Estimation of the risk difference under a noncompliance randomized clinical trial with missing outcomes

In a randomized clinical trial (RCT), we often come across the situations in which there are patients who do not comply with their assigned treatments or whose outcomes are missing due to their refusal or loss to follow-up. Because noncompliance and missing outcomes do not generally occur completely at random, analyzing data as treated or excluding patients with missing outcomes from our analysis can produce a biased estimate of a treatment effect. In this paper, we consider estimation of the risk difference (RD) in the presence of both noncompliance and missing outcomes under a RCT. On the basis of a constant risk additive model proposed elsewhere, we derive the maximum likelihood estimator (MLE) and develop three asymptotic interval estimators in closed form for the RD when we have outcome missing at random. We apply Monte Carlo simulation to evaluate and compare the performance of these estimators in a variety of situations. We note that all interval estimators developed here can perform well with respect to the coverage probability in all the situations considered here. We find that the interval estimator using tanh-1(x) transformation is generally more precise than the other two estimators with respect to the average length. Finally, we use the data taken from a randomized trial studying the association between flu vaccine and the risk of flu-related hospitalization to illustrate the practical use of these interval estimators.