Estimating the Efficacy of Receiving Treatment in Randomized Clinical Trials with Noncompliance

Analysis of a randomized trial is problematic when there is noncompliance with the treatment assignment. An intent-to-treat (ITT) analysis estimates the effect of randomization rather than the effect for those who actually receive the treatment. An alternative to the ITT is the as treated analysis, in which subjects are classified by the treatment actually received. However, the as treated analysis is also flawed since confounders are likely to be associated with switching treatment.We propose the use of an instrumental variable estimate (using the randomization as the instrument) in combination with propensity score adjustment. In addition, we consider the assumptions implicit in the instrumental variable methodology.These methods are illustrated with data from the Multimodal Treatment of ADHD (MTA) Study of treatment efficacy for children with attention deficit hyperactivity disorder. We show how the addition of the propensity score adjustment to the instrumental variable analysis uncovers some surprising results concerning the children who were assigned to behavioral therapy only but switched to medication.