Correcting for non-compliance in randomized trials using structural nested mean models

In a randomized trial designed to study the effect of a treatment of interest on the evolution of the mean of a time-dependent outcome variable, subjects are assigned to a treatment regime, or, equivalently, a treatment protocol. Unfortunately, subjects often fail to comply with their assigned regime. From a public health point of view, the causal parameter of interest will often be a function of the treatment differences that would have been observed hadcontrary to fact, all subjects remained on protocol. This paper considers the identification and estimation of these treatment differences based on a new class of structural models, the multivariate structural nested mean models, when reliable estimates of each subject's actual treatment are available. Estimates of “actual treatment” might, for example, be obtained by measuring the amount of “active drug” in the subject's blood or urine at each follow-up visit or by pill counting techniques. In addition, we discuss a natural extension of our methods to observational studies.