A Negative Control Outcome Regression Accounting for Unobserved Confounding and Lagged Causal Effects

Abstract Background: Epidemiologists are increasingly interested in using negative controls to eliminate unobserved confounding. Particularly, difference-in-differences method, which uses pre-exposure outcomes as negative control outcomes, is widely used. However, it obtains biased estimations when pre-exposure outcome has lagged causal effect on post-exposure outcome.Methods: Taking advantage of pre-exposure outcomes as negative control outcomes, Negative Control Outcome Regression (NCOR) is proposed to eliminate unobserved confounding. The intercept term of NCOR provides an unbiased causal effect estimate of exposure on post-exposure outcome, and the slope minus 1 denotes the lagged causal effect estimation of pre-exposure outcome on post-exposure outcome. We then illustrate the potential of NCOR in a challenging application to estimate the causal association of PM₂.₅ on all-cause mortality rates (AMR) and lagged causal effect of pre AMR on post AMR.Results: Both theoretical justifications and simulation studies validate that the causal effect of exposure on outcome, along with the lagged causal effect of outcomes are identifiable and can be estimated by proposed NCOR model. The application results demonstrate that the previously estimated association between PM₂.₅ and AMR can be attributed to the unobserved confounding. Furthermore, the NCOR model reveal that pre AMR has no causal association with post AMR.Conclusion: The proposed NCOR model can obtain unbiased and robust causal effect estimation of exposure on outcome, and the lagged causal effect of outcomes. The proposed NCOR is implemented as an R package, called NCOR, and is freely available on GitHub.