Statistical considerations in the intent-to-treat principle

This paper describes some of the statistical considerations in the intent-to-treat design and analysis of clinical trials. The pivotal property of a clinical trial is the assignment of treatments to patients at random. Randomization alone, however, is not sufficient to provide an unbiased comparison of therapies. An additional requirement is that the set of patients contributing to an analysis provides an unbiased assessment of treatment effects, or that any missing data are ignorable. A sufficient condition to provide an unbiased comparison is to obtain complete data on all randomized subjects. This can be achieved by an intent-to-treat design wherein all patients are followed until death or the end of the trial, or until the outcome event is reached in a time-to-event trial, irrespective of whether the patient is still receiving or complying with the assigned treatment. The properties of this strategy are contrasted with those of an efficacy subset analysis in which patients and observable patient data are excluded from the analysis on the basis of information obtained postrandomization. I describe the potential bias that can be introduced by such postrandomization exclusions and the pursuant effects on type I error probabilities. Especially in a large study, the inflation in type I error probability can be severe, 0.50 or higher, even when the null hypothesis is true. Standard statistical methods for the analysis of censored or incomplete observations all require the assumption of missing at random to some degree, and none of these methods adjust for the potential bias introduced by post hoc subset selection. Nor is such adjustment possible unless one posits a model that relates the missing observations to other observed information for each subject-models that are inherently untestable. Further, the subset selection bias is confounded with the subset-specific treatment effect, and the two components are not identifiable without additional untestable assumptions. Methods for sensitivity analysis to assess the impact of bias in the efficacy subset analysis are described. It is generally believed that the efficacy subset analysis has greater power than the intent-to-treat analysis. However, even when the efficacy subset analysis is assumed to be unbiased, or have a true type I error probability equal to the desired level alpha, situations are described where the intent-to-treat analysis in fact has greater power than the efficacy subset analysis. The intent-to-treat design, wherein all possible patients continue to be followed, is especially powerful when an effective treatment arrests progression of disease during its administration. Thus, a patient benefits long after the patient becomes noncompliant or the treatment is terminated. In such cases, a landmark analysis using the observations from the last patient evaluation is likely to prove more powerful than life-table or longitudinal analyses. Examples are described.