Design and analysis of randomized trials to estimate spatio-temporally heterogeneous treatment effects

In this article, we consider randomized trial design to evaluate interventions with spatially or spatio-temporally heterogeneous effects. A common approach in this setting is the cluster randomized trial. In many cases, clusters are constituted as discrete subdivisions of a contiguous area of interest. However, cluster trials designed in this way may suffer from issues of spillover and may fail to capture the relevant spatial and temporal effects. We define possible randomization schemes and consider the identifiability of the causal effects of the intervention and the required trial design assumptions. We develop mixed model and dose response function specifications that satisfy the required assumptions. We show that the dose response functions are identifiable under certain randomization schemes and compare the performance of estimators in a simulation-based study. We demonstrate that obtaining valid inference may be difficult in these settings but that design-based estimators of confidence intervals and p-values generally perform well. Finally, we present design examples, including a re-analysis of data from a trial of an interventions to reduce the risk of malaria. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.