Multiple conditional randomization tests for lagged and spillover treatment effects

TL;DR

This paper introduces a method for constructing multiple independent conditional randomization tests from a single dataset, enabling valid individual and combined inference for complex treatment effects.

Contribution

It presents a simple sequential construction of multiple tests and applies it to various problems including observational studies, stepped-wedge trials, and interference effects.

Findings

The proposed method allows valid multiple testing with independent p-values.

It performs well compared to existing methods in simulations and real data.

A general condition for the independence of conditional randomization tests is established.

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 effect in stepped-wedge trials, and spillover effect 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.