Sample size estimation in educational intervention trials with subgroup heterogeneity in only one arm.

We present closed form sample size and power formulas motivated by the study of a psycho-social intervention in which the experimental group has the intervention delivered in teaching subgroups whereas the control group receives usual care. This situation is different from the usual clustered randomized trial because subgroup heterogeneity only exists in one arm. We take this modification into consideration and present formulas for the situation in which we compare a continuous outcome at both a single point in time and longitudinally over time. In addition, we present the optimal combination of parameters such as the number of subgroups and number of time points for minimizing sample size and maximizing power subject to constraints such as the maximum number of measurements that can be taken (i.e., a proxy for cost).