# Mendelian Randomization With Longitudinal Exposure Data: Simulation Study and Real Data Application

## TL;DR

This paper introduces a new method for Mendelian randomization using longitudinal data to study time-varying causal effects of exposures.

## Contribution

A novel approach to analyze mean, slope, and variability of time-varying exposures in a multivariable MR framework.

## Key findings

- High power was observed for detecting causal effects of the mean and slope in simulations.
- Variability effects were low powered when SNPs were shared between the mean and variability.
- Real data applications showed significant causal estimates for mean and slope but not for variability.

## Abstract

Mendelian randomization (MR) is a widely used tool to estimate causal effects using genetic variants as instrumental variables. MR is limited to cross‐sectional summary statistics of different samples and time points to analyze time‐varying effects. We aimed at using longitudinal summary statistics for an exposure in a multivariable MR setting and validating the effect estimates for the mean, slope, and within‐individual variability.

We tested our approach in 12 scenarios for power and type I error, depending on shared instruments between the mean, slope, and variability, and regression model specifications. We observed high power to detect causal effects of the mean and slope throughout the simulation, but the variability effect was low powered in the case of shared SNPs between the mean and variability. Mis‐specified regression models led to lower power and increased the type I error.

We applied our approach to two real data sets (POPS, UK Biobank). We detected significant causal estimates for both the mean and the slope in both cases, but no independent effect of the variability. However, we only had weak instruments in both data sets.

We used a new approach to test a time‐varying exposure for causal effects of the exposure's mean, slope and variability. The simulation with strong instruments seems promising but also highlights three crucial points: (1) The difficulty to define the correct exposure regression model, (2) the dependency on the genetic correlation, and (3) the lack of strong instruments in real data. Taken together, this demands a cautious evaluation of the results, accounting for known biology and the trajectory of the exposure.