Adjusting for collider bias in genetic association studies using instrumental variable methods

Genome-wide association studies have provided many genetic markers that can be used as instrumental variables to adjust for confounding in epidemiological studies. Recently, the principle has been applied to other forms of bias in observational studies, especially collider bias that arises when conditioning or stratifying on a variable that is associated with the outcome of interest. An important case is in studies of disease progression and survival. Here, we clarify the links between the genetic instrumental variable methods proposed for this problem and the established methods of Mendelian randomisation developed to account for confounding. We highlight the critical importance of weak instrument bias in this context and describe a corrected weighted least-squares procedure as a simple approach to reduce this bias. We illustrate the range of available methods on two data examples. The first, waist-hip ratio adjusted for body-mass index, entails statistical adjustment for a quantitative trait. The second, smoking cessation, is a stratified analysis conditional on having initiated smoking. In both cases, we find little effect of collider bias on the primary association results, but this may propagate into more substantial effects on further analyses such as polygenic risk scoring and Mendelian randomisation.