Primary Submission Category: Sensitivity Analysis
Multivariate one-sided testing via sample splitting in an observational study of the effect of poverty on children’s physical fitness
Authors: William Bekerman, Dylan Small, Colin Fogarty,
Presenting Author: William Bekerman*
When assessing the causal effect of a treatment on two or more outcomes in an observational study, a linear combination of outcomes may lessen the sensitivity of a test of the global null hypothesis to potential unmeasured biases. While all linear combinations of scored outcomes can be considered using Scheffé projections, finding the contrast that minimizes sensitivity to unmeasured biases requires corrections for multiple testing which can erode power, especially when many outcomes are of interest. To mitigate this issue, we propose splitting the sample into a planning sample to identify the optimal contrast and an analysis sample to conduct inference. We introduce a novel minimax theorem for this problem and find that the design sensitivity on the whole sample equals the design sensitivity when using split samples. We also conduct extensive simulation studies demonstrating enhanced power in finite samples. Finally, we apply our method to investigate the broad effects of low family income on children’s physical activity and fitness.