Presenter: Wen-Ching Lan Date: 2018/03/28 Assessing the impact of unmeasured confounding for binary outcomes using confounding functions Jessica Kasza, RoryWolfe, Tibor Schuster International Journal of Epidemiology, 2017 Presenter: Wen-Ching Lan Date: 2018/03/28

Introduction The aim of causal inference is the estimation of causal quantities. The unconditional/ unadjusted estimate of an exposure–outcome association will be biased for the true underlying causal quantity of interest. Random variables that mimic these common causes of exposures and outcomes are commonly called confounding variables or confounders. Design strategies include matching or stratification. Analysis strategies include adjustment for covariates using a multivariable regression analysis, or using propensity score based approaches. 1

Confounding function : which adjusts estimates using confounding functions that describe the degree of unmeasured confounding. Sensitivity analyses are conducted by varying the confounding functions. We provide results for odds ratios and discuss implicit assumptions regarding effect modification. 2

Measured confounders Inverse probability of treatment weighting (IPTW) to incorporate measured confounders in the estimation of marginal effect parameters, and all relevant probabilities defining the effect parameters are estimated within the weighted space. 3

Causal effects in the form of odds ratios and risk ratios Marginal odds ratios and risk ratios 4

If causal inference assumptions are satisfied, ORc =OR. 5

The confounding function approach Adjust estimates using a confounding function that describes the degree of unmeasured confounding A = 0 ) no treatment, A = 1 ) received treatment:   c(0) = c(1) = 1 No unmeasured confounding is present. c(0) > 1; c(1) > 1; c(0) = c(1) Risk of (both) potential outcomes higher among those actually treated. 6

Example abciximab and death 7

Example abciximab and death 996 percutaneous coronary intervention (PCI) patients 698 received abciximab (70%) 298 patients who did not receive abciximab (30%) Adjust for sex, height, diabetes, recent MI, left ventricle ejection fraction, number of vessels in PCI, insertion of coronary stent using inverse probability of treatment weighting 11 died (1.6 % of 698) 15 died (5.0 % of 298) RR for mortality = 0.31 95%CI = 0.15-0.67 8

Example abciximab and death 9

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Discussion The confounding function approach discussed here is useful in settings where interest is in understanding the entire impact of all unmeasured confounding Confounding functions are infrequently used to assess the impact of unmeasured confounding. The confounding function approach requires comparing the expectation of potential outcomes in exposed and unexposed groups on the balance of all unmeasured confounding. 11

Reference Assessing the impact of unmeasured confounding: confounding functions for causal inference. Association of Varicose Veins With Incident Venous Thromboembolism and Peripheral Artery Disease. JAMA