Propensity Score-based Sensitivity Analysis Method for Uncontrolled Confounding

Abstract

The authors developed a sensitivity analysis method to address the issue of uncontrolled confounding in observational studies. In this method, the authors use a 1-dimensional function of the propensity score, which they refer to as the sensitivity function (SF), to quantify the hidden bias due to unmeasured confounders. The propensity score is defined as the conditional probability of being treated given the measured covariates. Then the authors construct SF-corrected inverse-probability-weighted estimators to draw inference on the causal treatment effect. This approach allows analysts to conduct a comprehensive sensitivity analysis in a straightforward manner by varying sensitivity assumptions on both the functional form and the coefficients in the 1-dimensional SF. Furthermore, 1-dimensional continuous functions can be well approximated by low-order polynomial structures (e.g., linear, quadratic). Therefore, even if the imposed SF is practically certain to be incorrect, one can still hope to obtain valuable information on treatment effects by conducting a comprehensive sensitivity analysis using polynomial SFs with varying orders and coefficients. The authors demonstrate the new method by implementing it in an asthma study which evaluates the effect of clinician prescription patterns regarding inhaled corticosteroids for children with persistent asthma on selected clinical outcomes.