Quantifying the bias due to observed individual confounders in causal treatment effect estimates

It is often of interest to use observational data to estimate the causal effect of a target exposure or treatment on an outcome. When estimating the treatment effect, it is essential to appropriately adjust for selection bias due to observed confounders using, for example, propensity score weighting. Selection bias due to confounders occurs when individuals who are treated are substantially different from those who are untreated with respect to covariates that are also associated with the outcome. A comparison of the unadjusted, naive treatment effect estimate with the propensity score adjusted treatment effect estimate provides an estimate of the selection bias due to these observed confounders. In this article, we propose methods to identify the observed covariate that explains the largest proportion of the estimated selection bias. Identification of the most influential observed covariate or covariates is important in resource-sensitive settings where the number of covariates obtained from individuals needs to be minimized due to cost and/or patient burden and in settings where this covariate can provide actionable information to healthcare agencies, providers, and stakeholders. We propose straightforward parametric and nonparametric procedures to examine the role of observed covariates and quantify the proportion of the observed selection bias explained by each covariate. We demonstrate good finite sample performance of our proposed estimates using a simulation study and use our procedures to identify the most influential covariates that explain the observed selection bias in estimating the causal effect of alcohol use on progression of Huntington's disease, a rare neurological disease.