1.Joint Models of Multi-Outcome Data under Mean Residual Model

In many clinical trials, multiple outcomes can be observed simultaneously and measured on the same subject, e.g., longitudinal biomarkers and terminal events (e.g., death). A great deal of literature has been established on joint analysis or modeling of failure time data and longitudinal data. However, most of the existing methods focus on the hazard-based models, while there is a lack of mean residual life (MRL)-based analysis. We have made several contributions in extending joint modeling to MRL framework.

MRL is a very useful and commonly used tool in many areas, including demographical studies, life insurance, medical studies, and reliability experiments. Unlike hazard function, it measures the remaining life expectancy of a subject who has survived until time t. In Alzheimer’s disease (AD) studies, there exists a correlation between longitudinal outcome AD assessment scale score 13 (ADAS13) and AD conversion time: patients with higher ADAS13 scores had a higher hazard of AD conversion rate rates as well as shorter expectancy time between stage mild cognitive impairment (MCI) to AD conversion. Ignoring such correlation could lead to biased estimates. We developed a shared frailty (random effects) model to jointly analyze survival when longitudinal outcomes are assumed to follow a linear mixed model and failure time of interest is assumed to follow a proportional mean residual life model [Reference #2 in my CV]. By applying the proposed method to Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset, we found that the baseline Functional Assessment Questionnaire (FAQ) in functional domain, middle temporal gyrus from neuroimaging domain, and Rey’s Auditory Verbal Learning Test (RAVLT) in cognitive domain had significant impact on expectancy time between stage MCI to AD conversion. We also studied the relationship between longitudinal outcomes FAQ and Mini-Mental State Examination (MMSE) with an AD conversion under MRL, where longitudinal outcomes are assumed to follow a generalized linear mixed model survival. To handle complicated computational issues in these models, we proposed a quasi-likelihood procedure with the use of Laplace approximation. The simulation studies indicated that the proposed methods work well in practical situations. After applying the proposed method to ADNI dataset, we found both MMSE and FAQ are negatively correlated with expectancy time between stage MCI to AD conversion.