Datasets:
metadata
license: apache-2.0
Machine Learning for Two-Sample Testing under Right-Censored Data: A Simulation Study
- Petr PHILONENKO, Ph.D. in Computer Science;
- Sergey POSTOVALOV, D.Sc. in Computer Science.
The paper can be downloaded here.
About
This dataset is a supplement to the github repositiry 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
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, 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, 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, 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:
- 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;
- 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;
- 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. 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
#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 ); //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<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;
}
simulation_for_machine_learning.h
#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<HomogeneityTest*> &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; i<D.size(); i++)
{
char title_of_test[512];
D[i]->TitleTest(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<int> 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<int> 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<H.size(); i++)
{
int Hyp = H[i];
if(rank == 0)
printf("\tH = %d\n",Hyp);
for(int per = 0; per<51; per+=10)
{
// ---- Getting Hi ----
AlternativeHypotheses H0_1(Hyp,1,0), H0_2(Hyp,2,0);
AlternativeHypotheses H1_1(Hyp,1,per), H1_2(Hyp,2,per);
for(int jj=0; jj<sample_sizes.size(); jj++)
{
int n = sample_sizes[jj];
// ---- Simulation samples ----
//competing hypothesis H0
Sample A0(*H0_1.D,n,Gw);
Sample B0(*H0_1.D,n,Gw);
if( per > 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; j<D.size(); j++)
{
auto Sn_H0 = D[j]->CalculateStatistic(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; j<D.size(); j++)
{
auto Sn_H1 = D[j]->CalculateStatistic(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<HomogeneityTest*> &D)
{
int N = 37650; // number of the Monte-Carlo replications
#pragma omp parallel for
for(int k=0; k<N; k++)
{
int rank = omp_get_thread_num();
auto gen = GwMT19937[rank];
if(rank == 0)
printf("\r%d", k);
Simulation(k, D, rank, gen);
}
}
};
#endif