Ridge rerandomization: An experimental design strategy in the presence of covariate collinearity

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.

Quasi-rerandomization for observational studies

BACKGROUND

In the causal analysis of observational studies, covariates should be carefully balanced to approximate a randomized experiment. Numerous covariate balancing methods have been proposed for this purpose. However, it is often unclear what type of randomized experiments the balancing approaches aim to approximate; and this may cause ambiguity and hamper the synthesis of balancing characteristics within randomized experiments.

METHODS

Randomized experiments based on rerandomization, known for significant improvement on covariate balance, have recently gained attention in the literature, but no attempt has been made to integrate this scheme into observational studies for improving covariate balance. Motivated by the above concerns, we propose quasi-rerandomization, a novel reweighting method, where observational covariates are rerandomized to be the anchor for reweighting such that the balanced covariates obtained from rerandomization can be reconstructed by the weighted data.

RESULTS

Through extensive numerical studies, not only does our approach demonstrate similar covariate balance and comparable estimation precision of treatment effect to rerandomization in many situations, but it also exhibits advantages over other balancing techniques in inferring the treatment effect.

CONCLUSION

Our quasi-rerandomization method can approximate the rerandomized experiments well in terms of improving the covariate balance and the precision of treatment effect estimation. Furthermore, our approach shows competitive performance compared with other weighting and matching methods. The codes for the numerical studies are available at https://github.com/BobZhangHT/QReR .