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Abstract It is common to conduct causal inference in matched observational studies by proceeding as though treatment assignments within matched sets are assigned uniformly at random and using this distribution as the basis for inference. This approach ignores observed discrepancies in matched sets that may be consequential for the distribution of treatment, which are succinctly captured by within-set differences in the propensity score. We address this problem via covariate-adaptive randomization inference, which modifies the permutation probabilities to vary with estimated propensity score discrepancies and avoids requirements to exclude matched pairs or model an outcome variable. We show that the test achieves type I error control arbitrarily close to the nominal level when large samples are available for propensity score estimation. We characterize the large-sample behaviour of the new randomization test for a difference-in-means estimator of a constant additive effect. We also show that existing methods of sensitivity analysis generalize effectively to covariate-adaptive randomization inference. Finally, we evaluate the empirical value of combining matching and covariate-adaptive randomization procedures using simulations and analyses of genetic damage among welders and right-heart catheterization in surgical patients. 

ABSTRACT Disparities in health or well‐being experienced by minority groups can be difficult to study using the traditional exposure‐outcome paradigm in causal inference, since potential outcomes in variables such as race or sexual minority status are challenging to interpret. Causal decomposition analysis addresses this gap by positing causal effects on disparities under interventions to other intervenable exposures that may play a mediating role in the disparity. While invoking weaker assumptions than causal mediation approaches, decomposition analyses are often conducted in observational settings and require uncheckable assumptions that eliminate unmeasured confounders. Leveraging the marginal sensitivity model, we develop a sensitivity analysis for weighted causal decomposition estimators and use the percentile bootstrap to construct valid confidence intervals for causal effects on disparities. We also propose a two‐parameter reformulation that enhances interpretability and facilitates an intuitive understanding of the plausibility of unmeasured confounders and their effects. We illustrate our framework on a study examining the effect of parental support on disparities in suicidal ideation among sexual minority youth. We find that the effect is small and sensitive to unmeasured confounding, suggesting that further screening studies are needed to identify mitigating interventions in this vulnerable population.