Model Assisted Sensitivity Analyses for Hidden Bias in Causal Inference with Binary Outcomes
Bo Lu, Division of Biostatistics, College of Public Health, The Ohio State University
In medical, health and social sciences, observational studies are major data sources for inferring causal relationships. Unlike randomized experiments, observational studies are vulnerable to the hidden bias introduced by unmeasured confounders. The impact of unmeasured covariates on the causal effect can be assessed by conducting a sensitivity analysis. A comprehensive framework of sensitivity analyses has been developed for matching designs. Sensitivity parameters are introduced to capture the association between the missing confounder and the exposure or the outcome. Fixing sensitivity parameter values, it is possible to compute the bounds of the p-value of a randomization test on causal effects. We propose a model assisted sensitivity analysis with binary outcomes for the general 1:k matching design, which provides results equivalent to the conventional nonparametric approach. By introducing a conditional logistic outcome model, we substantially simplify the implementation and interpretation of the sensitivity analysis. More importantly, we are able to provide a closed form representation for the set of sensitivity parameters for which the maximum p-values are non-significant. This methodology can be easily extended to matching designs with multilevel treatments, referred as “poly-matching”. We illustrate our method using a U.S. trauma care database to examine mortality difference between trauma care centers.
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