--- license: cc-by-4.0 --- # 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. # 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. # Repository The files of this dataset have following structure: ~~~ data ├── 1_raw │ └── two_sample_problem_dataset.tsv.gz ├── 2_samples │ ├── sample_train.tsv.gz │ └── sample_simulation.tsv.gz └── 3_dataset_with_ML_pred └── dataset_with_ML_pred.tsv.gz ~~~ - **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/_ # Dataset & Samples In these files there are following fields: 1) PARAMETERS OF SAMPLE SIMULATION - **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 test statistics were simulated under S1(t)=S2(t); if **H1**, then test statistics were simulated under S1(t)≠S2(t); - **Hi** is an alternative hypothesis (H01-H09, H11-H19, or H21-H29) for 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 sample 1; - **real_perc2** is an actual censoring rate of 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). # Dataset 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 the file main.cpp only. ```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 ); //based on the Kaplan-Meier estimator 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; } ```