--- license: apache-2.0 --- # Machine Learning for Two-Sample Testing under Right-Censored Data: A Simulation Study - [Petr PHILONENKO](https://orcid.org/0000-0002-6295-4470), Ph.D. in Computer Science; - [Sergey POSTOVALOV](https://orcid.org/0000-0003-3718-1936), D.Sc. in Computer Science. The paper can be downloaded [here](https://arxiv.org/abs/2409.08201). # About This dataset is a supplement to the [github repositiry](https://github.com/pfilonenko/ML_for_TwoSampleTesting) and paper addressed to solve the two-sample problem under right-censored observations using Machine Learning. The problem statement can be formualted as H0: S1(t)=S2(t) versus H: S1(t)≠S_2(t) where S1(t) and S2(t) are survival functions of samples X1 and X2. This dataset contains the synthetic data simulated by the Monte Carlo method and Inverse Transform Sampling. **Contents** - [About](#about) - [Citing](#citing) - [Repository](#repository) - [Fields](#fields) - [Simulation](#simulation) - [main.cpp](#maincpp) - [simulation_for_machine_learning.h](#simulation_for_machine_learningh) # Citing ~~~ @misc {petr_philonenko_2024, author = { {Petr Philonenko} }, title = { ML_for_TwoSampleTesting (Revision a4ae672) }, year = 2024, url = { https://huggingface.co/datasets/pfilonenko/ML_for_TwoSampleTesting }, doi = { 10.57967/hf/2978 }, publisher = { Hugging Face } } ~~~ # Repository The files of this dataset have following structure: ~~~ data ├── 1_raw │ └── two_sample_problem_dataset.tsv.gz (121,986,000 rows) ├── 2_samples │ ├── sample_train.tsv.gz (24,786,000 rows) │ └── sample_simulation.tsv.gz (97,200,000 rows) └── 3_dataset_with_ML_pred └── dataset_with_ML_pred.tsv.gz (97,200,000 rows) ~~~ - **two_sample_problem_dataset.tsv.gz** is a raw simulated data. In the [github repositiry](https://github.com/pfilonenko/ML_for_TwoSampleTesting), this file must be located in the _ML_for_TwoSampleTesting/proposed_ml_for_two_sample_testing/data/1_raw/_ - **sample_train.tsv.gz** and **sample_simulation.tsv.gz** are train and test samples splited from the **two_sample_problem_dataset.tsv.gz**. In the [github repositiry](https://github.com/pfilonenko/ML_for_TwoSampleTesting), these files must be located in the _ML_for_TwoSampleTesting/proposed_ml_for_two_sample_testing/data/2_samples/_ - **dataset_with_ML_pred.tsv.gz** is the test sample supplemented by the predictions of the proposed ML-methods. In the [github repositiry](https://github.com/pfilonenko/ML_for_TwoSampleTesting), this file must be located in the _ML_for_TwoSampleTesting/proposed_ml_for_two_sample_testing/data/3_dataset_with_ML_pred/_ # Fields In these files, there are following fields: 1) PARAMETERS OF SAMPLE SIMULATION - **iter** is an iteration number of the Monte Carlo replication (in total, 37650); - **sample** is a type of the sample (train, val, test). This field is used to split dataset into train-validate-test samples for ML-model training; - **H0_H1** is a true hypothesis: if **H0**, then samples X1 and X2 were simulated under S1(t)=S2(t); if **H1**, then samples X1 and X2 were simulated under S1(t)≠S2(t); - **Hi** is an alternative (H01-H09, H11-H19, or H21-H29) with competing hypotheses S1(t) and S2(t). Detailed description of these alternatives can be found in the paper; - **n1** is the size of the sample 1; - **n2** is the size of the sample 2; - **perc** is a set (expected) censoring rate for the samples 1 and 2; - **real_perc1** is an actual censoring rate of the sample 1; - **real_perc2** is an actual censoring rate of the sample 2; 2) STATISTICS OF CLASSICAL TWO-SAMPLE TESTS - **Peto_test** is a statistic of the Peto and Peto’s Generalized Wilcoxon test (which is computed on two samples under parameters described above); - **Gehan_test** is a statistic of the Gehan’s Generalized Wilcoxon test; - **logrank_test** is a statistic of the logrank test; - **CoxMantel_test** is a statistic of the Cox-Mantel test; - **BN_GPH_test** is a statistic of the Bagdonavičius-Nikulin test (Generalized PH model); - **BN_MCE_test** is a statistic of the Bagdonavičius-Nikulin test (Multiple Crossing-Effect model); - **BN_SCE_test** is a statistic of the Bagdonavičius-Nikulin test (Single Crossing-Effect model); - **Q_test** is a statistic of the Q-test; - **MAX_Value_test** is a statistic of the Maximum Value test; - **MIN3_test** is a statistic of the MIN3 test; - **WLg_logrank_test** is a statistic of the Weighted Logrank test (weighted function: 'logrank'); - **WLg_TaroneWare_test** is a statistic of the Weighted Logrank test (weighted function: 'Tarone-Ware'); - **WLg_Breslow_test** is a statistic of the Weighted Logrank test (weighted function: 'Breslow'); - **WLg_PetoPrentice_test** is a statistic of the Weighted Logrank test (weighted function: 'Peto-Prentice'); - **WLg_Prentice_test** is a statistic of the Weighted Logrank test (weighted function: 'Prentice'); - **WKM_test** is a statistic of the Weighted Kaplan-Meier test; 3) STATISTICS OF THE PROPOSED ML-METHODS FOR TWO-SAMPLE PROBLEM - **CatBoost_test** is a statistic of the proposed ML-method based on the CatBoost framework; - **XGBoost_test** is a statistic of the proposed ML-method based on the XGBoost framework; - **LightAutoML_test** is a statistic of the proposed ML-method based on the LightAutoML (LAMA) framework; - **SKLEARN_RF_test** is a statistic of the proposed ML-method based on Random Forest (implemented in sklearn); - **SKLEARN_LogReg_test** is a statistic of the proposed ML-method based on Logistic Regression (implemented in sklearn); - **SKLEARN_GB_test** is a statistic of the proposed ML-method based on Gradient Boosting Machine (implemented in sklearn). # Simulation For this dataset, the full source code (C++) is available [here](https://github.com/pfilonenko/ML_for_TwoSampleTesting/tree/main/dataset/simulation). It makes possible to reproduce and extend the simulation by the Monte Carlo method. Here, we present two fragments of the source code (**main.cpp** and **simulation_for_machine_learning.h**) which can help to understand the main steps of the simulation process. ### main.cpp ```C++ #include"simulation_for_machine_learning.h" // Select two-sample tests vector AllTests() { vector D; // ---- Classical Two-Sample tests for Uncensored Case ---- //D.push_back( new HT_AndersonDarlingPetitt ); //D.push_back( new HT_KolmogorovSmirnovTest ); //D.push_back( new HT_LehmannRosenblatt ); // ---- Two-Sample tests for Right-Censored Case ---- D.push_back( new HT_Peto ); D.push_back( new HT_Gehan ); D.push_back( new HT_Logrank ); D.push_back( new HT_BagdonaviciusNikulinGeneralizedCox ); D.push_back( new HT_BagdonaviciusNikulinMultiple ); D.push_back( new HT_BagdonaviciusNikulinSingle ); D.push_back( new HT_QTest ); //Q-test D.push_back( new HT_MAX ); //Maximum Value test D.push_back( new HT_SynthesisTest ); //MIN3 test D.push_back( new HT_WeightedLogrank("logrank") ); D.push_back( new HT_WeightedLogrank("Tarone–Ware") ); D.push_back( new HT_WeightedLogrank("Breslow") ); D.push_back( new HT_WeightedLogrank("Peto–Prentice") ); D.push_back( new HT_WeightedLogrank("Prentice") ); D.push_back( new HT_WeightedKaplanMeyer ); return D; } // Example of two-sample testing using this code void EXAMPLE_1(vector &D) { // load the samples Sample T1(".//samples//1Chemotherapy.txt"); Sample T2(".//samples//2Radiotherapy.txt"); // two-sample testing through selected tests for(int j=0; jTitleTest(test_name); double Sn = D[j]->CalculateStatistic(T1, T2); double pvalue = D[j]->p_value(T1, T2, 27000); // 27k in accodring to the Kolmogorov's theorem => simulation error MAX||G(S|H0)-Gn(S|H0)|| <= 0.01 printf("%s\n", &test_name); printf("\t Sn: %lf\n", Sn); printf("\t pv: %lf\n", pvalue); printf("--------------------------------"); } } // Example of the dataset simulation for the proposed ML-method void EXAMPLE_2(vector &D) { // Run dataset (train or test sample) simulation (results in ".//to_machine_learning_2024//") simulation_for_machine_learning sm(D); } // init point int main() { // Set the number of threads int k = omp_get_max_threads() - 1; omp_set_num_threads( k ); // Select two-sample tests auto D = AllTests(); // Example of two-sample testing using this code EXAMPLE_1(D); // Example of the dataset simulation for the proposed ML-method EXAMPLE_2(D); // Freeing memory ClearMemory(D); printf("The mission is completed.\n"); return 0; } ``` ### simulation_for_machine_learning.h ```C++ #ifndef simulation_for_machine_learning_H #define simulation_for_machine_learning_H #include"HelpFucntions.h" // Object of the data simulation for training of the proposed ML-method class simulation_for_machine_learning{ private: // p-value computation using the Test and Test Statistic (Sn) double pvalue(double Sn, HomogeneityTest* Test) { auto f = Test->F( Sn ); double pv = 0; if( Test->TestType().c_str() == "right" ) pv = 1.0 - f; else if( Test->TestType().c_str() == "left" ) pv = f; else // "double" pv = 2.0*min( f, 1-f ); return pv; } // Process of simulation void Simulation(int iter, vector &D, int rank, mt19937boost Gw) { // preparation the file to save char file_to_save[512]; sprintf(file_to_save,".//to_machine_learning_2024//to_machine_learning[rank=%d].csv", rank); // if it is the first iteration, the head of the table must be read if( iter == 0 ) { FILE *ou = fopen(file_to_save,"w"); fprintf(ou, "num;H0/H1;model;n1;n2;perc;real_perc1;real_perc2;"); for(int i=0; iTitleTest(title_of_test); fprintf(ou, "Sn [%s];p-value [%s];", title_of_test, title_of_test); } fprintf(ou, "\n"); fclose(ou); } // Getting list of the Alternative Hypotheses (H01 - H27) vector H; int l = 1; for(int i=100; i<940; i+=100) // Groups of Alternative Hypotheses (I, II, III, IV, V, VI, VII, VIII, IX) { for(int j=10; j<40; j+=10) // Alternative Hypotheses in the Group (e.g., H01, H02, H03 into the I and so on) //for(int l=1; l<4; l++) // various families of distribution of censoring time F^C(t) H.push_back( 1000+i+j+l ); } // Sample sizes vector sample_sizes; sample_sizes.push_back( 20 ); // n1 = n2 = 20 sample_sizes.push_back( 30 ); // n1 = n2 = 30 sample_sizes.push_back( 50 ); // n1 = n2 = 50 sample_sizes.push_back( 75 ); // n1 = n2 = 75 sample_sizes.push_back( 100 ); // n1 = n2 = 100 sample_sizes.push_back( 150 ); // n1 = n2 = 150 sample_sizes.push_back( 200 ); // n1 = n2 = 200 sample_sizes.push_back( 300 ); // n1 = n2 = 300 sample_sizes.push_back( 500 ); // n1 = n2 = 500 sample_sizes.push_back( 1000 ); // n1 = n2 = 1000 // Simulation (Getting H, Simulation samples, Computation of the test statistics & Save to file) for(int i = 0; i 0 ) { A0.CensoredTypeThird(*H1_1.D,Gw); B0.CensoredTypeThird(*H1_1.D,Gw); } //competing hypothesis H1 Sample A1(*H0_1.D,n,Gw); Sample B1(*H0_2.D,n,Gw); if( per > 0 ) { A1.CensoredTypeThird(*H1_1.D,Gw); B1.CensoredTypeThird(*H1_2.D,Gw); } // ---- Computation of the test statistics & Save to file ---- //Sn and p-value computation under H0 FILE *ou = fopen(file_to_save, "a"); auto perc1 = A0.RealCensoredPercent(); auto perc2 = B0.RealCensoredPercent(); fprintf(ou,"%d;", iter); fprintf(ou,"H0;"); fprintf(ou,"%d;", Hyp); fprintf(ou,"%d;%d;", n,n); fprintf(ou,"%d;%lf;%lf", per, perc1, perc2); for(int j=0; jCalculateStatistic(A0, B0); auto pv_H0 = 0.0; // skip computation (it prepares in ML-framework) fprintf(ou, ";%lf;0", Sn_H0); } fprintf(ou, "\n"); //Sn and p-value computation under H1 perc1 = A1.RealCensoredPercent(); perc2 = B1.RealCensoredPercent(); fprintf(ou,"%d;", iter); fprintf(ou,"H1;"); fprintf(ou,"%d;", Hyp); fprintf(ou,"%d;%d;", n,n); fprintf(ou,"%d;%lf;%lf", per, perc1, perc2); for(int j=0; jCalculateStatistic(A1, B1); auto pv_H1 = 0.0; // skip computation (it prepares in ML-framework) fprintf(ou, ";%lf;0", Sn_H1); } fprintf(ou, "\n"); fclose( ou ); } } } } public: // Constructor of the class simulation_for_machine_learning(vector &D) { int N = 37650; // number of the Monte-Carlo replications #pragma omp parallel for for(int k=0; k