A logrank test-based method for sizing clinical trials with two co-primary time-to-event endpoints

Abstract

We discuss sample size determination for clinical trials evaluating the joint effects of an intervention on two potentially correlated co-primary time-to-event endpoints. For illustration, we consider the most common case, a comparison of two randomized groups, and use typical copula families to model the bivariate endpoints. A correlation structure of the bivariate logrank statistic is specified to account for the correlation among the endpoints, although the between-group comparison is performed using the univariate logrank statistic. We propose methods to calculate the required sample size to compare the two groups and evaluate the performance of the methods and the behavior of required sample sizes via simulation.

Keywords: Bivariate dependence; Censored data; Copula model; Logrank statistic; Power.

Fig. 1.

Contour plots of the required total sample size with the hazard ratios of time-to-events of virologic and regimen failures, and correlation for the three copulas. The sample size was calculated to detect the joint reduction for both time-to-event outcomes with the overall power of 0.90 at the one-sided significance level of 0.0125, where ρ=ρ⁽¹⁾=ρ⁽²⁾=0.0, 0.3, 0.5, and 0.8; , and ; τ_a=0, and τ_f=96; a⁽¹⁾=0.5.