Multiple conditional randomization tests for lagged and spillover treatment effects

Abstract We consider the problem of constructing multiple independent conditional randomization tests using a single dataset. Because the tests are independent, the randomization p-values can be interpreted individually and combined using standard methods for multiple testing. We give a simple, sequential construction of such tests and then discuss its application to three problems: Rosenbaum’s evidence factors for observational studies, lagged treatment effects in stepped-wedge trials, and spillover effects in randomized trials with interference. We compare the proposed approach with some existing methods using simulated and real datasets. Finally, we establish a more general sufficient condition for independent conditional randomization tests.