A novel method for controlling unobserved confounding using double confounders

Controlling unobserved confounding still remains a great challenge in observational studies, and a series of strict assumptions of the existing methods usually may be violated in practice. Therefore, it is urgent to put forward a novel method.

We are interested in the causal effect of an exposure on the outcome, which is always confounded by unobserved confounding. We show that, the causal effect of an exposure on a continuous or categorical outcome is nonparametrically identified through only two independent or correlated available confounders satisfying a non-linear condition on the exposure. Asymptotic theory and variance estimators are developed for each case. We also discuss an extension for more than two binary confounders.

The simulations show better estimation performance by our approach in contrast to the traditional regression approach adjusting for observed confounders. A real application is separately applied to assess the effects of Body Mass Index (BMI) on Systolic Blood Pressure (SBP), Diastolic Blood Pressure (DBP), Fasting Blood Glucose (FBG), Triglyceride (TG), Total Cholesterol (TC), High Density Lipoprotein (HDL) and Low Density Lipoprotein (LDL) with individuals in Shandong Province, China. Our results suggest that SBP increased 1.60 (95% CI: 0.99-2.93) mmol/L with per 1- kg/m² higher BMI and DBP increased 0.37 (95% CI: 0.03-0.76) mmol/L with per 1- kg/m² higher BMI. Moreover, 1- kg/m² increase in BMI was causally associated with a 1.61 (95% CI: 0.96-2.97) mmol/L increase in TC, a 1.66 (95% CI: 0.91-55.30) mmol/L increase in TG and a 2.01 (95% CI: 1.09-4.31) mmol/L increase in LDL. However, BMI was not causally associated with HDL with effect value - 0.20 (95% CI: - 1.71-1.44). And, the effect value of FBG per 1- kg/m² higher BMI was 0.56 (95% CI: - 0.24-2.18).

We propose a novel method to control unobserved confounders through double binary confounders satisfying a non-linear condition on the exposure which is easy to access.