numbers) in the NCBI GEO database are used, and the chip used is the Affymetrix Murine Genome U74 Version 2 Array.
More specifically, FIG. 4 shows the sPCs1 and sPCs2 values, which are scaled principal components of the sample. In the figure, numerical values from 1 to 6 indicate the progress of pregnancy, 7 to 9 after childbirth, 10 after weaning, and data for 4 samples in each group.
FIG. 4A shows an example in which an axis is found from all data. FIG. 4B shows an example in which an axis is found from training data consisting of an average value of each group.
As is clear from this result, it is considered that sPCs1 detects the development process of the mammary gland for breast milk production, and sPCs2 detects the process after weaning as the axis.
Thus, the use of training data reduces the variation within the county, which is particularly noticeable with sPCs2.
That is, by separating the training data for finding and defining the axis and the data to be analyzed, the analysis becomes more suitable for the purpose. This effect appears as an improvement in separation between groups, for example.
In fact, in FIG. 4 (b), the separation between groups is significantly improved. This is presumably because the axis of sPCs2 is more immune to the effects of individual differences in the sample and reflects the phenomenon better.

[Example 2]
Next, referring to FIG. 5, the results used for analyzing data in the so-called toxicology field are shown. In this experiment, the highly toxic samples 1, 3, 5 were compared to the other 2, 4, 6 and group C, which did not receive the drug. Non-toxic groups 2, 4 and 6 are located close to group C. Note that one of the six samples was probably mistaken for a toxic sample.
More specifically, FIG. 5A shows an observation example in which a sample for finding an axis is biased. FIG. 5B shows an example in which there is no bias.
In FIG. 5, the axis of each result is determined using the average value of the group as training data. However, in FIG. 5A, only the group 5 (highlighted with an asterisk) includes all data, not representative values, in the training data. This operation artificially caused a bias in the number of data and observed the effect.
In FIG. 5 (a), it is clear that sPCs2 is spent separating the differences within group 5 counties. On the other hand, in FIG. 5B, each group has the same main component, and in sPCs2, groups 1, 3, and 5 are separated. Of course, the differences within the county reflect the individual differences in the sample and are not important to note.
That is, in FIG. 5A, the bias of the sample hides the original investigation purpose. This is a phenomenon that cannot be avoided by the conventional principal component analysis method when the types of samples are biased.
On the other hand, FIG. 5B shows that the influence of bias can be avoided by using appropriate training data even in such a case.
That is, by using training data, the axis weighting error due to sample bias is solved. This appears as robustness against sample bias.

FIG. 6 shows a so-called biplot in which sPCs and sPCg are simultaneously displayed for the same data as in FIG. 4B.
One circle in the figure indicates the sPCg of each gene, and the number indicates the sPCs of each group.
The fact that sPCs having about 10,000 measurement items and sPCg calculated from at most 10 sample representative values are displayed on the same axis directly represents the effect of scaling of the principal component.
Here, referring to Non-Patent Document 4, the axis scale cannot be shared unless scaling is performed.
On the other hand, in FIG. 6, it can be easily understood that the genes having negative sPC characterize the group 10.

Further, in Example 1 in FIG. 4 and Example 2 in FIG. 5, the scale of the axis was almost the same, although the measurement was completely different.
This indicates that the scale of transcriptome change in these experiments was roughly the same.
That is, one of the effects of scaling of the main components is that such a comparison can be performed even though the chip contents such as mRNA for measurement are different and the number of genes is different.

Principal component analysis is a method for defining trends by finding trends from data with a large number of measurement items.
By using the transcriptome principal component analysis method according to the present embodiment described above, using training data, for example, from the data obtained in the health check, the measurement items suggesting a specific disease and the respective weights are obtained. Can be found. By applying this axis to individual measurement data, it is possible to find the disease.

Moreover, in the principal component analysis method for transcriptome according to the present embodiment, when analyzing a microarray such as toxicology, an axis is defined using appropriate training data and applied to data of individual samples. This makes it possible to classify samples.
This makes it possible to determine what kind of toxicity the new sample has.

In the transcriptome principal component analysis method according to the first embodiment of the present invention, the principal component is divided by the square root of the number of samples or the number of measurement items used to calculate the principal component. It is characterized by scaling.
The transcriptome principal component analysis method according to the first embodiment of the present invention is characterized by comparing a plurality of scaled principal components.
In addition, the principal component analysis method for transcriptome according to the first embodiment of the present invention is characterized in that training data is used to obtain an axis of a principal component represented by a singular vector. And
In the principal component analysis method for transcriptome according to the first embodiment of the present invention, when selecting training items by selecting data measurement items, data of items not selected is selected. It is characterized by maintaining the size of the original matrix by replacing with zero.
The principal component analysis method for transcriptome according to the first embodiment of the present invention is characterized in that missing data is replaced with zero when calculating a principal component.
In addition, the principal component analysis method for transcriptome according to the first embodiment of the present invention is characterized in that data is evaluated using an axis obtained from training data and a principal component is obtained.
The principal component analysis method for transcriptome according to the first embodiment of the present invention is characterized in that an axis obtained from training data is used as a weight for data evaluation.
In addition, the principal component analysis method for transcriptome according to the first embodiment of the present invention is characterized in that, when determining an axis from training data, any data other than the data average is used as a reference. And
The principal component analysis method for transcriptome according to the first embodiment of the present invention uses any data other than the data average as a reference when obtaining the principal component.
A computer program according to the first embodiment of the present invention is characterized by executing the principal component analysis method for transcriptome.
The computing device according to the first embodiment of the present invention is characterized by executing the principal component analysis method for transcriptome.

<Second Embodiment>
<Method of creating index of skin aging process using gene expression>
Next, a method for creating an index of the skin aging process using gene expression according to the second embodiment of the present invention will be described. In the method for creating an index of the skin aging process using gene expression according to the second embodiment of the present invention, the principal component analysis method for transcriptome according to the first embodiment described above is used. Analyzes the transcriptome of aging of the skin and creates an index of the skin aging process.

Aging, like many other physiological phenomena, is considered not a single gene but a phenomenon involving multiple genes.
The nature of skin tissue changes with aging. Detecting this change and objectively measuring the extent of aging are important in researching aging and developing measures to combat aging.

The method for creating an index of the skin aging process using gene expression according to the second embodiment of the present invention provides a list of genes whose expression is specifically changed in skin tissue.
Further, the present invention provides a method for calculating an index of skin aging by multiplying a value obtained by measuring the expression level of a gene described in the gene list and then adding the coefficient.

  One of the purposes of use of the indicator is, for example, screening for substances, therapy, and treatment. Various agents can be administered using the skin of living organisms or cultured cells, and those that change the index of aging can be selected.

The index is also important when measuring the degree of skin aging of living organisms. This is used, for example, to determine whether the screened substance actually has an effect.
According to the skin aging index creation method according to the embodiment of the present invention, the degree of skin aging can be objectively evaluated.

(Create metrics)
By exhaustively examining gene expression using a microarray, we clarified which genes are involved in aging and how much. At the time of data analysis, by analyzing principal component data of samples under a plurality of physiological conditions, genes that specifically act on aging were identified, and a list of genes listed in Tables 1 and 2 was created.

For standardization of data, a method using a three-parameter lognormal distribution, which is an objective parametric method, was used. This is a method of standardizing data to a normal distribution by obtaining a statistical parameter distribution and obtaining a parameter of the distribution.
Specific standardization execution methods include International Publication No. WO 02/001477, International Publication No. 2008/056693, Japanese Translation of PCT International Publication No. 2010-510557, Japanese Unexamined Patent Publication No. 2004-013573, and Japanese Unexamined Patent Publication No. 2006-236011. , Konishi, Tomokazu (2004), 'Three-parameter logistic distribution, bifoundatively found in cDNA microarray data and its applications. , Konishi, Tomokazu (2008), 'Data Distribution of Short ligation and Amplification of Affects of the Federation and the Construction of the Federation. , 7 (1), Article 25. It can be realized with reference to the above.

In the data analysis, the transcriptome principal component analysis method according to the first embodiment was used. The configuration of the analysis device at this time is the same as that of the analysis device 10 according to the first embodiment.
Principal component analysis is originally highly objective because there are no free parameters set by the analyst user. In addition, the transcriptome principal component analysis method according to the first embodiment can obtain highly objective analysis data even in data that may not be highly independent, such as microarray data.
The principal component analysis is suitable for separating and distinguishing the influence of signals having different directions such as aging and ultraviolet (UV) stimulation.
Hereinafter, details of an example in which the principal component analysis method for transcriptome is executed using microarray experimental data on skin aging will be described.

(Explanation of axis discovery of transcriptome principal component analysis method and application to sample)
First, z-standardized microarray data is represented by a matrix of sample s and gene g. From this matrix, for each gene, the average of the gene is reduced, so-called centering is performed, and re-standardization is performed. This is a process of superimposing zero of the result of the principal component analysis on the origin by subtracting the value of each gene by the average of all the data for each gene. This restandardized data matrix X _s is used as an object for calculation of axis setting / discovery processing.
In addition, representative values of samples of each experimental group p are represented by a matrix of similar data. As this representative value, for example, an average value of genes within the group can be used. The matrix of representative value data of this sample is also re-standardized by centering. This re-standardized data matrix X _p is also used for calculation of axis setting / discovery processing.
Expressing these X _s and X _p as vectors, they are as follows:

Next, when the standardized data matrix X _p is subjected to singular value decomposition, a left singular vector U _p , a diagonal matrix L ^1/2 and a right singular vector V _p are obtained. U _p and V _p are the same vectors as U _t and V _{t according} to the first embodiment, respectively.
The relationship among X _p , U _p , L ^1/2 , and V _p at this time is as follows:

ここで、Ｖ_p’はＶ_pの転置行列である。

Here, V _p ′ is a transposed matrix of V _p .

The principal component PC _{s for} each sample is calculated by the following mathematical formula.

Further, the main component PC _g per gene, is calculated by the following equation.

(Generation of gene list)
Genes associated with aging were identified as follows, for example, and Tables 1 and 2 were prepared.

Skin tissue was obtained from 3 groups of mice (BL6), 1 week old, their mother (2 months old), and retired old mice (2 years old), and total RNA was extracted from each group, manufactured by Affymetrix Microarray measurement was performed using GeneChip.
The measured values were standardized by a parametric method, and it was confirmed that there was a significant difference in expression between groups for each gene with a p-value threshold of 0.01 using the ANOVA method.
Furthermore, for genes for which significant differences were confirmed, X _p was determined using the average value of each group, and principal component analysis was performed by the above-described transcriptome principal component analysis method. As a result, PC1 and PC2 were obtained.
PC1 is the main component of microarray data focusing on the sample corresponding to PCs.
PC2 is the main component of microarray data focusing on the item corresponding to PCg. Here, PCg represents a gene.

The PC1 and PC2 will be described with reference to FIG. In FIG. 7, the principal component score of PC1 is shown on the horizontal axis, and the principal component score of PC2 is shown on the vertical axis. Each circle corresponds to one gene. The letter C represents a week from birth, M represents a 2 month old mother, and O represents a 2 year old mouse sample.
Regarding PC1, many genes having large absolute values were specifically expressed in the skin. Also, PC2 was found to be greatly involved in mammary gland and antibody production. Therefore, it was judged that PC2 had the characteristics of a breastfeeding mother and PC1 had developed skin aging. In fact, the age of each mouse individual and the position on PC1 corresponded.
The PC value of each sample is plotted using 6 times the value.

  The list of gene groups serving as indicators of aging has a significant difference in expression (P <0.01), the absolute value of the PC1 principal component score is large (0.3 or more), and the PC2 component score of PC2 It was selected on the basis of a small absolute value (0.3 or less).

Table 1 below shows a group of genes selected using PC1 and PC2 to increase gene expression by aging. Table 1 also shows the principal components PC _g 1 and PC _g 2 used for selection.
As a means for specifying this gene, an Affymetrix ID number, an abbreviation of a commonly used gene, and a UniGeneID number as a public database registration number are shown. The sequences of these genes are known and can be easily searched from their respective numbers.

  In addition, Table 2 below shows gene groups that decrease gene expression due to aging.

That is, the expression level of genes such as Affymetrix's gene ID number measured in the following chip content and its ortholog mRNA can be used as an indicator of skin aging:
1439200_x_at, 1439625_at, 1453511_at, 1429835_at, 1457967_at, 1450455_s_at, 1416239_at, 1449475_at, 1441991_at, 1421001_a_at, 1422825_at, 1451382_at, 1453009_at, 1416776_at, 1435792_at, 1418989_at, 1437431_at, 1431171_at, 1450475_at, 1448470_at, 1451424_at, 1423271_at, 1448397_at, 1442089_at, 1448303_at, 1420538_at, 1448932_at, 1430132_at, 1421589_at , 1427179_at, 1420409_at, 1436557_at, 1427378_at, 1460185_at, 1431165_at, 1450536_s_at, 1426203_at, 1421691_at, 1429957_at, 1427366_at, 1431650_at, 1450540_x_at, 1422209_s_at, 1436055_at, 1450774_at, 1438239_at, 1430635_at, 1449559_at, 1435184_at, 1419323_at, 1419767_at, 1422760_at, 1449170_at, 1420467_at 1422240_s_at, 1448021_at, 1427866_x_at, 1433 24_at, 1460049_s_at, 1415927_at, 1415832_at, 1436119_at, 1434449_at, 1419028_at, 1448421_s_at, 1424266_s_at, 1450871_a_at, 1431856_a_at, 1424528_at, 1418796_at, 1427168_a_at, 1427884_at, 1422437_at, 1426251_at, 1452968_at, 1450839_at, 1441928_x_at, 1420854_at, 1434202_a_at, 1416803_at, 1438966_x_at, 1429403_x_at, 1436115_at, 1417836_at, 1448194_a_at , 1417714_x_at, 1422610_s_at, 1437665_at, 1451047_at, 1416640_at, 1418538_at, 1418063_at, 1435851_at, 1448228_at, 1417275_at, 1454651_x_at, 1426758_s_at, 1417359_at, 1424010_at, 1423253_at, 1419487_at, 1435382_at, 1450079_at, 1417149_at, 1428896_at, 1417355_at, 1456315_a_at, 1424556_at, 1427580_a_at, 1448201_at , 1420884_at, 1436853_a_at, 1449206_at, 435585_at, 1422973_a_at, 1416713_at, 1451801_at, 1454608_x_at, 1419063_at and its orthologs.

Moreover, the expression level of the gene having the UniGene ID number and the ortholog mRNA thereof can also be used as an index of skin aging:
Mm. 464886, Mm. 454526, Mm. 158766, Mm. 333661, Mm. 86331, Mm. 27447, Mm. 3217, Mm. 273271, Mm. 425491, Mm. 232523, Mm. 75498, Mm. 35083, Mm. 339332, Mm. 9114, Mm. 362644, Mm. 230249, Mm. 320317, Mm. 171357, Mm. 5194, Mm. 423078, Mm. 99989, Mm. 390683, Mm. 2562, Mm. 340791, Mm. 302602, Mm. 49902, Mm. 422799, Mm. 180256, Mm. 439673, Mm. 439738, Mm. 37952, Mm. 291498, Mm. 106868, Mm. 441672, Mm. 34372, Mm. 196689, Mm. 46109, Mm. 30967, Mm. 158281, Mm. 416844, Mm. 389993, Mm. 422800, Mm. 290677, Mm. 246697, Mm. 34441, Mm. 138437, Mm. 1763, Mm. 25259, Mm. 20854, Mm. 20851, Mm. 250358, Mm. 85253, Mm. 34201, Mm. 10663, Mm. 440167, Mm. 467495, Mm. 392176, Mm. 50109, Mm. 686, Mm. 2679, Mm. 263138, Mm. 250786, Mm. 297444, Mm. 383216, Mm. 29110, Mm. 4606, Mm. 34776, Mm. 45127, Mm. 20428, Mm. 297859, Mm. 249555, Mm. 10299, Mm. 108557, Mm. 41556, Mm. 407415, Mm. 271973, Mm. 275320, Mm. 256060, Mm. 24720, Mm. 287146, Mm. 191281, Mm. 81916, Mm. 2014, Mm. 14802, Mm. 196110, Mm. 281018, Mm. 331979, Mm. 193, Mm. 58507, Mm. 298199, Mm. 6228, Mm. 298251, Mm. 172, Mm. 39040, Mm. 252063, Mm. 289645, Mm. 7386, Mm. 272278, Mm. 9986, Mm. 379067, Mm. 400253, Mm. 22367, Mm. 3705, Mm. 284246, Mm. 389800, Mm. 241205, Mm. 127773, Mm. 293263, Mm. 19155, Mm. 29132, Mm. 17484, Mm. 316885, Mm. 18125, Mm. 28585, Mm. 29358, Mm. 338508, Mm. 2108, Mm. 306021 and its ortholog.

(Calculation of indicators)
Next, measure the expression level of one of the genes in the list, preferably multiple genes, in the sample to be measured, compare the expression level of those genes with a predetermined reference value, and change the expression level. Check out.

  The change in the expression level is multiplied by a predetermined coefficient. The coefficient is determined so that, for example, a gene whose expression is known to decrease with aging becomes a negative value, and a gene whose expression increases increases to a positive value.

The values obtained for each gene above are added together as an index of aging.
Here, the index AI _s of the sample s is obtained from the measured values x _{s, g} of the n genes g using the following formula.

Here, b _g is a reference value of the gene, and k _g is a coefficient for each gene.

  The gene used for the indicator can be obtained by using any one or some combination of the genes shown in Table 1 and Table 2.

The measured value x _{s, g} is the z-score in the case of z-standardized microarray data, or a z-score that is centered and re-standardized can be used.

As the so-called “expression level”, for example, when numerical values not logarithmically converted are obtained as measured values, such as intracellular concentrations and activities of mRNA and protein, x _{s, g} is the logarithmic value of those values. Use.
At this time, the base of the logarithm must be unified, but any value is acceptable.

The reference value b _g can be defined for each gene as, for example, an average value in a 1-week-old mouse.

Coefficient k _g can be used left singular vectors U _p of the two types of unitary matrix obtained by the principal component, or singular value decomposition with respect to the gene.
Of course, since the analyst cannot specify the direction of the vector, the sign of the result of the principal component analysis can be reversed. In that case, it is only necessary to reverse the sign to make the direction in which aging progresses positive. Moreover, in order to make it easy to handle a value as an index, a common arbitrary constant may be multiplied.

The coefficient k _g can be most simply set to, for example, plus 1 if the main component is positive and minus 1 if the main component is negative.

In addition, some genes tend to fluctuate expression and others do not. This in order to standardize the variation in gene expression can be dealt with by the value obtained by dividing the 1 in the main component to the coefficient k _g.

With the configuration described above, the following effects can be obtained.
Conventionally, it has been difficult to obtain a list of gene candidates that serve as indicators of aging from genetic data of experiments concerning aging. This is because exhaustive gene expression data includes measurement errors, and gene expression changes even under conditions other than aging. That is, it has been a difficult task to find out which genes should be focused on from comprehensive gene expression data.

As a specific example of this conventional problem, there is some fluctuation in the expression level of any gene. The measurement value includes an error. In addition, any gene can change its expression with a stimulus independent of aging.
Thus, the results of single gene expression measurements do not necessarily reflect aging correctly. For example, in JP-A-10-123130, only the activity of elastase is measured, but the fluctuation of this activity is reflected in the data as it is.

  Moreover, it is not clear that the gene of interest is the most appropriate for the purpose of examining skin aging by not examining genes exhaustively.

From the viewpoint of completeness, for example, a method for determining a gene group by a differential screening method as disclosed in JP-T-2002-535997 is incomplete.
This is because only partial results of the gene group can be observed depending on the primers used or the screening conditions.
In general, since this type of method does not have quantitativeness, it is difficult to select an appropriate gene from gene expression that changes due to many factors other than aging.

  However, exhaustive genetic measurements often involve difficulties in mathematical processing of data. Specifically, the data cannot be processed objectively, and the error of interpreting the measurement noise as a signal tends to be wrong.

  In particular, exhaustive analysis means such as microarrays calculate data with incomplete relative values, so data standardization has a great influence on the analysis results.

In addition, each gene has different properties depending on how much the expression fluctuation can be changed under conditions other than aging, and how much the expression fluctuation is caused by aging.
For example, as can be seen in Japanese Patent Application Laid-Open No. 2007-259851, such a characteristic cannot be reflected if a gene is selected merely because of its large expression fluctuation. This is a cause of error.

As a method for visually assisting an analyst in understanding the expression change, for example, there are various types of clustering. However, these methods are performed after defining the similarity of change, but the definition is not objective.
However, these methods are sometimes used for gene selection as seen in JP-A-2008-178390, JP-T-2005-524382, and the like. However, due to its theoretical limitations, gene group selection using clustering is often a source of major errors.

In addition, it is important how to objectively integrate multiple gene expressions and present them as one or a limited number of indicators. That is, conventionally, the gene change could not be evaluated unless the expression changes of each gene were collected and used as one to several indices. In addition, the index required objectivity.
This is because information on a large number of gene expressions is difficult to understand by itself.

In contrast, the list according to the second embodiment of the present invention provides an index using gene expression in order to objectively evaluate aging.
For this reason, in the second embodiment of the present invention, microarray measurements were performed on a plurality of experimental groups to examine gene expression, which was examined by principal component analysis to obtain principal components. A list of genes involved in aging was obtained using as an index the involvement of this principal component and no involvement of other factors. By examining the gene expression of the genes in this list in the subject and adding the values together, it becomes an index of aging. For the summing process, coefficients obtained from the principal component analysis are used.
As a result, the data can be processed objectively, robust to fluctuations in the expression level, and more accurate than conventional clustering, and gene expression can be obtained as a small number of indices. Therefore, the list according to the second embodiment of the present invention can provide an index using gene expression related to aging.

(Application to organisms other than mice)
Skin aging is also thought to occur in other organisms, particularly higher animals including other mammals, in the same manner as mice.
Aging is a genome-dominated phenomenon that occurs in a similar process, such as loss of elasticity, loss of gloss, and hair loss.

Many of the genes are common among these higher animals. In other words, genes of the same origin are working.
In addition, many genes are common to many species, and each plays a common role.
Such a homologous gene in another organism is called an ortholog of the gene.
Naturally, gene orthologs found in mice have the same function in humans, for example. Genes that are expressed at the aging stage of mice are also expected to be expressed at the aging stage in humans.

  That is, it is clear that the orthologs of the mouse genes listed above work in common in other species including humans as in the case of mice.

Such orthologs of organisms other than mice can be easily identified by the method described below.
The ortholog can be searched first from the information provided by Affymetrix. For example, Mouse 430_2. na30. ortholog. A file called csv is published and provided through the Internet.
This is a file created by searching for an ortholog of a gene in the Mouse430_2 chip used in this experiment from another chip of the same company. By designating the Probe Set ID, which gene of which chip is the ortholog is indicated by the Probe Set ID of the chip.
By specifying the chip and Probe Set ID, the UniGene ID of the gene can be searched for in the annotation file prepared by the company. For example, if the Mouse 430_2 chip, the Mouse 430_2. na30. annot. A file called csv is published.
By specifying this ID, the base sequence of the gene can be known through a public database such as NCBI.

With reference to FIG. 8, an example in which orthologs are searched for several genes is shown. FIG. 8 shows an example in which the Probe Set ID of the human chip is searched from the Probe Set ID of the Mouse 430_2 chip, and the UniGene ID is obtained from each.
Such a series of operations can be easily performed by those skilled in the art. The target species to be searched for is not limited to humans, and all species provided by Affymetrix can be targeted.

In addition, orthologues can be searched from a database using sequence similarity of the gene.
The base sequence of the gene of the content of the Mouse 430_2 chip described in the above example is disclosed. An ortholog can be found by searching a public database using a local alignment algorithm such as BLAST using the base sequence and further translated amino acid sequence. At this time, an ortholog can be found under the condition that the score is the highest among the species of interest or the E value is the lowest.
This makes it possible to discover orthologs even for species not provided by Affymetrix. A series of operations can be easily performed by those skilled in the art.

In addition, it is possible to identify orthologs by cloning using sequence similarity.
In addition, a gene can be cloned from a DNA library of a biological species of interest using a mouse gene probe.
Similarly, primers can be designed based on the sequence of the mouse gene, and the gene can be amplified and cloned using the RT-PCR method or the like.
Moreover, it can also clone using an expression library using an antibody.
A series of operations can be easily performed by those skilled in the art.

For the creation of the list according to the second embodiment of the present invention, a microarray capable of comprehensive measurement was used. Of course, the microarray can also be used for screening and measuring the aging degree.
However, the principal component analysis method for transcriptome of the present embodiment can perform principal component analysis using matrix data other than microarray data.
For example, it is possible to create a list even if the expression level is measured by a simpler method other than microarray. This is because completeness is unnecessary.

As a method for measuring the expression level other than the microarray, it is first considered to measure the amount of mRNA as a transcript by a technique such as RT-PCR method or real-time PCR method.
At this time, it can be standardized using a transcript such as a housekeeping gene as a control, and how much the transcript differs from the reference value can be measured.

(Definition of expression level)
In the first or second embodiment of the present invention, the “expression level” of a gene is produced by the amount of transcript from the gene, the amount of translation product, the activity of translation product, and its activity. Indicates the amount of substance.

That is, in the first and second embodiments of the present invention, the “expression level” is defined not only as an increase / decrease in the amount of mRNA but also as a broader concept.
For example, an increase or decrease in the amount of mRNA is considered to correspond to an increase or decrease in the amount of the encoded protein. That is, if a protein is detected using a specific antibody, the measurement can be performed more simply. This can be obtained as matrix data of “expression level”. For the detection of this protein, an index can be obtained by multiplying the logarithmic value of the increase / decrease ratio of each protein by a coefficient and adding them together.
Further, not only mRNA but also “expression level” of RNA involved in intracellular regulation such as snRNA can be measured and used as matrix data.

  It is also possible to use the protein activity in the matrix data as the “expression amount” instead of the protein amount.

Moreover, it is also possible to use it for matrix data as “expression level” using data of a screening system using cultured cells.
Regarding the construction of this screening system, a gene in which a reporter gene is connected to a regulatory region of the gene of interest, that is, a promoter sequence or a cis sequence, can be prepared, and an indicator gene (construct) for which activity measurement can be easily performed. As the reporter gene, a reporter gene having an enzyme activity such as CAT (chlorphenicol acetate transferase) or a gene exhibiting luminescence such as luciferase can be used.
By introducing the selected gene into the cultured cell, it becomes possible to screen easily while measuring the activity of the reporter gene.

(Application to other fields of principal component calculation method according to embodiments of the present invention)
Note that the principal component calculation method according to the first or second embodiment of the present invention is an extended principal component analysis method, in which not only transcriptome analysis but also measurement items such as medical examinations are hospitals, for example. Although it differs to some extent, it can also be applied to data with many measurement items.
For example, when it is desired to examine the possibility that some kind of illness is found in any item of the medical examination, the disease group and the control group are set, and the representative value of each group is obtained by taking an average or the like. At this time, the measured value is represented by a numerical value that is as linear as possible, and is qualitative data. Then, the data is centered for each item so that the average of each item becomes zero. Further, if a certain item is not measured in some hospitals, the missing value is replaced with zero. From the two-group / multi-item matrix thus obtained, each unitary matrix representing the axis, PCg1 (principal component of the item), and PCs1 can be obtained. The measurement item group having a large absolute value in PCg1 is an item that well represents the disease. Moreover, the unitary matrix V _p obtained, to PCs1 not each person can be obtained SPCs1.
As a result, the threshold value can be calculated using the calculation method described in Example 4 below by examining the distribution of PCs1 to sPCs1 of each individual using a random sample from a somewhat large population.
In this case, when the distribution of the main component PCs is substantially normal distribution, or the proportion of individuals having PCs whose absolute value is larger than the threshold is clearly smaller than the prevalence of the disease, The disease cannot be evaluated by the health check items used. If the opposite is true, the disease can be assessed on that item. Furthermore, when paying attention only to a certain disease, it is possible to select items to be performed while taking into consideration the ease of measurement and cost of items for which PC1g has a large absolute value. Of course, PC1g is also an important finding in studying the cause and treatment of the disease.
An individual whose PCs1 exceeds the threshold is suspected of the disease. Needless to say, when attention is paid to a plurality of diseases, the number of disease groups increases and the number of main components to be noted also increases. However, it is not necessarily the same number as the disease. Probably, a group of diseases having similar symptoms affects the same main component, and is thus determined by the main component.

Example 3
With reference to FIG. 9, a case where 10 genes are selected from the genes in the list according to the second embodiment of the present invention and the aging degree of each sample is measured will be described.
FIG. 9 shows a method of obtaining an index from the centered standardized data.
The reference value was determined from these data as the average of young mice for each gene. The coefficient used was a value obtained by multiplying the main component PC _g 1 by a constant 17 for making the index easy to see.
The obtained values were added together to obtain an index. The value of each sample is shown as a bar graph.
Hereinafter, the specific calculation method of the third embodiment will be described in more detail.

(Standardization)
First, 40 data from Series GSM202666 to GSM202705 in the NCBI GEO database similar to Example 1 were acquired as matrix data of a microarray.
Using this data, a Super NORM data standardization service of Skylight Biotech Co., Ltd. was used to standardize PM data by a parametric method using a three-parameter lognormal distribution, and a z score was obtained.
Moreover, the expression level of each gene was calculated | required from the trim average of standardized PM data. The level of expression of this gene, "Konishi T (2008) Data Distribution of Short Oligonucleotide Expression Arrays and Its Application to the Construction of a Generalized Intellectual Framework Stat Appl Genet Mol Biol 7:. Article 25.""Konishi T. (2004) Three-parameter logistic distribution ubiquitously found in cDNA microarray data and its application to parametric data treatment. MC Bioinformatics, 5, was determined according to 5. ".

(Parameters calculated by standardization)
With reference to FIG. 10, the parameter calculated by the above-mentioned standardization will be described. Each parameter is as follows:

Lower lower confidence interval upper upper confidence interval saturation Measurement limit gamma γ (background)
sigma σ (width of distribution)
mu μ (center of distribution)

The base of the logarithm used is 10.

(Select sufficient genes for repeated measurements)
Principal component analysis is also a method for knowing overall trends in data, and therefore variations due to individual differences in individual samples included in the data act as noise.
Some genes are unstable, and unless a certain number of repeated measurements are performed, changes in the gene expression level, etc. will not be apparent. This is the same even if the expression level or the like changes greatly.
Of course, since the number of microarray repetitions that can be measured from the same sample is limited, for example, there is a possibility that a sufficient number of repeated measurements have not been made with about half of the gene of the chip content.
The information from these genes is considered to be noisy and may reduce the accuracy of principal component analysis. Therefore, we decided to remove information from these genes.
For this reason, in order to determine whether there is a sufficient number of observations for each gene, analysis of variance (2-way ANOVA) was performed for each gene. This is a method for testing whether there is a significant difference in expression between groups while associating the z-score of PM data corresponding to each gene. The null hypothesis is that the expression levels are the same in each group. The assumed formula is:

Difference in expression level = Difference in PM cell sensitivity + Difference between groups

Then, a two-sided test with a threshold value of 0.002 was performed. That is, a gene having a P value calculated for the difference between groups of 0.001 or less was selected as having a sufficient number of observations. This threshold setting is normally used as a test for microarray data.
A large number of tests will be performed, but the multiplicity of the tests is not taken into consideration. This is because the stability of genes differs from one individual to another, and the test results for each gene should be judged individually.
This test is, "Konishi T, Konishi F, Takasaki S, Inoue K, Nakayama K, Konagaya A (2008) Coincidence between Transcriptome Analyses on Different Microarray Platforms Using a Parametric Framework PLoS ONE 3: e3555.." Was carried out according to the method of .

(Data for principal component analysis for microarray)
For this analysis, PM data was collected for each gene (by trim average). Specifically, the z score in the PIVOT output file provided by the SuperNORM data standardization service manufactured by Skylight Biotech was used.
At this time, in order to remove information on genes for which the null hypothesis was not rejected in the above analysis of variance, the values of these genes were all replaced with zero.
Thereby, noise can be prevented from affecting the result of the principal component analysis. In addition, by deleting a specific gene, it is possible to prevent the matrix form from changing.
All deleted data was replaced with zero. The reason for this is that, as described above, if there is missing data, the calculation of the principal component analysis cannot be performed, and this needs to be replaced. At this time, replacing the deleted data with zero is a so-called fail-safe measure. This is because, as described above, as long as missing data is replaced with zero, it does not cause false positives.

Next, the data was centered for every measurement element (gene) of the matrix data in which the deleted data was replaced. This centering is a process of reducing the value of each gene with an average for each gene of all data. Thereby, zero of the result of the principal component analysis can be superimposed on the origin.
If it is reduced by the value of any control experiment, the origin overlaps that experiment. In addition, since the difference in gene expression level correlates with the function of the living body, the distribution is not unified.

The average value of each gene was obtained for each group and used as a representative value for each group. Singular value decomposition was performed using this representative value as Xt, and three matrices U _t , L ^1/2 _t and V _t ′ were obtained.
As described in the first or second embodiment, the contents of X are different from each other in the case where the axis is determined from all the data or in the simulation when the group is biased.
PC _g, which is the main component for each gene, was determined from X _t and U _t .
In addition, PC _s, which is a main component of the sample was determined from all of the data X and V _t. For this reason, the value of each sample is calculated instead of the representative value of the group. This is a measure for making it possible to observe how much individual differences exist between samples.

Thus, matrix data X _s was created and stored in the microarray data 251. Thereafter, the transcriptome principal component analysis method of the first embodiment and each process of the second embodiment were performed to obtain a gene list.

Example 4
Next, a method for selecting genes from the results of microarray data principal component analysis will be described with reference to FIGS.
First, 40 data from Series GSM202666 to GSM202705 in the NCBI GEO database similar to the above-described first embodiment are acquired as matrix data of the microarray, and the microarray data principal component analysis method according to the first embodiment described above is performed. Was used for analysis. Subsequently, genes were selected.

As described above, each principal component in the principal component analysis is obtained by adding a large number. For example, the main component of the gene is the sum of the elements calculated for each sample.
If these elements have little biological significance, there is no clear correlation between the elements and they are independent.
And since each element is obtained from the difference between samples, it can be processed when the distribution pattern is the same.
Furthermore, if the elements are of a nature that can be simulated with a random number, the central limit theorem predicts that the result of the summation will be normally distributed.

FIG. 11 is a graph histogram showing the frequency distribution of the acquired sPC1g. The vertical axis represents frequency, and the horizontal axis represents the number of each element. The confirmed distribution of sPC1g in FIG. 11 was normally distributed. In particular, the distribution center has a distribution along a normal distribution.
FIG. 12 is an example of a QQ plot comparing the acquired distribution of sPC1g with a theoretical normal distribution. The QQ plot is a probability plot in which q1 and q2 which are two probability points (quantiles) are plotted on the vertical axis and the horizontal axis when given a certain probability p (“Gnanadesikan, R .; Wilk, MB (1968), “Probability Plotting Methods for the Analysis of Data”, Biometrica 55 (1): 1-17 ”. In this QQ plot, the sorted actual data of sPC1g and the theoretical value of the normal distribution were first-order approximated.
A robust Tukey method was used to obtain the parameter only from the straight line portion while avoiding the influence of noise (see “Tukey, JW (1977). Exploratory Data Analysis, Reading Massachets: Addison-Wesley.”). ). The solid line in FIG. 12 shows an approximate linear equation (y = 0.09x).
According to the QQ plot of FIG. 12, it is clear that the distribution center is distributed along the normal distribution. However, the tendency that the both ends of the distribution show larger absolute values is remarkable, and the plot is bent in the vertical direction of the graph. This suggests that there is a correlation between non-random elements.
Specifically, the approximate line and the actual data start to deviate from about ± 0.17 as the actual data value. From this value, it can be considered that a gene group with a strong meaning is mixed. Conversely, assuming that everything was random, the actual data would have been on this approximate line.

Assuming that false positives on both sides with a probability of 0.001 are accepted as a combination of random elements, z-score ± 3.3 as a theoretical value is a predetermined threshold value. This is shown as a vertical wavy line in FIG.
Alternatively, a random effect such as that observed at the center of the distribution with a probability of 0.001 / 2 can record a z-score of ± 3.3. This corresponds to ± 0.3 as the value of sPC1g from the approximate straight line. This is shown as a horizontal wavy line in FIG.
Therefore, genes with sPC1g values exceeding these were selected. The expected false positive probability for this selected gene is less than 0.001.
A similar calculation was performed on sPCg2, which is an analysis result from data in the field of Example 2 toxicology, and a threshold value of 0.3 was obtained. It was also possible to obtain genes related to toxicology with a predetermined threshold.

  Note that the configuration and operation of the above-described embodiment are examples, and it is needless to say that the configuration and operation can be appropriately changed and executed without departing from the gist of the present invention.

DESCRIPTION OF SYMBOLS 10 Analysis apparatus 100 Control part 110 Storage part 130 Input part 140 Display part 150 Network input / output part 210 Training data creation part 220 Singular vector calculation part 230 Principal component calculation part 240 Principal component scaling part 250 Database 251 Microarray data 252 Training data 253 Axis Data 254 Principal component data

Claims (19)

A transcriptome analysis method for analyzing a transcriptome by calculating a principal component from a data matrix using an analysis device,
The analyzer scales the main component by dividing it by the square root of the number of samples or measurement items used to calculate the main component,
The analysis apparatus selects a sample with a predetermined threshold from the scaled principal components,
Calculating the principal component from the data matrix of the expression level change related to the transcriptome;
The principal component is scaled by dividing by the square root of the number of samples of the data matrix used for the calculation of the principal component, or the square root of the number of measurement items of the data matrix used for the calculation of the principal component,
From the scaled principal component, it is determined and selected that the expression level has changed at the predetermined threshold,
In order to find the axis of the principal component represented by a singular vector, training data is used,
The training data is standardized by using the representative value of each group consisting of the average value of the group, setting the reference value of the item,
The reference value is set by specifying data to be used as a reference, the set reference data is the origin of the principal component, and the axis of the principal component is used as the reference while being shared by a plurality of measurement values. Data is determined by each measured value,
A transcriptome analysis method comprising classifying samples by defining the principal component axis using the training data and applying the principal component axis to individual sample data. The representative value of the training data is
The transcriptome analysis method according to claim 1, wherein a sample and a measurement item are selected and determined by confirming a significant difference between groups in advance by analysis of variance and narrowing down measurement items. The change in the expression level includes any of the amount of RNA, the amount of translated protein, the activity of the translated protein, and the amount of metabolite produced by protein metabolism. 3. The transcriptome analysis method according to 1 or 2. 4. The threshold value according to claim 1, wherein the predetermined threshold value is a threshold value that allows false positives on both sides with a probability of 0.001 by comparing the scaled principal component with a normal distribution. 5. Transcriptome analysis method. The transcriptome analysis method according to any one of claims 1 to 4, wherein it is determined that the expression level has changed by comparing two or more scaled principal components. The training data is created by selecting measurement items of the data matrix,
The transcriptome analysis method according to any one of claims 1 to 5, wherein the size of the original matrix is maintained by replacing data of items not selected with zero. The transcriptome analysis method according to any one of claims 1 to 6, wherein when the principal component is calculated, the deleted data is replaced with zero. The transcriptome analysis method according to claim 1, wherein the principal component is calculated by applying an axis obtained from the training data to the data matrix. The transcriptome analysis method according to any one of claims 1 to 8, wherein an axis obtained from the training data is used as a weight for data evaluation. The transcriptome analysis method according to any one of claims 1 to 9, wherein, when obtaining an axis from training data, selected data other than the data average is used as a reference. . The transcriptome analysis method according to any one of claims 1 to 10, wherein when the principal component is calculated, selected data other than the data average is used as a reference. When calculating the principal component, using the data matrix X _s and the data matrix X _p that are re-standardized by performing centering according to the following formula,

Here, p is an experimental group number. The transcriptome analysis method according to any one of claims 1 to 11, wherein: When the singular value decomposition is performed on the data matrix X _p , the relationship between the left singular vector U _p , the diagonal matrix L ^1/2 and the right singular vector V _p is expressed by the following equation.

The transcriptome analysis method according to claim 12 . Among the main components, the main component PC _s for each sample is represented by the following formula.

The transcriptome analysis method according to claim 12 or 13 , characterized in that: Among the main components, the main component PC _g for each gene is represented by the following formula.

The transcriptome analysis method according to any one of claims 12 to 14, wherein A principal component calculation method for calculating a principal component from a data matrix using an analysis device,
The analyzer scales the main component by dividing it by the square root of the number of samples or measurement items used to calculate the main component,
The analysis apparatus selects a sample with a predetermined threshold from the scaled principal components,
Compare the disease group with the control group,
Calculating the principal component from the data matrix for the measurement items of the health check,
The principal component is scaled by dividing by the square root of the number of samples of the data matrix used for the calculation of the principal component, or the square root of the number of measurement items of the data matrix used for the calculation of the principal component,
From the scaled main component, it is determined and selected that the measurement item of the health check has changed at the predetermined threshold,
In order to find the axis of the principal component represented by a singular vector, training data is used,
The training data is standardized by using the representative value of each group consisting of the average value of the group, setting the reference value of the item,
The reference value is set by specifying data to be used as a reference, the set reference data is the origin of the principal component, and the axis of the principal component is used as the reference while being shared by a plurality of measurement values. Data is determined by each measured value,
A disease determination method comprising: classifying a sample by defining an axis of the principal component using the training data and applying the axis of the principal component to data of each sample. A computer program for executing the transcriptome analysis method according to claim 1 or the disease determination method according to claim 16.   A storage medium storing the computer program according to claim 17. A principal component calculation unit for calculating a principal component from a data matrix;
Principal component scaling that scales by dividing the principal component by the square root of the number of samples of the data matrix used to calculate the principal component or the square root of the number of measurement items of the data matrix used to calculate the principal component And
With a training data creation unit that selects the sample and the measurement item and creates training data,
From the scaled principal component, a sample is selected with a predetermined threshold,
The principal component calculation unit calculates the principal component from the data matrix for a measurement item of a transcriptome or a medical examination,
The scaling unit divides the principal component by a square root of the number of samples of the data matrix used for calculating the principal component or a square root of the number of measurement items of the data matrix used for calculating the principal component. From the scaled main component, it is determined and selected that the expression level or the measurement item of the health checkup according to the transcriptome has changed at the predetermined threshold,
The training data creation unit uses a representative value of each group consisting of an average value of the group as the training data, sets a reference value of the item, standardizes the reference value, and the reference value is used as a reference Specify and set the data, the data to be set as the reference is the origin of the principal component, the axis of the principal component is shared by a plurality of measurement values, the data to be the reference is determined by each measurement value,
An analysis apparatus comprising: classifying samples by defining an axis of the principal component using the training data and applying the axis of the principal component to individual sample data.

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