RU2456926C2 - Method of predicting distant results of urinary bladder cancer treatment - Google Patents

Abstract

FIELD: medicine.

SUBSTANCE: invention relaters to medicine, namely to oncology and surgery, and is intended for predicting outcome of treatment of patient with urinary bladder cancer. Determined are depth of tumour invasion into urinary bladder (a₁), histologic type of urinary bladder cancer (a₂), histopathologic gradation of urinary bladder cancer (a₃), tumour sensitivity to PCT (a₄), volume of performed treatment (a₅), diseases of genitourinary system, leading to infravesical obstruction (a₆), tumour localisation (a₇). After that, prediction of distant results of urinary bladder cancer treatment is determined by formula: y = a₀+a₁x+a₂x+a₃x+a₄x+a₅x+a₆x+a₇x, where a₀ (free member) = -1.35, a₁ = 0.26, a₂ = 0.13, a₃ =0.22, a₄ = 0.41, a₅ = 0.37, a₆ = 0.15, a₇ = 0.06, x is numerical value, taken for certain patient and selected from table 1 given in description, depending on type and degree of parameters of prognostic factors (a₁ - a₇). Prediction is considered good if y lies within the interval 0-2.5, prediction is considered to ne satisfactory if the number is within the interval 2.6-3.5, prediction is considered to be doubtful if y value is within the interval 3.6-4.5, prediction is considered unsatisfactory if y value is larger than 4.6.

EFFECT: method makes it possible to determine prediction prospectively, optimise treatment tactics and form complex of measures of tertiary prevention.

2 tbl, 1 ex

Description

The invention relates to medicine, namely to Oncology, and can be used to predict long-term results of treatment of bladder cancer.

The closest way to the claimed is to predict the results of treatment of bladder cancer according to TNMG classification.

The technical result is the determination of the possible outcome of the treatment of bladder cancer.

The specified technical result is achieved by the fact that in the method for predicting long-term results of treatment of bladder cancer using correlation and regression analysis, prediction of the results of organ-preserving treatment is carried out, which is based on determining the influence of a complex of epidemiological, clinical, morphological and therapeutic factors in the treatment of bladder cancer, s conducting a correlation analysis, the results of which exclude factors that do not affect the outcome of the problem Evan and factors correlated with each other. In this case, a correlation analysis with the exception of factors that do not affect the outcome of the disease, as well as factors correlated with each other, is performed using the least squares method of the coefficients of the linear regression model.

Having studied the influence of individual factors on the outcome of organ-preserving treatment of bladder cancer, it is very advisable to create a mathematical model for the prognosis of bladder cancer, taking into account the combined effect of the most significant and significant factors. To solve this problem, a sample consisting of data from 1248 patients was used. The following morphological and informative signs were used as input (independent) variables x _j : timely treatment, tumor size, its location, the nature of bladder cancer growth, the number of tumors, the functional state of the kidneys, the extent of cancer, the volume of treatment and its duration, the amount of surgical aid, the sensitivity of bladder cancer to systemic polychemotherapy, the histological structure of the tumor and its histopathological gradation, invasion of the cancer into the urine wall of the bladder and into the lymphatic and venous vessels, gender and age of the patient, the recurrent nature of the tumor, the presence of concomitant obstructive diseases of the genitourinary system. A total of 19 input variables. As the output (dependent) variable y, we take the level of the patient’s state of health.

Each of the input and output variables was assigned a particular discrete numerical value of the natural series in accordance with the degree of manifestation of the variable for each patient. The outgoing variable - the outcome of the disease took numerical values of the natural series from 1 to 3: 1 - the patient lives without relapse for more than 5 years; 2 - the patient is alive, but he had a relapse of bladder cancer within 5 years; 3 - fatal outcome due to the generalization of the cancer process. The numerical value of the incoming variables is presented in Table 1.

At the first stage, to assess the influence of factors on the outcome of the disease, the coefficients of pair and multiple correlations R, which characterize the degree of tightness of the relationship between the values, were calculated. To assess the significance of the correlation coefficients, procedures for testing statistical hypotheses are used.

At the first stage of the study, pair correlation coefficients were calculated by the formula

for all information signs x _j and the output variable y.

The confidence interval for the correlation coefficient is constructed using the Fisher Z-transform (Sachs L., 1976, Ferster E., 1983).

n is the sample size, R is the correlation coefficient.

Next, a mathematical model for the prognosis of bladder cancer is developed, taking into account the combined influence of the most significant and significant factors. Informative signs correlated among themselves and signs not related to the outcome of the disease were excluded from the model. A total of 7 signs were used (m = 7).

The next stage of the study addressed the issue of multicollinearity. The phenomenon of multicollinearity consists in the existence of a linear relationship between explanatory variables. The presence of multicollinearity causes technical difficulties associated with a decrease in the accuracy of the estimation of certain parameters or even the impossibility of evaluation in general. To determine the presence of multicollinearity, pair correlation coefficients between all explanatory variables were calculated using formula (1), in which the outgoing variable was replaced by an explanatory variable.

By the absolute value of the correlation coefficient, it is problematic to judge the tightness of relations from a quantitative point of view. Therefore, in this case, statistical hypothesis testing procedures were involved (Sachs L., 1976, Ferster E., 1983). The significance verification procedure begins with the formulation of the hypothesis being tested or the null hypothesis H ₀ . For example, in this case, H ₀ : R = 1. (Correlation takes place). Then the alternative hypothesis is written as H ₁ : R = 0. (No correlation). The significance of the multiple correlation coefficient is estimated using statistics:

which has an F - distribution with f ₁ = m and f ₂ = nm-1 degrees of freedom for the significance level α. The statistic value _{Fabl is} compared with the tabular value F _{f1; f2; α} . If F _obs > F _{f1; f2; α} , then the null hypothesis H _{0 is} accepted, and the alternative H _{1 is} rejected, and the probability of rejecting the correct hypothesis H ₀ is equal to the significance level α. Otherwise, H _{1 is} accepted and H _{0 is} rejected.

The least informative signs (R _yx <0.09) were as follows: gender of the patient, the volume of surgery. These factors were removed from the study.

Such an informative sign as the size of the tumor and the nature of its growth, the functional state of the kidneys, invasion of the venous and lymphatic vessels, the time elapsed from the moment of illness to the start of treatment, reliably correlate with the depth of invasion of bladder cancer. The recurrent nature of the tumor correlates with histopathological gradation. The number of tumors is reliably associated with localization. The nature of preoperative and postoperative treatment correlates with the volume of treatment. A significant correlation was noted between the patient's age and the presence of infravesical obstruction.

Therefore, signs that have virtually no effect on the dependent variable y, as well as factors correlated with each other, were excluded from the study and a total of 7 signs were used (m = 7).

The study was based on the multiple linear regression equation. To solve the equation according to the available data (n = 1248, m = 7), the values of the coefficients of multiple linear regression by the least squares method are found.

When studying the influence of informative factors on the survival of cancer patients, the equation of multiple linear regression was used.

, y) линейной. Очевидно, что сумма некоторого числа линейных зависимостей есть зависимость линейная. Однако следует признать и возможность ситуации, когда сумма некоторого числа нелинейных зависимостей есть зависимость линейная (в случае, например, когда сокращаются все слагаемые степени выше одного).In practice, in each case, you should first make sure whether the dependence between the considered quantities (x _j ,

, y) linear. Obviously, the sum of a certain number of linear relationships is a linear relationship. However, one should also recognize the possibility of a situation where the sum of a certain number of nonlinear dependences is a linear dependence (in the case, for example, when all terms of the degree above one are reduced).

When studying the relationship between two x, y values, a procedure is known (testing the statistical hypothesis), the use of which allows us to answer the question of whether the dependence between these values is linear y = ax + b (E. Furster, 1983). For all independent features x _j , j = 1.7 and the dependent variable y for the significance level α = 0.01, a statistical hypothesis was tested on whether the relationship between the values of x _j , y is linear. It turned out that the relationship is non-linear for the following independent signs: tumor localization, treatment volume, histopathological gradation and degree of tumor invasion into the bladder wall.

In the case where the relationship between the quantities x, y is not linear, we can use the quasilinear dependence

точность

(Мацкевич И.П. с соавт., 1996), где y_i - исходные данные,

- результаты расчетов. Отметим, что дисперсию остатков

можно рассматривать как относительную характеристику, тогда как величину L - как абсолютную. Вычисленные значения для некоторых признаков приведены в табл. 2.because it is known that with an increase in the degree of the polynomial, the accuracy of approximation increases (Ferster E., 1983). For all the signs listed above, up to k = 15, the coefficients of relation (4) were calculated by the least squares method (least squares method) (Sachs L., 1976, Ferster E., 1983), the dispersion of residues

accuracy

(Matskevich I.P. et al., 1996), where y _i are the initial data,

- calculation results. Note that the variance of residues

can be considered as a relative characteristic, while the value of L - as absolute. The calculated values for some signs are given in table. 2.

table 2 The dispersion of residuals and the magnitude of the error depending on the degree to which the independent variable is raised. Tumor invasion depth Histopathological gradation K = 1 Su2 = 0.4319431 L,% = 13.11024 k = 1 Su2 = 0.8701608 L,% = 24.07504 K = 2 Su2 = 0.4103538 L,% = 11.67544 k = 2 Su2 = 0.8675915 L,% = 23.7342 K = 3 Su2 = 0.4014881 L,% = 11.13785 k = 3 Su2 = 0.8624043 L,% = 23.39204 K = 4 Su2 = 0.4003371 L,% = 11.03056 k = 4 Su2 = 0.8259581 L,% = 23.18447 K = 5 Su2 = 0.4002574 L,% = 11.02352 k = 5 Su2 = 0.8259577 L,% = 23.18445 K = 6 Su2 = 0.4003121 L,% = 11.02166 k = 6 Su2 = 0.8259585 L,% = 23.18439 K = 7 Su2 = 0.4008229 L,% = 11.05327 k = 7 Su2 = 0.8259575 L,% = 23.18434 K = 8 Su2 = 0.4002176 L,% = 11,00041 k = 8 Su2 = 0.8259578 L,% = 23.18446 K = 9 Su2 = 0.4002187 L,% = 11.00248 k = 9 Su2 = 0.825958 L,% = 23.18443 K = 10 Su2 = 0.4002178 L,% = 10.99883 k = 10 Su2 = 0.8259577 L,% = 23.18447 K = 11 Su2 = 0.4002179 L,% = 10,9999 k = 11 Su2 = 0.8259567 L,% = 23.18447 K = 12 Su2 = 0.4002183 L,% = 10,9999 k = 12 Su2 = 0.8259581 L,% = 23.18448 K = 13 Su2 = 0.4002185 L,% = 10,99938 k = 13 Su2 = 0.8259577 L,% = 23.18433 K = 14 Su2 = 0.4002182 L,% = 10.99889 k = 14 Su2 = 0.8259575 L,% = 23.1851 K = 15 Su2 = 0.4002178 L,% = 11,00029 k = 15 Su2 = 0.8259566 L,% = 23.18443

For other signs, the nature of the change in the variance of residuals and error values is similar. As follows from the data in Table 2, an increase in the order of the polynomial k practically does not lead to a decrease in the variance of residuals and error values. Therefore, we can use the multiple linear regression equation

In the future, using some indirect statistical estimates, we will try to justify this choice.

Let us dwell briefly on the least-squares method. Given n pieces of observation lines x _i0 , x _i1 , x _i2 , ..., x _im , y _i , where x _i0 = 1 is a dummy variable. Then if we put that

then we write equation (6) in matrix form as y = Xa.

It is necessary to find the values of the coefficients of the multiple linear regression equation for which the sum of the squared deviations of the experimental and theoretical values of the dependent variable

where n is the sample size is minimal. Relation (8) is a function of m + 1 variable (a ₀ , a ₁ , ..., a _m ). It is known that a function of a m + 1 variable can reach its local extremum when all its partial derivatives vanish simultaneously. Performing the latter, we obtain a system of linear algebraic equations, called a normal system, with m + 1 unknown in matrix form X'Xa = X'y, the solution of which a = (X'X) ^-1 X'y and allows you to find unknown values a ₀ , a ₁ , ..., a _m , at which (7) reaches its minimum (Sachs L., 1976, Ferster E., 1983). Where X is the matrix of individual values of informative features, the symbol "top stroke" means the transpose of the matrix, the symbol "-1" means the operation of calculating the inverse matrix.

The following ratio coefficients (a) were obtained: free member (a0) = - 1.35, depth of tumor invasion into the bladder wall (a1) = 0.26, histological type of bladder cancer (a2) = 0.13, histopathological grade of cancer bladder (a3) = 0.22, tumor sensitivity to PCT (a4) = 0.47, treatment volume (a5) = 0.37, diseases of the genitourinary system leading to infravesical obstruction (a6) = 0.15, localization tumors (a7) = 0.06.

According to available data (n = 1248, m = 7), MNC estimates of the coefficients of the ratio (5) and confidence intervals (L.G. - left border, P.G. - right border) were found.

The linear correlation coefficient R _yx characterizes the degree of tightness of the relationship between the values of x, y (Sachs L., 1976).

The multiple correlation coefficient is used to characterize the tightness of the relationship between the dependent quantity y and several independent values x ₁ , x ₂ , ..., x _m and is calculated by the equation (Sachs L., 1976, Ferster E., 1983):

- результаты расчетов по формуле (5),where y _i - source data,

- calculation results according to the formula (5),

- среднее значение зависимой переменной.

- the average value of the dependent variable.

(Sachs L., 1976; Forster E., 1983).

To characterize the tightness of the relationship between the dependent quantity y and several independent values x ₁ , x ₂ , ..., x _m , the multiple correlation coefficient was calculated, which turned out to be equal to R _{y.12 ... m} = 0.73 (F observed = 156.1; F critical = 2.0), which indicates a high tightness of the relationship between y and x ₁ , x ₂ , ..., x _m , and can serve as an indirect justification for choosing a function in the form of a multiple linear regression equation.

For the data under consideration, the multiple correlation coefficient turned out to be equal to R _{y.12 ... m} = 0.73 (F observed = 156.1; F critical = 2.0), which practically does not differ from unity and indicates a high tightness of the relationship between y and x ₁ , x ₂ , ..., x _m , and in this regard can serve as an indirect justification for choosing a function in the form of a multiple linear regression equation (6). Note that for 17 signs (including the age and gender of the patient, the volume of surgery, the ultrasound structure of bladder cancer, the size of the tumor, the nature of its growth and the stage of cancer according to TNM), the multiple correlation coefficient turned out to be R _{y.12 ... m} = 0 73, practically does not differ from the above, which indirectly confirms the exclusion of 10 signs from consideration.

. Для вычисленного прогноза

может быть построен доверительный интервал для уровня значимости α=0,01 с использованием неравенств

, где t_f,α - квантиль t-распределения при заданном уровне значимости α и числе степеней свободы f=n-m-1,

, где X - матрица отдельных значений информативных признаков, символ "верхний штрих" означает операцию транспонирования, символ "-1" означает операцию вычисления обратной матрицы (Закс Л., 1976, Ферстер Э., 1983). Тогда с вероятностью P=0,99 (1-α) можно утверждать, что истинное значение

при фиксированных значениях признаков x отдельного пациента находится в этом интервале.To determine the prognosis of the long-term results of organ-preserving treatment of bladder cancer, knowing the values of a, it is enough to substitute in the formula y = a ₀ + a ₁ x + a ₂ x + a ₃ x + a ₄ x + a ₅ x + a ₆ x + a ₇ x, where x is the numerical value that is taken for a particular patient and is selected from table 1 depending on the type and degree of parameters of prognostic factors (a ₁ -a ₇ ). The described method can be used to predict the outcome of organ-preserving treatment in a single patient. To find the forecast, if the coefficients a ₀ , a ₁ , ..., a _m are found by the least-squares method, it is sufficient to substitute the individual values of the patient’s signs in the form of the vector x in relation (6) and calculate

. For the calculated forecast

a confidence interval can be constructed for the significance level α = 0.01 using the inequalities

, where t _{f, α} is the quantile of the t-distribution for a given significance level α and the number of degrees of freedom f = nm-1,

where X is the matrix of individual values of informative features, the symbol "top stroke" means the transpose operation, the symbol "-1" means the operation of computing the inverse matrix (Sachs L., 1976, Ferster E., 1983). Then with probability P = 0.99 (1-α) it can be stated that the true value

at fixed values of signs x of an individual patient is in this interval.

The method allows you to calculate the magnitude of the prognosis of bladder cancer and confidence interval. The prognosis is considered good (relapse-free survival of 10 years or more), if u is in the range of 0-2.5; the prognosis is considered satisfactory (relapse-free survival from 5 to 10 years), if the number is in the range of 2.6-3.5; the prognosis is considered doubtful (the patient's survival is more than 5 years, but a relapse of the disease has occurred) if the y value is in the range of 3.6-4.5; the forecast is considered unsatisfactory (lethal outcome within 5 years) if y exceeds 4.6.

Since the values of informative signs consist of the values of the natural series (from 0 to 6), and the forecast value, in the general case, will not take integer values, we can only talk about falling into an interval whose boundaries are equally spaced from integer values. The prognosis is considered good (relapse-free survival of 5 years or more), if the number is in the range of 0-1.5; the prognosis is considered doubtful (the patient's survival is more than 5 years, but a relapse of the disease has occurred), if the number is in the range of 1.6-2.5; the forecast is considered unsatisfactory (fatal outcome within 5 years) if the number exceeds 2.6.

Using this technique allows you to calculate an individual prognosis of the possibility of using organ-preserving treatment for each patient prospectively. Using the program, it is possible to develop a set of measures for the tertiary prevention of the disease, to select the necessary volume of therapy, taking into account individual characteristics.

Example. Patient S., 72 years old. Complaints on admission to macrohematuria. Considers himself ill for 3 months, when an impurity of blood in the urine first appeared. The patient underwent a clinical laboratory examination. A 32 × 25 mm bladder tumor was detected on the left side wall ((a7) = 0.06 × 1 = 0.06) with invasion into the muscle layer (according to ultrasound and CT) ((a1) = 0.26 × 3 = 0.78). Tumor biopsy was taken - moderately differentiated ((a3) = 0.22 × 2 = 0.44) transitional cell carcinoma ((a2) = 0.13 × 1 = 0.13). Of the accompanying diseases of the genitourinary system in a patient, benign prostatic hyperplasia ((a6) = 0.15 × 2 = 0.30). The patient was diagnosed with bladder cancer T2aN0M0G2. The patient underwent neoadjuvant chemotherapy with 5-fluorouracil, cyclophosphamide, vinblastine, metarexate, doxorubicin, cisplatin with the effect of partial tumor regression ((a4) = 0.47 × 2 = 0.94). The disease prognosis was calculated using the formula y = a ₀ + a ₁ x + a ₂ x + a ₃ x + a ₄ x + a ₅ x + a ₆ x + a ₇ x. The following data were obtained y = (a0) -1.35+ (a7) 0.06+ (a1) 0.78+ (a3) 0.44+ (a2) 0.13+ (a6) 0.30+ (a4 ) 0.94+ (a5) = 1.30 + (a5). A method of treating this patient was selected - complex organ-preserving using transurethral tumor resection ((a5) = 0.37 × 2 = 0.74). T.O. forecast (y) = 1.30 + 0.74 = 2.04, which is considered good (relapse-free survival of 10 years or more), because y is in the range of 0-2.5. The patient was under follow-up for 10 years, the patient is alive, no tumor recurrence was detected.

The developed forecast method can be used to evaluate the course and prognosis of bladder cancer in clinical practice for each individual patient prospectively. The method lies at the heart of a set of measures for tertiary prevention of bladder cancer, allowing patients with a high risk of relapse and death to choose the necessary amount of treatment, recommendations for post-operative monitoring and lifestyle.

Claims (1)

A method for predicting long-term results of treatment of bladder cancer using correlation and regression analysis, characterized in that during the process, the depth of tumor invasion into the bladder wall is determined (a ₁ ), the histological type of bladder cancer (a ₂ ), histopathological gradation of bladder cancer bladder (a ₃ ), tumor sensitivity to PCT (a ₄ ), the volume of treatment (a ₅ ), diseases of the genitourinary system leading to infravesical obstruction (a ₆ ), tumor localization (a ₇ ), then determine prognosis of long-term results of treatment of bladder cancer according to the formula: y = a ₀ + a ₁ x + a ₂ x + a ₃ x + a ₄ x + a ₅ x + a ₆ x + a ₇ x, where a ₀ (free member) = -1.35, a ₁ = 0.26, a ₂ = 0.13, a ₃ = 0.22, a ₄ = 0.47, a ₅ = 0.37, a ₆ = 0.15, a ₇ = 0 , 06, x is a numerical value that is taken for a particular patient and is selected from table 1 in the description, depending on the type and degree of parameters of prognostic factors (a ₁ - a ₇ ), while the prognosis is considered good if y is in in the range of 0-2.5, the forecast is considered satisfactory, if the number is in the range of 2.6-3.5, the forecast is considered doubtful, if y is in the range of 3.6–4.5; the forecast is considered unsatisfactory if y exceeds 4.6.