Fast autoregressive model for multivariate dependent outcomes with application to lipidomics analysis for Alzheimer’s disease and APOE-ε4

Association analysis of multivariate omics outcomes is challenging due to the high dimensionality and inter-correlation among outcome variables. In practice, the classic multi-univariate analysis approaches are commonly employed, utilizing linear regression models for each individual outcome followed by adjustments for multiplicity through control of the false discovery rate (FDR) or family-wise error rate (FWER). While straightforward, these multi-univariate methods overlook dependencies between outcome variables. This oversight leads to less accurate statistical inferences, characterized by lower power and an increased false discovery rate, ultimately resulting in reduced replicability across studies. Recently, advanced frequentist and Bayesian methods have been developed to account for these dependencies. However, these methods often pose significant computational challenges for researchers in the field. To bridge this gap, a computationally efficient autoregressive multivariate regression model is proposed that explicitly accounts for the dependence structure among outcome variables. Through extensive simulations, it is demonstrated that the approach provides more accurate multivariate inferences than traditional methods and remains robust even under model misspecification. Additionally, the proposed method is applied to investigate whether the associations between serum lipidomics outcomes and Alzheimer’s disease differentiate in $\epsilon 4$ allele carriers and non-carriers of the apolipoprotein E (APOE) gene.