Motivated by a recent National Research Council study, we discuss three aspects of the analysis of clinical trials when participants prematurely discontinue treatments. First, we distinguish treatment discontinuation from missing outcome data. Data collection is often stopped after treatment discontinuation, but outcome data could be recorded on individuals after they discontinue treatment, as the National Research Council study recommends. Conversely, outcome data may be missing for individuals who do not discontinue treatment, as when there is loss to follow up or missed clinic visits. Missing outcome data is a standard missing data problem, but treatment discontinuation is better viewed as a form of noncompliance and treated using ideas from the causal literature on noncompliance. Second, the standard intention to treat estimand, the average effect of randomization to treatment, is compared with three alternative estimands for the intention to treat population: the average effect when individuals continue on the assigned treatment after discontinuation, the average effect when individuals take a control treatment after treatment discontinuation, and a summary measure of the effect of treatment prior to discontinuation. We argue that the latter choice of estimand has advantages and should receive more consideration. Third, we consider when follow-up measures after discontinuation are needed for valid measures of treatment effects. The answer depends on the choice of primary estimand and the plausibility of assumptions needed to address the missing data. Ideas are motivated and illustrated by a reanalysis of a past study of inhaled insulin treatments for diabetes, sponsored by Eli Lilly. Copyright © 2014 John Wiley & Sons, Ltd.