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.

Figure 1.

Point estimates (solid line) of the risk difference for uncontrolled asthma between daily use and periodic use of inhaled corticosteroids in children with mild persistent asthma, assuming constant sensitivity functions, Parent Asthma Communication Experience Study, 2007–2008. The authors vary the values of c(1, e) and r = c(0, e)/c(1, e). A) r = 1; B) r = 1.2; C) r = 1.5; D) r = 2. The 95% bootstrap confidence intervals (dotted lines) were obtained using the 2.5% and 97.5% percentiles among the 1,000 bootstrap replications.