CN101215602A - Method for screening gene chip difference expression gene - Google Patents

Abstract

The invention provides a process of screening gene chip diversity expression gene, relating to an algorism for screening diversity expression gene in gene chip diversity expression analysis. The invention comprises following steps that firstly normalized processing chip data, secondly building up linear mold of logarithmic proportionality x ij= mu + mu j + epsilon, thirdly calculating globe mean value mu and the values of column effect mu j and variance sigma, fourthly calculating 2*ln (odd ratio) of each gene through utilizing mu, mu j and sigma, and fifthly setting localized value of X2 cutoff and n, and the gene of n is defined as diversity expression gene when the value of 2*ln (odd ratio) in the fourth step is larger than X2 cutoff. The invention designs appropriate statistic through building up statistical mode, and finally provides a significant probability numerical value for each gene as the standard of screening gene through utilizing the method of hypothesis test. The process overcomes the weaknesses that the conventional multiple process is lack of statistics basis and is difficult to assess the sensibility and specificity of the algorism self.

Description

A kind of method of screening-gene chip differences expressing gene

Technical field

This patent relates to a kind of algorithm of difference expression gene screening in a kind of gene chip data analysis.This algorithm is applicable to the gene chip experiment design that lacks the multiple small sample.

Background technology

Gene chip claims gene microarray (microarray) again, be meant many known array oligonucleotide or cDNA fragment are arranged on the substrate regularly, with behind the sample mark to be measured with chip on nucleotide sequence hybridize by the base complementrity pair principle.By fluorescence detecting system chip is scanned, and be equipped with computer system and the fluorescent signal on each probe is made detected and relatively, can draw experimental result rapidly.Utilize gene chip once carrying out fast, to detect accurately and efficiently up to ten thousand kinds of expression of gene levels in the experiment, and the requirement of sample can significantly reduce.Biochip technology be present gene studies aspect most advanced, also be one of effective means, at life science and put into practice, every field such as medical research and clinical, medicinal design, environment protection, agricultural, military affairs has a wide range of applications.

The screening of difference expression gene is that gene chip is analyzed a most key step.No multiple chip data for two samples, can use method of multiplicity (Gerhold D, Lu M, Xu J, Austin C, Caskey CT, Rushmore T.Monitoring expression of genesinvolved in drug metabolism and toxicology using DNAmicroarrays.Physiol Genomics 2001; 5:161-170) or z-score (Cheadle C, Vawter MP, Freed WJ and Becker KG.Analysis ofmicroarray data using z score trahsformation.J Mol Diagn2003:5, method 73-81); The multiple chip data that has for two samples then can use method of multiplicity or t check (Baldi P, Long AD.A Bayesian framework for theanalysis of microarray expression data:regularized t-testand statistical inferences of gene changes.Bioinformatics2001; Method such as 17:509-519).The multiple chip data that has for a plurality of groupings then can user's difference analysis (Pavlidis P.Using ANOVA for gene selectionfrom microarray studies of the nervous system.Methods2003:31 (4): 282-9).Generally can use fitting of a curve (StoreyJD for long time series, Xiao W, Leek JT, Tompkins RG, Davis RW.Significanceanalysis of time course microarray experiments.Proc Natl AcadSci U S A.2005,102 (36): method 12837-4).

But in actual applications, because the expense costliness of gene chip, the investigator often can only bear the chip design (sample size＜6) of a small amount of sample, and each sample also just carry out single or twice technology repeats, this shortage multiple small sample gene chip experiment design is very very general at present.This class chip data does not have good analytical procedure at present, mainly be to adopt method of multiplicity, and method of multiplicity is a kind of empirical algorithms that the sensitivity and specificity of algorithm itself is to be difficult to estimate, can cause bigger experimental error.In order to remedy this technological gap, we propose a kind of new algorithm based on statistical model this patent, come small sample, and the differential gene that no multiple gene chip produces screens.

Summary of the invention

The invention provides a kind of by setting up the method that statistical model comes screening-gene.

The present invention is achieved in that and mainly comprises following flow process: step 1, chip data is carried out normalized; Step 2 is set up logarithm ratio x _Ij=μ+μ _j+ ε linear model; Step 3 calculates overall average μ, column effect μ _jValue with variances sigma; Step 4 is utilized μ, μ _jAnd σ, calculate the 2 * ln (odd ratio) of each gene; Step 5 is set thresholding χ ² _{Cutoff, n}, 2 * ln in step 4 (odd ratio) is worth greater than χ ² _{Cutoff, n}Gene be decided to be difference expression gene.

Annotate: ln () is for being the natural logarithm at the end with e.

The invention has the advantages that: by setting up statistical model, design suitable statistic, use the method for test of hypothesis to give the probability numbers of a significance of each gene at last, as the standard of screening-gene.This method has overcome the weakness that conventional method of multiplicity lacks statistical basis and the sensitivity and specificity of algorithm own is difficult to estimate.

Description of drawings

Fig. 1 is the schema of the method for screening-gene chip differences expressing gene of the present invention.

Embodiment

Concrete grammar is described below:

At first use chip scanning image processing software (for example GenePix pro 4.0) to obtain the expression values data of gene level.Then chip data is carried out the normalized of chip chamber.Then the signal value of chip results is converted to ratio with respect to control experiment.Get the logarithm (get with e is to be good the end) of ratio.We are with the basis of this logarithm ratio (ln ratio) as analysis.

Suppose that we have n to open gene chip (a corresponding n sample, typical, 1＜n≤5), every chip has m gene.We obtain a numerical matrix like this:

X wherein _IjBe that ((1≤j≤n) opens the ln ratio numerical value in the chip to the individual gene of 1≤i≤m) to i at j.

Then we set up a linear model:

x _ij＝μ+μ _j+ε ②

Wherein μ is the average of the overall situation, μ _jBe column effect, ε is a residual error.We suppose ε～N (0, σ ²).Suppose promptly that in different chips it is 0 that residual epsilon meets average, variance is the normal distribution of σ.As variances sigma, what it embodied is the average of all chips " in the chip " variance.μ j is as column effect, expression be the parameter of difference between the different chips.μ is the average of the overall situation and since generally speaking in the chip expression values of most gene be constant, so μ approaches 0.This model promptly is that the expression values of a gene on a chip is decomposed into overall effect, row (chip) effect and residual error.

Parameter to model is estimated:

Utilize maximum likelihood estimation, the estimated value of μ is the average of the overall situation, promptly

$\widehat{\mathrm{\μ}}=\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}}{\mathrm{mn}}$ ③

μ _jBe column effect, the mean value of promptly every row (being every chip) is (in the following formula

Approach 0):

${\widehat{\mathrm{\μ}}}_j=\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}}{m}-\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}}{\mathrm{mn}}$ ④

The estimated value of σ is got " in the group " variance:

$\widehat{\mathrm{\σ}}=\sqrt{\frac{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(x_{\mathrm{ij}}-\frac{\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{x}_{\mathrm{ij}}}{m})}^2}{\mathrm{mn}}}$

Set up test-hypothesis:

For each gene i,

H ₀: x _I1, x _I2... x _InIt is an example of above-mentioned linear model.

H ₁: x _I1, x _I2... x _InIndependent fully with above-mentioned linear model.

We use p (x _I1, x _I2... x _In| μ, μ _j, σ, H ₀) represent that gene i is the probability of an example of this linear model (being population distribution), with p (x _I1, x _I2... x _iN| μ, μ _j, σ, H ₁) represent that gene i comes from this linear model, but come from the probability of any other model (distribution).Traditionally, we represent the departure degree of data to model with odds ratio odd ratio,

$\mathrm{oddratio}=\frac{p(x_{i1},x_{i2},...x_{\mathrm{in}}|\mathrm{\μ},{\mathrm{\μ}}_j,\mathrm{\σ},H_1)}{p(x_{i1},x_{i2},...x_{\mathrm{in}}|\mathrm{\μ},{\mathrm{\μ}}_j,\mathrm{\σ},H_0)}$ ⑥

As seen the value of odds ratio odd ratio is big more, and it is obvious more to illustrate that gene i departs from population distribution, might be the differential gene that we will seek more.

For gene i, 2 * ln (odd ratio) then can write:

${\mathrm{OR}}_i=2\ln \left[\frac{p(x_{i1},x_{i2},...x_{\mathrm{in}}|\mathrm{\μ},{\mathrm{\μ}}_j,\mathrm{\σ},H_1)}{p(x_{i1},x_{i2},...x_{\mathrm{in}}|\mathrm{\μ},{\mathrm{\μ}}_j,\mathrm{\σ},H_0)}\right]$

$=2\ln \left[\frac{\underset{j=1}{\overset{n}{\mathrm{\Π}}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{x_{\mathrm{ij}}-x_{\mathrm{ij}}}{\mathrm{\σ}}\right)}^2}}{\underset{j=1}{\overset{n}{\mathrm{\Π}}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\σ}}{e}^{-\frac{1}{2}{\left(\frac{x_{\mathrm{ij}}-\mathrm{\μ}-{\mathrm{\μ}}_i}{\mathrm{\σ}}\right)}^2}}\right]=\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\left(\frac{x_{\mathrm{ij}}-\mathrm{\μ}-{\mathrm{\μ}}_j}{\mathrm{\σ}}\right)}^2$ ⑦

In the top formula, use the value of joint probability calculation odds ratio odd ratio.From final our statistic OR as can be seen as a result _iMeet the χ that degree of freedom is n ²Distribute.Therefore, the tolerance that is used as the differential expression of gene with 2 * ln (odd ratio) is rational, and its significant result can use χ ²Check provides, that is:

Set certain threshold value (cutoff), the cutoff optimum value is 0.01, if OR _i＞χ ² _{Cutoff, n}, promptly p＜0.01 can think that so then i gene is difference expression gene.

By calculating the OR of each gene _iValue is with χ ²The threshold value χ that distributes ² _{Cutoff, n}Compare, can filter out all difference expression genes.

One, there not to be the expression profiles of gene chip data instance of the Affymetrix company that repeats 4 samples:

Obtain the gene level expression data.Convert the signal value of chip results to ratio with respect to control experiment.Get the logarithm of ratio.

Set up linear model x _Ij=μ+μ _j+ ε, j=1...4.μ is the average of the overall situation, μ _jBe column effect, ε is a residual error, and ε～N (0, σ ²).

Calculate above-mentioned PARAMETERS IN THE LINEAR MODEL μ, μ _jEstimated value with σ

With

These estimated values will be used for the calculating of statistic 2 * ln (odd ratio).

For each gene i, utilize formula $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\left(\frac{x_{\mathrm{ij}}-\mathrm{\μ}-{\mathrm{\μ}}_j}{\mathrm{\σ}}\right)}^2$ , calculate 2 * ln (odd ratio) value of each gene.This value has reflected the departure degree of gene i expression data and population distribution, and this value meets the χ that degree of freedom is n=4 simultaneously ²Distribute.

Set cutoff=0.01, look into χ ²Distribution table obtains χ ² _0.01,4=13.28.Promptly when statistic greater than 13.28 the time, p＜0.01.

Screening 2 * ln (odd ratio) value is difference expression gene greater than the gene of 13.28 (being equivalent to p＜0.01).

Two, to repeat the gene chip data instance of 5 samples for 2 times:

Obtain the gene level expression data.Convert the signal value of chip results to ratio with respect to control experiment.Get the logarithm of ratio.

Set up linear model x _Ij=μ+μ _j+ ε, j=1...5.

Calculate above-mentioned PARAMETERS IN THE LINEAR MODEL μ, μ _jEstimated value with σ.

For each gene i, utilize formula $\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\left(\frac{x_{\mathrm{ij}}-\mathrm{\μ}-{\mathrm{\μ}}_j}{\mathrm{\σ}}\right)}^2$ , calculate 2 * ln (odd ratio) value of each gene.

Set cutoff=0.01, look into χ ²Distribution table obtains χ ² _0.01,10=23.21.

Screening 2 * ln (odd ratio) is worth the gene greater than 23.21, is difference expression gene.

More than be the description of this invention and non-limiting, based on other embodiment of inventive concept, all among protection scope of the present invention.

Claims (3)

1. the method for a screening-gene chip differences expressing gene is characterized in that this method includes following steps:

Step 1 is carried out normalized to chip data;

Step 2 is set up logarithm ratio x _Ij=μ+μ _j+ ε linear model;

Step 3 calculates overall average μ, column effect μ _jValue with variances sigma;

Step 4 is utilized μ, μ _jAnd σ, calculate the 2 * ln (odd ratio) of each gene;

Step 5 is set thresholding χ ² _{Cutoff, n}, 2 * ln in step 4 (odd ratio) is worth greater than χ ² _{Cutoff, n}Gene be decided to be difference expression gene.

2. the method for a kind of screening-gene chip differences expressing gene according to claim 1 is characterized in that: in step 1, the sample number when carrying out the normalized of gene chip data is between 1～5 example.

3. the method for a kind of screening-gene chip differences expressing gene according to claim 1 is characterized in that: in step 3 or step 4,

$\mathrm{oddratio}=\frac{p(x_{i1},x_{i2},...x_{\mathrm{in}}|\mathrm{\μ},{\mathrm{\μ}}_j,\mathrm{\σ},H_1)}{p(x_{i1},x_{i2},...x_{\mathrm{in}}|\mathrm{\μ},{\mathrm{\μ}}_j,\mathrm{\σ},H_0)}.$