Negative Control Exposures: Causal Effect Identifiability and Use in Probabilistic-bias and Bayesian Analyses With Unmeasured Confounders

Background: Probabilistic bias and Bayesian analyses are important tools for bias correction, particularly when required parameters are nonidentifiable. Negative controls are another tool; they can be used to detect and correct for confounding. Our goals are to present conditions that assure identifiability of certain causal effects and to describe and illustrate a probabilistic bias analysis and related Bayesian analysis that use a negative control exposure. Methods: Using potential-outcome models, we characterized assumptions needed for identification of causal effects using a dichotomous, negative control exposure when residual confounding exists. We defined bias parameters, characterized their relationships with the negative control and with specified causal effects, and described the corresponding probabilistic-bias and Bayesian analyses. We present analytic examples using data on hormone therapy and suicide attempts among transgender people. To address possible confounding by healthcare utilization, we used prior tetanus-diphtheria-pertussis (TdaP) vaccination as a negative control exposure. Results: Hormone therapy was weakly associated with risk (risk ratio [RR] = 0.9). The negative control exposure was associated with risk (RR = 1.7), suggesting confounding. Based on an assumed prior distribution for the bias parameter, the 95% simulation interval for the distribution of confounding-adjusted RR was (0.17, 1.6), with median 0.5; the 95% credibility interval was similar. Conclusions: We used dichotomous negative control exposure to identify causal effects when a confounder was unmeasured under strong assumptions. It may be possible to relax assumptions and the negative control exposure could prove helpful for probabilistic bias analyses and Bayesian analyses.