Targeted estimation and inference for the sample average treatment effect in trials with and without pair-matching.

In cluster randomized trials, the study units usually are not a simple random sample from some clearly defined target population. Instead, the target population tends to be hypothetical or ill-defined, and the selection of study units tends to be systematic, driven by logistical and practical considerations. As a result, the population average treatment effect (PATE) may be neither well defined nor easily interpretable. In contrast, the sample average treatment effect (SATE) is the mean difference in the counterfactual outcomes for the study units. The sample parameter is easily interpretable and arguably the most relevant when the study units are not sampled from some specific super-population of interest. Furthermore, in most settings, the sample parameter will be estimated more efficiently than the population parameter. To the best of our knowledge, this is the first paper to propose using targeted maximum likelihood estimation (TMLE) for estimation and inference of the sample effect in trials with and without pair-matching. We study the asymptotic and finite sample properties of the TMLE for the sample effect and provide a conservative variance estimator. Finite sample simulations illustrate the potential gains in precision and power from selecting the sample effect as the target of inference. This work is motivated by the Sustainable East Africa Research in Community Health (SEARCH) study, a pair-matched, community randomized trial to estimate the effect of population-based HIV testing and streamlined ART on the 5-year cumulative HIV incidence (NCT01864603). The proposed methodology will be used in the primary analysis for the SEARCH trial.