Unmatched spatially stratified controls: A simulation study examining efficiency and precision using spatially-diverse controls and generalized additive models

Unmatched spatially stratified random sampling (SSRS) of non-cases selects geographically balanced controls by dividing the study area into spatial strata and randomly selecting controls from all non-cases within each stratum. The performance of SSRS control selection was evaluated in a case study spatial analysis of preterm birth in Massachusetts. In a simulation study, we fit generalized additive models using controls selected by SSRS or simple random sample (SRS) designs. We compared mean squared error (MSE), bias, relative efficiency (RE), and statistically significant map results to the model results with all non-cases. SSRS designs had lower average MSE (0.0042-0.0044) and higher RE (77-80%) compared to SRS designs (MSE: 0.0072-0.0073; RE across designs: 71%). SSRS map results were more consistent across simulations, reliably identifying statistically significant areas. SSRS designs improved efficiency by selecting controls that are geographically distributed, particularly from low population density areas, and may be more appropriate for spatial analyses.