Primary Submission Category: Design-Based Causal Inference
Randomization Inference with Sample Selection
Authors: Zeyang Yu, Xinran Li, Peizan Sheng,
Presenting Author: Zeyang Yu*
Randomization inference (RI) is widely used in scientific fields due to its two key advantages: it makes no distributional assumptions and leverages the structure of the experimental design. Most literature focuses on the ideal scenario with no missing outcomes, but sample attrition is common in experiments. Current work often relies on strong assumptions, like missing at random or sharp missingness, to validate RI. When this assumption fails, it can cause severe size distortion in the RI procedure. We first show that when testing a sharp null hypothesis, we can obtain a valid p-value by using the worst-case p-value under arbitrary missingness mechanisms. Finding the worst-case p-value boils down to finding an imputation of the missing outcomes that minimizes a distribution-free test statistic. We then extend the worst-case inferential approach to test the quantiles of the individual effect. This involves utilizing the worst-case imputation for missing outcomes and the imputation procedure in Caughey et al. (2023), simultaneously. Furthermore, we show that the conservative test for testing a sharp null and treatment effect quantile can be improved by incorporating additional assumptions on missingness mechanisms, namely, monotone missingness, sharp missingness, and missing at random. We illustrate our methods with simulations and an application.