Parametric randomization-based methods for correcting for treatment changes in the assessment of the causal effect of treatment

Abstract

We develop parametric maximum likelihood methods to adjust for treatment changes during follow-up in order to assess the causal effect of treatment in clinical trials with time-to-event outcomes. The accelerated failure time model of Robins and Tsiatis relates each observed event time to the underlying event time that would have been observed if the control treatment had been given throughout the trial. We introduce a bivariate parametric frailty model for time to treatment change and time to trial endpoint. Estimating equations which respect the randomization are constructed and compared to maximum likelihood methods in a simulation study. The Concorde trial of immediate versus deferred zidovudine in HIV infection is used as a motivating example and illustration of the methods.