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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.<\/p><\/abstract><\/jats:p>","DOI":"10.3934\/mbe.2023784","type":"journal-article","created":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T10:58:25Z","timestamp":1694775505000},"page":"17646-17660","source":"Crossref","is-referenced-by-count":1,"title":["Comparison of methods to testing for differential treatment effect under non-proportional hazards data"],"prefix":"10.3934","volume":"20","author":[{"given":"Mar\u00eda del Carmen","family":"Pardo","sequence":"first","affiliation":[{"name":"Department of Statistics and O.R., Complutense University of Madrid, Plaza de Ciencias 3, Madrid 28040, Spain"},{"name":"Institute of Interdisciplinary Mathematics, Complutense University of Madrid, Plaza de Ciencias 3, Madrid 28040, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Beatriz","family":"Cobo","sequence":"additional","affiliation":[{"name":"Department of Quantitative Methods for Economics and Business, University of Granada, Paseo de Cartuja 7, Granada 18011, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/mbe.2023784-1","doi-asserted-by":"publisher","unstructured":"R. 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