Clinical trials comparing two treatment policies: which aspects of the treatment policies make a difference?

We discuss pragmatic clinical trials with survival endpoints in which subjects commonly change treatment during follow-up. Suppose that an intention-to-treat (ITT) analysis shows a significant difference between the randomized groups. We may want to ask questions about the reason for such a difference in outcome between randomized groups: for example, was the difference due to different policies for change to a third more beneficial regime? We address such questions using the semi-parametric accelerated life models of Robins, which exploit the randomization assumption fully and avoid direct comparisons of possibly differently selected subgroups. No assumption is made about the relationship of treatment actually prescribed to prognosis. A sensitivity analysis, using a range of plausible values for the causal effect of a covariate, estimates the contrasts between randomized groups that would have been observed if the covariate had universally been 0. The main technical problem is in dealing with censoring, for the method requires different degrees of recensoring for different values of the causal effect, and this can lead to estimates of low precision. The methods are applied to a randomized comparison of two anti-hypertensive treatments in which approximately half the subjects changed treatment during follow-up. Various time-dependent covariates, representing patterns of side-effects and treatments, are used in the model. We find that the observed difference in cardiovascular deaths between the randomized groups cannot be explained in this way by their different covariate patterns.