Randomization-based methods for correcting for treatment changes: examples from the Concorde trial

We develop analysis methods for clinical trials with time-to-event outcomes which correct for treatment changes during follow-up, yet are based on comparisons of randomized groups and not of selected groups. A causal model relating observed event times to event times that would have been observed under other treatment scenarios is fitted using the semi-parametric approach of Robins and Tsiatis (avoiding assumptions about the relationship between treatment changes and prognosis). The methods are applied to the Concorde trial of immediate versus deferred zidovudine, to investigate how the results would have differed if no participant randomized to deferred zidovudine had started treatment before reaching ARC or AIDS. We consider issues relating to model choice, non-constant treatment effects and censoring.