Gaussian prepivoting for finite population causal inference

Testing weak nulls in matched observational studies

We develop sensitivity analyses for the sample average treatment effect in matched observational studies while allowing unit-level treatment effects to vary. The methods may be applied to studies using any optimal without-replacement matching algorithm. In contrast to randomized experiments and to paired observational studies, we show for general matched designs that over a large class of test statistics, any procedure bounding the worst-case expectation while allowing for arbitrary effect heterogeneity must be unnecessarily conservative if treatment effects are actually constant across individuals. We present a sensitivity analysis which bounds the worst-case expectation while allowing for effect heterogeneity, and illustrate why it is generally conservative if effects are constant. An alternative procedure is presented that is asymptotically sharp if treatment effects are constant, and that is valid for testing the sample average effect under additional restrictions which may be deemed benign by practitioners. Simulations demonstrate that this alternative procedure results in a valid sensitivity analysis for the weak null hypothesis under a host of reasonable data-generating processes. The procedures allow practitioners to assess robustness of estimated sample average treatment effects to hidden bias while allowing for effect heterogeneity in matched observational studies.

Pair-switching rerandomization

Rerandomization discards assignments with covariates unbalanced in the treatment and control groups to improve estimation and inference efficiency. However, the acceptance-rejection sampling method used in rerandomization is computationally inefficient. As a result, it is time-consuming for rerandomization to draw numerous independent assignments, which are necessary for performing Fisher randomization tests and constructing randomization-based confidence intervals. To address this problem, we propose a pair-switching rerandomization (PSRR) method to draw balanced assignments efficiently. We obtain the unbiasedness and variance reduction of the difference-in-means estimator and show that the Fisher randomization tests are valid under PSRR. Moreover, we propose an exact approach to invert Fisher randomization tests to confidence intervals, which is faster than the existing methods. In addition, our method is applicable to both nonsequentially and sequentially randomized experiments. We conduct comprehensive simulation studies to compare the finite-sample performance of the proposed method with that of classical rerandomization. Simulation results indicate that PSRR leads to comparable power of Fisher randomization tests and is 3-23 times faster than classical rerandomization. Finally, we apply the PSRR method to analyze two clinical trial datasets, both of which demonstrate the advantages of our method.