title: Heterogeneous treatment effects in stratified clinical trials with time-to-event endpoints.
abstract: When analyzing clinical trials with a stratified population, homogeneity of treatment effects is a common assumption in survival analysis. However, in the context of recent developments in clinical trial design, which aim to test multiple targeted therapies in corresponding subpopulations simultaneously, the assumption that there is no treatment-by-stratum interaction seems inappropriate. It becomes an issue if the expected sample size of the strata makes it unfeasible to analyze the trial arms individually. Alternatively, one might choose as primary aim to prove efficacy of the overall (targeted) treatment strategy. When testing for the overall treatment effect, a violation of the no-interaction assumption renders it necessary to deviate from standard methods that rely on this assumption. We investigate the performance of different methods for sample size calculation and data analysis under heterogeneous treatment effects. The commonly used sample size formula by Schoenfeld is compared to another formula by Lachin and Foulkes, and to an extension of Schoenfeld's formula allowing for stratification. Beyond the widely used (stratified) Cox model, we explore the lognormal shared frailty model, and a two-step analysis approach as potential alternatives that attempt to adjust for interstrata heterogeneity. We carry out a simulation study for a trial with three strata and violations of the no-interaction assumption. The extension of Schoenfeld's formula to heterogeneous strata effects provides the most reliable sample size with respect to desired versus actual power. The two-step analysis and frailty model prove to be more robust against loss of power caused by heterogeneous treatment effects than the stratified Cox model and should be preferred in such situations.
authors.affiliation: Department of Biostatistics, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, D-69120, Heidelberg, Germany.
authors.forename: Christina
authors.initials: C
authors.lastname: Beisel
authors.affiliation: Department of Biostatistics, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, D-69120, Heidelberg, Germany.
authors.forename: Axel
authors.initials: A
authors.lastname: Benner
authors.affiliation: Department of Biostatistics, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, D-69120, Heidelberg, Germany.
authors.forename: Christina
authors.initials: C
authors.lastname: Kunz
authors.affiliation: Department of Biostatistics, German Cancer Research Center (DKFZ), Im Neuenheimer Feld 280, D-69120, Heidelberg, Germany.
authors.forename: Annette
authors.initials: A
authors.lastname: Kopp-Schneider
mesh_terms: D001699:Biometry / Q000379:methods*; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D003198:Computer Simulation; D006801:Humans; D015233:Models, Statistical; D018401:Sample Size; D016019:Survival Analysis; D013997:Time Factors
keywords: Biomarkers; Cox proportional hazards model; Log-rank test; Sample size; Shared frailty model