Some Statistical Methods for Causal Mediation Pathway Analysis

Abstract

Mediation analysis has been undertaken pervasively in practice. The primary goal of this analysis is to study whether the effect of an exposure on an outcome of interest is mediated by some intermediate factors such as epigenetic variants and metabolomic biomarkers. In this dissertation I develop new statistical methods to address some of statistical and scientific challenges arising from causal mediation pathway analyses.

Chapter II develops a simultaneous likelihood ratio (LR) test in the presence of multiple mediators. Statistical inference on the joint mediation effect is challenging due to the involvement of composite null hypotheses with a large number of parameter configurations. With an application of the Lagrange Multiplier approach, simultaneous LR test utilizes a block coordinate descent algorithm to solve the constrained likelihood under the irregular null parameter space. I establish the asymptotic null distribution and examine the finite-sample performance of the proposed joint test statistic via extensive simulations with comparisons to existing tests. The simulation results show that the joint testing method controls type I error properly and in general provides better power than existing tests. I apply this new method to investigate whether a group of glucose metabolites and acetylamino acids mediate the effect of nutrient intakes on insulin resistance.

Chapter III presents a unified framework of generalized structural equation models (GSEMs) for mediation analyses with data of mixed types to address practical needs in the analysis of biomedical data. This new class of models accommodates continuous, categorical, count variables. Using the Frechet's construction of multivariate distributions, I formulate GSEM as a hierarchical model consisting of (i) a Gaussian copula dependence model to characterize a directed acyclic graph (DAG) relationship among outcome variable, mediator and exposure variable, and (ii) generalized linear models (GLMs) to adjust confounding factors in marginal distributions. This new framework provides valid joint probability distributions and well-defined mediation effects for interpretation. I develop a pseudo-maximum likelihood estimation for various scenarios of mixed data types. I illustrate this new methodology via a dataset collected from a cohort study in environmental health sciences, where I study whether the tempo of reaching infancy BMI peak, an important early life growth milestone that may be measured as either a continuous variable or a binary variable (delay or not), may mediate the association between prenatal exposure to phthalates and pubertal health outcomes.

Chapter IV concerns a conceptual framework of generalized direct and indirect effects to relax the current definitions of causal mediation effects in the presence of categorical intervention or categorical exposure. I utilize the latent variable presentation to describe the role of a categorical “action” in a causal study. Specially, I focus on two important types of models, namely the effective dose model and the latent exposure model. I demonstrate that the proposed generalized direct and indirect effects are more desirable to quantify and interpret direct and indirect effects than the conventional approach. I develop maximum likelihood estimation for the model parameters, and examine numerically the performance of the estimation via simulation studies. Also, I illustrate this new causal mediation paradigm via a randomized trial from the ELEMENT study where I investigate whether the association of mother's calcium supplementation on offspring birth weight is mediated by mother's blood lead level measured during the third trimester.