  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.
