Abstract
BackgroundControlling 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.MethodsWe 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.ResultsThe 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).ConclusionsWe 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.
Highlights
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
We propose a novel method to control unobserved confounding through double confounders with two values satisfying a non-linear condition on the exposure
We focus on the average causal effect (ACE) of X on Y which is the difference in expectation of potential outcome at two different exposure levels 0 and 1, for instance, ACEX → Y = E(Y(1) − Y(0)) for a binary exposure
Summary
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. Controlling unobserved confounding is a great challenge when estimating the causal effect of an exposure on an outcome of interest in observational studies [1,2,3,4]. The observed data distribution may have compatibility with many contradictory causal explanations due to the existence of unobserved confounding. While a valid negative control outcome needs to be influenced by the same unobserved confounders of the exposure effects on the outcome in view, not directly influenced by the exposure This approach fails to obtain causal estimation of the exposure on the outcome [18]. Strict assumptions of the methods above usually may be violated in practice and impose restrictions on their generalization
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