The interpretation of clinical trials of immediate versus delayed therapy

Prospective, randomised clinical comparisons with a control group are the ideal way to evaluate the effectiveness of a new therapy. However if the new therapy is already available, then it may be unethical to refuse patients this treatment indefinitely. In some trials, patients randomised to the control group receive placebo until their condition deteriorates, and are then switched to the new therapy. Patients randomised to the experimental group receive the new treatment immediately. An analysis following the intention-to-treat principle will be a valid comparison of the two treatment policies actually used. However, such an analysis will underestimate the effect of immediate therapy relative to completely untreated controls, and in particular a negative conclusion should not be interpreted to mean that the therapy is ineffective. In this paper we introduce a parametric approach, which models the dependence between the survival time and the time of switching to the new treatment. This is used first to illustrate the lack of power of the intention-to-treat analysis for evaluating the therapy relative to a pure control. More speculatively, an alternative method of analysis based on our model is presented. We illustrate the issues with data from a prospective randomised study, in which one group of HIV-positive patients received zidovudine immediately after randomisation while control patients were switched to zidovudine only when their condition deteriorated.