title: Tests for equivalence of two survival functions: Alternative to the tests under proportional hazards.
abstract: For either the equivalence trial or the non-inferiority trial with survivor outcomes from two treatment groups, the most popular testing procedure is the extension (e.g., Wellek, A log-rank test for equivalence of two survivor functions, Biometrics, 1993; 49: 877-881) of log-rank based test under proportional hazards model. We show that the actual type I error rate for the popular procedure of Wellek is higher than the intended nominal rate when survival responses from two treatment arms satisfy the proportional odds survival model. When the true model is proportional odds survival model, we show that the hypothesis of equivalence of two survival functions can be formulated as a statistical hypothesis involving only the survival odds ratio parameter. We further show that our new equivalence test, formulation, and related procedures are applicable even in the presence of additional covariates beyond treatment arms, and the associated equivalence test procedures have correct type I error rates under the proportional hazards model as well as the proportional odds survival model. These results show that use of our test will be a safer statistical practice for equivalence trials of survival responses than the commonly used log-rank based tests.
authors.affiliation: 1 Department of Statistics, Florida State University, Tallahassee, USA.
authors.forename: Elvis E
authors.initials: EE
authors.lastname: Martinez
authors.affiliation: 1 Department of Statistics, Florida State University, Tallahassee, USA.
authors.forename: Debajyoti
authors.initials: D
authors.lastname: Sinha
authors.affiliation: 2 Department of Biostatistics, MD Anderson Cancer Center, University of Texas, Houston, USA.
authors.forename: Wenting
authors.initials: W
authors.lastname: Wang
authors.affiliation: 3 Harvard Medical School, Boston, USA.
authors.forename: Stuart R
authors.initials: SR
authors.lastname: Lipsitz
authors.affiliation: 4 UW-Madison, Biostatistics & Medical Informatics, Madison, USA.
authors.forename: Richard J
authors.initials: RJ
authors.lastname: Chappell
mesh_terms: D002648:Child; D000074099:Equivalence Trials as Topic; D006801:Humans; D016393:Lymphoma, B-Cell / Q000188:drug therapy; D016017:Odds Ratio; D016016:Proportional Hazards Models; D012107:Research Design
keywords: Cox’s model; clinical importance; critical region; proportional odds survival model