Augmented case-only designs for randomized clinical trials with failure time endpoints.

Under suitable assumptions and by exploiting the independence between inherited genetic susceptibility and treatment assignment, the case-only design yields efficient estimates for subgroup treatment effects and gene-treatment interaction in a Cox model. However it cannot provide estimates of the genetic main effect and baseline hazards, that are necessary to compute the absolute disease risk. For two-arm, placebo-controlled trials with rare failure time endpoints, we consider augmenting the case-only design with random samples of controls from both arms, as in the classical case-cohort sampling scheme, or with a random sample of controls from the active treatment arm only. The latter design is motivated by vaccine trials for cost-effective use of resources and specimens so that host genetics and vaccine-induced immune responses can be studied simultaneously in a bigger set of participants. We show that these designs can identify all parameters in a Cox model and that the efficient case-only estimator can be incorporated in a two-step plug-in procedure. Results in simulations and a data example suggest that incorporating case-only estimators in the classical case-cohort design improves the precision of all estimated parameters; sampling controls only in the active treatment arm attains a similar level of efficiency.