Robust inference in discrete hazard models for randomized clinical trials

Abstract

Time-to-event data in which failures are only assessed at discrete time points are common in many clinical trials. Examples include oncology studies where events are observed through periodic screenings such as radiographic scans. When the survival endpoint is acknowledged to be discrete, common methods for the analysis of observed failure times include the discrete hazard models (e.g., the discrete-time proportional hazards and the continuation ratio model) and the proportional odds model. In this manuscript, we consider estimation of a marginal treatment effect in discrete hazard models where the constant treatment effect assumption is violated. We demonstrate that the estimator resulting from these discrete hazard models is consistent for a parameter that depends on the underlying censoring distribution. An estimator that removes the dependence on the censoring mechanism is proposed and its asymptotic distribution is derived. Basing inference on the proposed estimator allows for statistical inference that is scientifically meaningful and reproducible. Simulation is used to assess the performance of the presented methodology in finite samples.

Fig. 1

Replicated progression-free survival curves for the Atrasentan phase 2 trial based on simulated data

Fig. 2

Illustration of the censoring-dependence and maximum observable time. a shows the survival curves for two groups exhibiting nonproportional hazards over the support [0,3]. b shows the survival curves for the same two groups over the support over [0,1]. c shows varying densities for the censoring times that correspond to different estimands in d

Fig. 3

Survival curves of the different scenarios under consideration for the simulation study. Solid line indicates the control group and dotted line indicates the treatment group

Fig. 4

Different censoring distributions, S_C (· | R), under consideration for the simulation study. Case 1 is that of C = ∞ and administrative censoring occurs at t = 4