Spatial cluster randomized trials - sampling design with spillover effects & spatial dependence

Investigators designing cluster randomized trials desire insights directing treatment assignment methodology for studies involving spillover effects and spatial dependence. Treatment assignment strategies including simple random sampling (SRS) and block stratified sampling (BSS) are defined and spatial autoregressive modeling is applied with consideration for spillover effects and spatial dependence for estimation of intervention effects. A simulation study is carried out comparing SRS and BSS sampling methods on spatial grids of varying sizes. A range of spillover effects and levels of spatial dependence were considered for estimation of the intervention effect via a spatial autoregressive (SAR) model. Findings of an extensive simulation study comparing simple random sampling and block stratification methods indicate that randomly selected treatment assignments result in best case reduced Mean Squared Error (MSE) when estimating intervention effects, but block stratified treatment assignments lead to minimal variation in MSE among a series of treatment combinations, indicating that a block stratified treatment arrangement will not achieve the minimal level of estimation error, but it remains robust across a range of selected parameters. While SRS achieves lower average MSE in certain scenarios, both designs exhibit substantial estimation bias when treatment and spillover indicators are collinear. Variation in performance across all possible treatment combinations and the worst-case allocation risk this entails motivates consideration of BSS as a more consistent alternative design. The relationship between spillover effects and mean squared errors (MSE) of intervention effect estimation is apparent. The MSE for the intervention effect, which is the average MSE over each of N simulation iterations, is minimized for some combinations of random sampling treatment assignment, but block stratified assignment minimizes variance among combinations of possible treatment arrangements. In short, SRS may achieve lower average MSE in some scenarios, but BSS bounds worst-case allocation risk through near-zero variation in estimation error across treatment combinations; the preferred strategy depends on the anticipated spillover mechanism, with BSS most advantageous when spillover is expected to flow primarily into control clusters.