README.md

---
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<HomogeneityTest*> AllTests()
{
	vector<HomogeneityTest*> 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<HomogeneityTest*> &D)
{
	// load the samples
	Sample T1(".//samples//1Chemotherapy.txt");
	Sample T2(".//samples//2Radiotherapy.txt");

	// two-sample testing through selected tests
	for(int j=0; j<D.size(); j++)
	{
		char test_name[512];
		D[j]->TitleTest(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<HomogeneityTest*> &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;
}
```