Multi-state Models for Recurrent Event and Terminal Event Data

Abstract

In medical studies, we often observe serial events along disease progression. The risk of different types of events vary across each other and are usually associated. In addition, some longitudinal markers carry information from the past event history and provide feedbacks for the future events. This dynamic feedback mechanism partly explains how event times are dependent upon each other. When the biomarkers are intermittently observed and mismeasured, estimating the association between markers and events in the presence of past event feedback could be challenging. Existing approaches handling time-dependent covariates in event history analysis can be problematic because they ignore the prior event feedback through biomarkers and thus the correlation structure among events is misspecified. In Chapter 2, a novel multi-state modelling framework for the analysis of single-type recurrent event and terminal event data, taking into account the dynamic longitudinal covariates and time-dependent/fixed coefficients is proposed. This class of models is flexible in handling multiple ordered events and enables one to take into account the dependence structure among consecutive events induced by dynamic longitudinal markers. One-step backfitting estimator of the semiparametric regression coefficients are proposed to improve computation efficiency and their asymptotic properties are provided. The model is applied to two datasets: the Atherosclerosis Risk in Communities Study and the FFCD 2000-05 trial of metastatic colorectal cancer. In Chapter 3, we develop a new multi-state modelling framework for the analysis of multi-type recurrent event and terminal event data when biomarkers contain dynamic event feedback but are intermittently observed and subject to measurement errors. This modelling framework is flexible in two aspects. First, the serial nature of a succession of events can be modelled with state-specific intensity functions assuming different formulation for each state transition or the same formulation for state transitions corresponded to the same type of event, depending on the demand of practical application. Second, the proposed model is able to capture both the temporal effects and time-fixed effects of the risk factors. Estimation procedure based on polynomial splines approximation and an extension to the corrected score approach is developed. The consistency and asymptotic normality of the proposed estimators are provided. We assess the performance of the proposed procedure through comprehensive simulations and it is shown that our method outperforms the naive estimation methods. The proposed model and inference procedure is applied to a data set from the Atherosclerosis Risk in Communities Study.

Date of Award	1 Aug 2019
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Alexander Donev (Supervisor) & Jianxin Pan (Supervisor)