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

Abstract: 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 validity can be guaranteed by 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 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 of no treatment effect. Second, under this general missingness mechanism, we propose a general framework called ``imputation and re-imputation" for conducting randomization tests in design-based causal inference with missing outcomes. We prove that our framework can still ensure finite-population-exact type-I error rate control even when the imputation model was misspecified or when unobserved covariates or interference exist in the missingness mechanism. Third, we extend our framework to conduct covariate adjustment in randomization tests and construct finite-population-valid confidence regions with missing outcomes. Our framework is evaluated via extensive simulation studies and applied to a large-scale randomized experiment.