Joint analysis of a quantile of longitudinal outcomes and multiple time to events with censoring

Lu, Xiaoming (2020) Joint analysis of a quantile of longitudinal outcomes and multiple time to events with censoring. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

It is very common in health science studies that we observe both longitudinal and survival data, within which different types of data are correlated and need to be analysed together to draw accurate conclusions. In this thesis, we propose a new method to jointly analyse observations of a longitudinal outcome and occurring times for multiple right- and interval-censored events to capture the underlying effects between them. In order to have a more complete view, we apply the quantile regression techniques to measure the effects of covariates on the longitudinal observations and then the effects of longitudinal observations on the occurring times of events at different levels of quantile. Semi-parametric proportional hazards models are proposed for both right and interval-censored events with a vector of possible time-varying covariates shared with the quantile regression model for the longitudinal outcome. We also assume a variable of random effects in the survival models to measure the dependence between different events. We develop a Monte Carlo Expectation Maximization (MCEM) algorithm for computing non-parametric maximum likelihood estimators of parameters. Our estimators are proved to be consistent and asymptotically normally distributed. Furthermore, our proposed joint model is illustrated through a series of extensive simulation studies and an application to a data set from a French cohort study, PAQUID, aiming at studying the cognitive decline, such as the disease of dementia, among the elderly.

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