Design-based causal inference is one of the most widely used frameworks for
testing causal null hypotheses or inferring about causal parameters from
experimental or observational data. The most significant merit of design-based
causal inference is that its statistical validity only comes from the study
design (e.g., randomization design) and does not require assuming any
outcome-generating distributions or models. Although immune to model
misspecification, design-based causal inference can still suffer from other
data challenges, among which missingness in outcomes is a significant one.
However, compared with model-based causal inference, outcome missingness in
design-based causal inference is much less studied, largely due to the
challenge that design-based causal inference does not assume any outcome
distributions/models and, therefore, cannot directly adopt any existing
model-based approaches for missing data. To fill this gap, we systematically
study the missing outcomes problem in design-based causal inference. First, we
use the potential outcomes framework to clarify the minimal assumption
(concerning the outcome missingness mechanism) needed for conducting
finite-population-exact randomization tests for the null effect (i.e., Fisher's
sharp null) and that needed for constructing finite-population-exact confidence
sets with missing outcomes. Second, we propose a general framework called
``imputation and re-imputation" for conducting finite-population-exact
randomization tests in design-based causal studies with missing outcomes. Our
framework can incorporate any existing outcome imputation algorithms and
meanwhile guarantee finite-population-exact type-I error rate control. Third,
we extend our framework to conduct covariate adjustment in an exact
randomization test with missing outcomes and to construct
finite-population-exact confidence sets with missing outcomes