Design-Based Causal Inference with Missing Outcomes: Missingness Mechanisms, Imputation-Assisted Randomization Tests, and Covariate Adjustment

Design-based causal inference, also known as randomization-based or finite-population causal inference, is one of the most widely used causal inference frameworks, largely due to the merit that its statistical validity can be guaranteed by the study design (e.g., randomized experiments) and does not require assuming specific outcome-generating distributions or super-population models. Despite its advantages, design-based causal inference can still suffer from other data-related issues, among which outcome missingness is a prevalent and significant challenge. This work systematically studies the outcome missingness problem in design-based causal inference. First, we propose a general and flexible outcome missingness mechanism that can facilitate finite-population-exact randomization tests for the null effect. Second, under this flexible missingness mechanism, we propose a general framework called "imputation and re-imputation" for conducting finite-population-exact randomization tests in design-based causal inference with missing outcomes. This framework can incorporate any imputation algorithms (from linear models to advanced machine learning-based imputation algorithms) while ensuring finite-population-exact type-I error rate control. Third, we extend our framework to conduct covariate adjustment in randomization tests and construct finite-population-valid confidence sets with missing outcomes. Our framework is evaluated via extensive simulation studies and applied to a cluster randomized experiment called the Work, Family, and Health Study. Open-source Python and R packages are also developed for implementation of our framework.