Negative Control Exposures: Causal effect Identifiability and Use in Probabilistic-Bias and Bayesian Analyses with Unmeasured Confounders

Probabilistic bias and Bayesian analyses are important tools for bias correction, particularly if required parameters are nonidentifiable. Negative controls are another tool; they can detect confounding and correct for confounders. 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. Using potential-outcome models, we characterize assumptions needed for identification of causal effects using a dichotomous, negative control exposure when residual confounding exists. We define bias parameters, characterize their relationships with the negative control and with specified causal effects, and describe the corresponding probabilistic-bias and Bayesian analyses. We exemplify analyses using data on hormone therapy and suicide attempts among transgender people. To address possible confounding by healthcare utilization, we used prior TdaP (tetanus-diphtheria-pertussis) vaccination as a negative control exposure. 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, 1.64), with median 0.5; the 95% credibility interval was similar. A dichotomous negative control exposure can be used to identify causal effects when a confounder is unmeasured under strong assumptions. More realistically, assumptions can be relaxed and the negative control exposure may prove helpful for probabilistic bias analyses and Bayesian analyses.