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Abstract:
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Modern biomedical and epidemiological studies often measure a large number of biomarkers such as gene expression and metabolite levels. These biomarkers may be mediators, explaining the relationship between an exposure and an outcome. Standard methods in mediation analysis and causal inference are available for evaluating whether a single variable is a mediator. However, few methods are available to simultaneously assess the impact of multiple mediators. Here we propose to jointly model a biological pathway between an exposure, latent mediators affecting multiple biomarkers, called 'factors', and an outcome. To ensure that latent factors influence only a small set of biomarkers, we incorporate L1- penalties to induce sparsity when fitting this joint model. We extend existing E-M algorithms for factor analysis to incorporate penalty functions and the joint relationship between the exposure, factors, and outcome. Our proposed methodology can accommodate continuous and categorical outcomes, and for binary outcomes we also assess retrospective sampling. We evaluate the performance of this methodology in small samples through simulations.
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