Mendelian randomization analysis of a time-varying exposure for binary disease outcomes using functional data analysis methods.

A Mendelian randomization (MR) analysis is performed to analyze the causal effect of an exposure variable on a disease outcome in observational studies, by using genetic variants that affect the disease outcome only through the exposure variable. This method has recently gained popularity among epidemiologists given the success of genetic association studies. Many exposure variables of interest in epidemiological studies are time varying, for example, body mass index (BMI). Although longitudinal data have been collected in many cohort studies, current MR studies only use one measurement of a time-varying exposure variable, which cannot adequately capture the long-term time-varying information. We propose using the functional principal component analysis method to recover the underlying individual trajectory of the time-varying exposure from the sparsely and irregularly observed longitudinal data, and then conduct MR analysis using the recovered curves. We further propose two MR analysis methods. The first assumes a cumulative effect of the time-varying exposure variable on the disease risk, while the second assumes a time-varying genetic effect and employs functional regression models. We focus on statistical testing for a causal effect. Our simulation studies mimicking the real data show that the proposed functional data analysis based methods incorporating longitudinal data have substantial power gains compared to standard MR analysis using only one measurement. We used the Framingham Heart Study data to demonstrate the promising performance of the new methods as well as inconsistent results produced by the standard MR analysis that relies on a single measurement of the exposure at some arbitrary time point.