Analytic methods for individually randomized group treatment trials and group-randomized trials when subjects belong to multiple groups

Participants in trials may be randomized either individually or in groups and may receive their treatment either entirely individually, entirely in groups, or partially individually and partially in groups. This paper concerns cases in which participants receive their treatment either entirely or partially in groups, regardless of how they were randomized. Participants in group-randomized trials are randomized in groups, and participants in individually randomized group treatment trials are individually randomized, but participants in both types of trials receive part or all of their treatment in groups or through common change agents. Participants who receive part or all of their treatment in a group are expected to have positively correlated outcome measurements. This paper addresses a situation that occurs in group-randomized trials and individually randomized group treatment trials-participants receive treatment through more than one group. As motivation, we consider trials in The Childhood Obesity Prevention and Treatment Research Consortium, in which each child participant receives treatment in at least two groups. In simulation studies, we considered several possible analytic approaches over a variety of possible group structures. A mixed model with random effects for both groups provided the only consistent protection against inflated type I error rates and did so at the cost of only moderate loss of power when intraclass correlations were not large. We recommend constraining variance estimates to be positive and using the Kenward-Roger adjustment for degrees of freedom; this combination provided additional power but maintained type I error rates at the nominal level.