From bad to worse: collider stratification amplifies confounding bias in the "obesity paradox"

Smoking is often identified as a confounder of the obesity-mortality relationship. Selection bias can amplify the magnitude of an existing confounding bias. The objective of the present report is to demonstrate how confounding bias due to cigarette smoking is increased in the presence of collider stratification bias using an empirical example and directed acyclic graphs. The empirical example uses data from the Atherosclerosis Risk in Communities (ARIC) study, a prospective cohort study of 15,792 men and women in the United States. Poisson regression models were used to examine the confounding effect of smoking. In the total ARIC study population, smoking produced a confounding bias of <3 percentage points. This result was obtained by comparing the incidence rate ratio (IRR) for obesity from a model adjusted for smoking was 1.07 (95 % CI 1.00, 1.15) with one that did not adjust for smoking was 1.10 (95 % CI 1.03, 1.18). However, among smokers with CVD, the obesity IRR was 0.89 (95 % CI 0.81, 0.99), while among non-smokers with CVD the obesity IRR was 1.20 (95 % CI 1.03, 1.41). The empirical and graphical explanations presented suggest that the magnitude of the confounding bias induced by smoking is greater in the presence of collider stratification bias.