Causal inference for randomized experiments and observational studies

Abstract

This thesis presents four new methods to infer causal effect for both randomized experiments and observational studies. Rerandomization (Morgan and Rubin, 2012) has recently attracted much attention in randomized experiments. It repeatedly performs the complete randomization until a well-balanced allocation is generated, which is shown to improve the inferential efficiency significantly. However, the original rerandomization scheme does not consider the response information, which may cause ethical concern in clinical trials because many patients might be assigned to the inferior treatment group. In addition, rerandomization may not work well for high-dimensional and high-collinear covariates, and no attempts have been made to combine this scheme with the causal analysis of observational studies. Three approaches are thus proposed to address those limitations, including the response-adaptive rerandomization, rerandomization based on principal component analysis (PCA), and quasi-rerandomization for observational studies. These methods have been evaluated through extensive numerical studies, demonstrating their superior performance in improving the covariate balance and promoting the precision of estimating treatment effect.

In response-adaptive rerandomization, the response information of the sequentially enrolled participants is incorporated via a Bayesian model when proposing the allocation. This method enjoys a good trade-off between the statistical efficiency and individual ethics for two-arm comparative clinical trials, and can be applied to both continuous and binary outcomes. It is also easy to implement and modify based on the practical needs.

PCA rerandomization exploits principal components rather than the covariates to calculate Mahalanobis distance, which is the balance criterion adopted in the original rerandomization. The proposed strategy can effectively reduce dimensionality and provide computational simplicity by focusing on the top orthogonal components. Furthermore, it preserves the desirable theoretical properties of covariate balance and statistical efficiency.

Quasi-rerandomization is a reweighting method designed for observational studies, where the observational covariates are rerandomized to guide the reweighting such that the weighted data resemble a randomized experiment with balanced covariates. Moreover, the weighted data can be conveniently paired with common weighted estimators for inferring the treatment effect.

Finally, this thesis extends the unit information prior (UIP) to enhance causal inference in randomized control trials by integrating the real-world evidence from multiple observational studies. Empowered with great interpretability, the UIP only requires summary statistics from published observational studies rather that individual level data. Our method reduces the potential bias in the real-world evidence via the reweighting scheme, which can also be readily applied to different types of outcome variables. Extensive numerical experiments show that UIP can improve the statistical efficiency for estimating the treatment effect. The practical potential of the proposed approach is further demonstrated on a real trial of hydroxychloroquine for treating COVID-19.