Proportion-based Sensitivity Analysis of Uncontrolled Confounding Bias in Causal Inference

Abstract

Uncontrolled confounding bias causes a spurious relationship between an exposure variable and an outcome variable and precludes reliable evaluation of the causal effect from observed data.Thus, it is important to observe a sufficient set of confounders to reliably evaluate the causal effect.However, there is no statistical method for judging whether an available set of covariates is sufficient to derive a reliable estimator for the causal effect.To address this problem, we focus on the fact that the mean squared error (MSE) of the outcome variable with respect to the average causal risk can be described as the sum of "the conditional variance of the outcome variable given the exposure variable" and "the square of the uncontrolled confounding bias".We then propose a novel sensitivity analysis, namely, the proportion-based sensitivity analysis of uncontrolled confounding bias in causal effects (PSA) in which the sensitivity parameter is formulated as the proportion of "the square of the uncontrolled confounding bias" to the MSE, and we clarify some properties.We also demonstrate the applicability of the PSA through two case studies.