  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 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 general 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 regions with missing outcomes. Our framework
is evaluated via extensive simulation studies and applied to a large-scale
randomized experiment. Corresponding Python and R packages are also developed.
