Characterization of direct and/or indirect genetic associations for multiple traits in longitudinal studies of disease progression

Abstract

When quantitative longitudinal traits are risk factors for disease progression, endogenous, and/or subject to random errors, joint model specification of multiple time-to-event and multiple longitudinal traits can effectively identify direct and/or indirect genetic association of single nucleotide polymorphisms (SNPs) with time-to-event traits. Here, we present a joint model that integrates: i) a linear mixed model describing the trajectory of each longitudinal trait as a function of time, SNP effects and subject-specific random effects, and ii) a frailty Cox survival model that depends on SNPs, longitudinal trajectory effects, and a subject-specific frailty term accounting for unexplained dependency between time-to-event traits. Inference is based on a two-stage approach with bootstrap joint covariance estimation. We develop a hypothesis testing procedure to identify direct and/or indirect SNP association with each time-to-event trait. Motivated by complex genetic architecture of type 1 diabetes complications (T1DC) observed in the Diabetes Control and Complications Trial (DCCT), we show by realistic simulation study that joint modelling of two time-to-T1DC (retinopathy, nephropathy) and two longitudinal risk factors (HbA1c, systolic blood pressure) reduces bias and improves identification of direct and/or indirect SNP associations, compared to alternative methods ignoring measurement errors in intermediate risk factors. Through analysis of DCCT, we identify two SNPs with indirect associations with multiple time-to-T1DC traits and obtain similar conclusions using alternative formulations of time-dependent HbA1c effects on T1DC. In total, joint analysis of multiple longitudinal and multiple time-to-event traits provides insight into etiology of complex traits.