Assessing the effectiveness of empirical calibration under different bias scenarios

Background: Estimations of causal effects from observational data are subject to various sources of bias. These biases can be adjusted by using negative control outcomes not affected by the treatment. The empirical calibration procedure uses negative controls to calibrate p-values and both negative and positive controls to calibrate coverage of the 95% confidence interval of the outcome of interest. Although empirical calibration has been used in several large observational studies, there is no systematic examination of its effect under different bias scenarios. Methods: The effect of empirical calibration of confidence intervals was analyzed using simulated datasets with known treatment effects. The simulations were for binary treatment and binary outcome, with simulated biases resulting from unmeasured confounder, model misspecification, measurement error, and lack of positivity. The performance of empirical calibration was evaluated by determining the change of the confidence interval coverage and bias of the outcome of interest. Results: Empirical calibration increased coverage of the outcome of interest by the 95% confidence interval under most settings but was inconsistent in adjusting the bias of the outcome of interest. Empirical calibration was most effective when adjusting for unmeasured confounding bias. Suitable negative controls had a large impact on the adjustment made by empirical calibration, but small improvements in the coverage of the outcome of interest were also observable when using unsuitable negative controls. Conclusions: This work adds evidence to the efficacy of empirical calibration on calibrating the confidence intervals of treatment effects in observational studies. We recommend empirical calibration of confidence intervals, especially when there is a risk of unmeasured confounding.