Abstract
Multivariable Mendelian randomization allows simultaneous estimation of direct causal effects of multiple exposure variables on an outcome. When the exposure variables of interest are quantitative omic features, obtaining complete data can be economically and technically challenging: the measurement cost is high, and the measurement devices may have inherent detection limits. In this paper, we propose a valid and efficient method to handle unmeasured and undetectable values of the exposure variables in a one-sample multivariable Mendelian randomization analysis with individual-level data. We estimate the direct causal effects with maximum likelihood estimation and develop an expectation-maximization algorithm to compute the estimators. We show the advantages of the proposed method through simulation studies and provide an application to the Hispanic Community Health Study/Study of Latinos, which has a large amount of unmeasured exposure data.