Assessing the effectiveness of empirical calibration under different bias scenarios

Estimations of causal effects from observational data are subject to various sources of bias. One method for adjusting for the residual biases in the estimation of treatment effects is through the use of negative control outcomes, which are outcomes not believed to be affected by the treatment of interest. The empirical calibration procedure is a technique that uses negative control outcomes to calibrate p-values. An extension of this technique calibrates the coverage of the 95% confidence interval of a treatment effect estimate by using negative control outcomes as well as positive control outcomes, which are outcomes for which the treatment of interest has known effects. Although empirical calibration has been used in several large observational studies, there is no systematic examination of its effect under different bias scenarios.

The effect of empirical calibration of confidence intervals was analyzed using simulated datasets with known treatment effects. The simulations consisted of binary treatment and binary outcome, with biases resulting from unmeasured confounder, model misspecification, measurement error, and lack of positivity. The performance of the empirical calibration was evaluated by determining the change in the coverage of the confidence interval and the bias in the treatment effect estimate.

Empirical calibration increased coverage of the 95% confidence interval of the treatment effect estimate under most bias scenarios but was inconsistent in adjusting the bias in the treatment effect estimate. Empirical calibration of confidence intervals was most effective when adjusting for the 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.

This work adds evidence to the efficacy of empirical calibration of the confidence intervals in observational studies. Calibration of confidence intervals is most effective where there are biases due to unmeasured confounding. Further research is needed on the selection of suitable negative controls.