Estimating Causal Effects on a Disease Progression Trait Using Bivariate Mendelian Randomisation

Genome-wide association studies (GWAS) have provided large numbers of genetic markers that can be used as instrumental variables in a Mendelian Randomisation (MR) analysis to assess the causal effect of a risk factor on an outcome. An extension of MR analysis, multivariable MR, has been proposed to handle multiple risk factors. However, adjusting or stratifying the outcome on a variable that is associated with it may induce collider bias. For an outcome that represents progression of a disease, conditioning by selecting only the cases may cause a biased MR estimation of the causal effect of the risk factor of interest on the progression outcome. Recently, we developed instrument effect regression and corrected weighted least squares (CWLS) to adjust for collider bias in observational associations. In this paper, we highlight the importance of adjusting for collider bias in MR with a risk factor of interest and disease progression as the outcome. A generalised version of the instrument effect regression and CWLS adjustment is proposed based on a multivariable MR model. We highlight the assumptions required for this approach and demonstrate its utility for bias reduction. We give an illustrative application to the effect of smoking initiation and smoking cessation on Crohn's disease prognosis, finding no evidence to support a causal effect.