Methods for clustered encouragement design studies with noncompliance and missing data.

Encouragement design studies are particularly useful for estimating the effect of an intervention that cannot itself be randomly administered to some and not to others. They require a randomly selected group receive extra encouragement to undertake the treatment of interest, where the encouragement typically takes the form of additional information or incentives. We consider a "clustered encouragement design" (CED), where the randomization is at the level of the clusters (e.g. physicians), but the compliance with assignment is at the level of the units (e.g. patients) within clusters. Noncompliance and missing data are particular problems in encouragement design studies, where encouragement to take the treatment, rather than the treatment itself, is randomized. The motivating study looks at whether computer-based care suggestions can improve patient outcomes in veterans with chronic heart failure. Since physician adherence has been inadequate, the original study focused on methods to improve physician adherence, although an equally important question is whether physician adherence improves patient outcomes. Here, we reanalyze the data to determine the effect of physician adherence on patient outcomes. We propose causal inference methodology for the effect of a treatment versus a control in a randomized CED study with all-or-none compliance at the unit level. These methods extend the current approaches to account for nonignorable missing data and use an alternative approach to inference using multiple imputation methods, which have been successfully applied to a wide variety of missing data problems and have recently been applied to the potential outcomes framework of causal inference (Taylor and Zhou, 2009b).