Comparison of methods to testing for differential treatment effect under non-proportional hazards data

María del Carmen Pardo; Beatriz Cobo; María del Carmen Pardo; Beatriz Cobo

doi:10.3934/mbe.2023784

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 10: 17646-17660. doi: 10.3934/mbe.2023784

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Comparison of methods to testing for differential treatment effect under non-proportional hazards data

María del Carmen Pardo ^1,2,
Beatriz Cobo ^{3
,
,}

1.
Department of Statistics and O.R., Complutense University of Madrid, Plaza de Ciencias 3, Madrid 28040, Spain
2.
Institute of Interdisciplinary Mathematics, Complutense University of Madrid, Plaza de Ciencias 3, Madrid 28040, Spain
3.
Department of Quantitative Methods for Economics and Business, University of Granada, Paseo de Cartuja 7, Granada 18011, Spain

Received: 04 July 2023 Revised: 28 August 2023 Accepted: 30 August 2023 Published: 15 September 2023

Many tests for comparing survival curves have been proposed over the last decades. There are two branches, one based on weighted log-rank statistics and other based on weighted Kaplan-Meier statistics. If we carefully choose the weight function, a substantial increase in power of tests against non-proportional alternatives can be obtained. However, it is difficult to specify in advance the types of survival differences that may actually exist between two groups. Therefore, a combination test can simultaneously detect equally weighted, early, late or middle departures from the null hypothesis and can robustly handle several non-proportional hazard types with no a priori knowledge of the hazard functions. In this paper, we focus on the most used and the most powerful test statistics related to these two branches which have been studied separately but not compared between them. Through a simulation study, we compare the size and power of thirteen test statistics under proportional hazards and different types of non-proportional hazards patterns. We illustrate the procedures using data from a clinical trial of bone marrow transplant patients with leukemia.
- Survival analysis,
- non-proportional hazards,
- weighted log-rank statistics,
- weighted Kaplan-Meier statistics,
- power
Citation: María del Carmen Pardo, Beatriz Cobo. Comparison of methods to testing for differential treatment effect under non-proportional hazards data[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 17646-17660. doi: 10.3934/mbe.2023784

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Abstract

Many tests for comparing survival curves have been proposed over the last decades. There are two branches, one based on weighted log-rank statistics and other based on weighted Kaplan-Meier statistics. If we carefully choose the weight function, a substantial increase in power of tests against non-proportional alternatives can be obtained. However, it is difficult to specify in advance the types of survival differences that may actually exist between two groups. Therefore, a combination test can simultaneously detect equally weighted, early, late or middle departures from the null hypothesis and can robustly handle several non-proportional hazard types with no a priori knowledge of the hazard functions. In this paper, we focus on the most used and the most powerful test statistics related to these two branches which have been studied separately but not compared between them. Through a simulation study, we compare the size and power of thirteen test statistics under proportional hazards and different types of non-proportional hazards patterns. We illustrate the procedures using data from a clinical trial of bone marrow transplant patients with leukemia.

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