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. One method of adjusting for the residual biases in the estimation of a treatment effect is through negative control outcomes, where the treatment does not affect the outcome. The empirical calibration procedure is a technique that uses negative controls to calibrate p-values. An extension of empirical calibration calibrates the coverage of the 95% confidence interval of a treatment effect estimate by using negative control outcomes as well as positive control outcomes (where treatment affects the outcome). Methods: 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. Results: 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.