We consider clinical trials in which information is available about subjects' treatment changes after randomization. To understand whether any difference between randomized groups in the intention-to-treat analysis can be explained by such treatment changes, we need analysis strategies which take account of treatment actually received. Selection bias is then a potentially serious problem. We relate risk in a time-dependent proportional hazards model to current treatment, with treatment combinations coded in two alternative ways. To reduce selection bias, treatment history (number of treatments dropped) and baseline covariates can be added to the model. Including current risk markers would also reduce selection bias but makes interpretation difficult. The methods are illustrated using data from the British Medical Research Council (MRC) elderly hypertension trial, with time to cardiovascular death as an outcome. Results for the comparison of diuretic and beta-blocker treatment are similar in all analyses, suggesting that selection bias is small and adding support to the hypothesis that the observed treatment differences are due to the randomized treatments themselves.
Introduction
In many clinical trials, individual subjects' prescribed treatment may change from their randomized treatment during follow-up.'* Either the subject or the clinician may choose to discontinue treatment, or the clinician may assign a new treatment because of side-effects or inadequate response to the previous treatment.
A pragmatic analysis of such a trial, as first described by Schwartz and LellouchY3 aims to compare two treatment policies: treatment A (with changes as necessary) against treatment B (with changes as necessary). For this, the correct and unbiased analysis is to compare the two groups as randomized, that is, analysis by intention-to-treat (ITT).
Schwartz and Lellouch also described an explanatory approach which aims to compare the effects of the two treatments themselves 'if other circumstances could be equalized'. For example, we might want to compare the effects of the two treatments if individual changes of treatment occurred under 'comparable circumstances' in the two groups, or alternatively if treatment changes did not occur at all. Equivalently, we might want to ask to what extent a difference (or the lack of a difference) found in the ITT analysis can be ascribed to particular aspects of the treatment changes such as a difference in the rates of side-effects. Some authors claim that little useful purpose is served by any analyses other than ITT 2* 4* because of their susceptibility to selection bias: for example, patients with poorer prognosis may be more prone to change treatment. However, the ITT analysis alone is inadequate to answer