Two sample Mendelian Randomisation using an outcome from a multilevel model of disease progression.

Identifying factors that are causes of disease progression, especially in neurodegenerative diseases, is of considerable interest. Disease progression can be described as a trajectory of outcome over time-for example, a linear trajectory having both an intercept (severity at time zero) and a slope (rate of change). A technique for identifying causal relationships between one exposure and one outcome in observational data whilst avoiding bias due to confounding is two sample Mendelian Randomisation (2SMR). We consider a multivariate approach to 2SMR using a multilevel model for disease progression to estimate the causal effect an exposure has on the intercept and slope. We carry out a simulation study comparing a naïve univariate 2SMR approach to a multivariate 2SMR approach with one exposure that effects both the intercept and slope of an outcome that changes linearly with time since diagnosis. The simulation study results, across six different scenarios, for both approaches were similar with no evidence against a non-zero bias and appropriate coverage of the 95% confidence intervals (for intercept 93.4-96.2% and the slope 94.5-96.0%). The multivariate approach gives a better joint coverage of both the intercept and slope effects. We also apply our method to two Parkinson's cohorts to examine the effect body mass index has on disease progression. There was no strong evidence that BMI affects disease progression, however the confidence intervals for both intercept and slope were wide.