title: Frailty Models for the Analysis of Recurrent Event Data in Studies of Chronic Diseases
Creators: name: Tawiah, Richard
Publisher: name: Griffith University
Year: 2019
Subjects: subject: Frailty models
subject: Chronic disease
subject: Multilevel structures
subject: Cure fraction
subject: Dependent censoring

description: Biomedical studies of chronic diseases often involve the observations of multiple failure times related to recurrent clinical events. Examples include, sequence of epileptic seizures in neurology studies, repeated attacks of myocardial infarctions in cardiovascular studies and multiple regional or metastatic recurrences in oncology studies. It is usually plausible to assume that the multiple failure times on the same individual are correlated (termed as intra-subject correlation). However, sometimes data from such event history studies are further characterised by multilevel structure (due to subjects nested within clusters by, for example, multi-institutional study design), cure fraction and a dependent censoring mechanism such as death. To model the intra-subject correlation explicitly, frailty (random e_ect) models are often considered. Nevertheless, in the presence of multilevel structure, cure fraction and dependent censoring, inferences considered in frailty models can be invalid, as they do not allow for the existence of these features. This thesis aims to consider multilevel structure, cure fraction and dependent censoring within frailty models and develop more general frailty-type models and inferential methodologies for estimation of model parameters and prediction of random effects. In the first study of the thesis, a multilevel frailty model is proposed to provide regression analysis of multilevel clustered recurrent event data from multi-institutional (multi-centre) clinical trials. With the use of random effects with unobservable and observable covariate design matrices, the proposed model extends the standard proportional hazards Cox model to incorporate subject effect and institutional effects, the later which is separately specified as institutional baseline risk heterogeneity and treatment-by-institution interaction. The attractive feature of the model is that the inherent intra-subject correlation is modelled by a multivariate random effect with a covariance structure driven by a first order autoregressive (AR(1)) process, thus providing a more general multilevel survival model that allows the frailties at subject-level to be time-varying. The model is formulated through the generalised linear mixed model methodology, with estimation facilitated by maximum likelihood and residual maximum likelihood techniques. Simulation studies are carried out to evaluate the performance of the maximum likelihood and the residual maximum likelihood estimators and to assess the impact of misspecifying random effects distribution on the proposed inference. Data sets from multi-institutionalised studies of rhDNase and recurrent urinary tract infections (UTI) are analysed for illustration of the model. With the second study, the concept of cure fraction is considered in the presence of uncured subjects who can experience the event of interest repeatedly over time. Two new models are developed within the framework of mixture cure models, by assuming a multivariate time-varying frailty with an AR(1) correlation structure for each uncured patient and addressing multilevel recurrent event data accrued from multi-institutional clinical trials, using extra random effect terms to adjust for main institution effect and treatment-by-institution interaction. To solve the difficulties in parameter estimation due to these highly complex correlation structures, an efficient estimation procedure is developed via the expectation-maximisation (EM) algorithm based on residual maximum likelihood through the generalised linear mixed model methodology. Simulation studies are presented to validate the performances of the models. Data sets from a colorectal cancer study and rhDNase multi-institutional clinical trials are analysed to exemplify the proposed models. The results demonstrate a large positive AR(1) correlation among frailties across successive gap times, indicating a constant frailty may not be realistic in some situations. Comparisons of findings with existing frailty models are discussed. Thirdly, recognising the possibility of cure fraction and death induced dependent censoring mechanism in some data sets, a bivariate joint frailty mixture cure model is proposed for recurrent event data. The latency part of the model consists of two intensity functions for the hazard rates of recurrent events and death, wherein a bivariate frailty is introduced by means of the generalised linear mixed model methodology to adjust for dependent censoring. The model allows covariates and frailties in both the incidence and the latency parts and it further accounts for the possibility of cure after each recurrence. It includes the joint frailty model and other related models as special cases. An EM-type algorithm is developed to provide residual maximum likelihood estimation of model parameters. Through simulation studies, the performance of the model is investigated under different magnitudes of dependent censoring. The model is applied to data sets from two colorectal cancer studies to illustrate its practical value. In general, the simulation studies indicate that the proposed models provide appropriate estimates with only small biases. Aspects of the real data applications demonstrate that the models provide results which are of practical importance and easy to interpret and articulate in the clinical setting. Extension of the proposed models to the context of interval-censored recurrent event data is discussed extensively. Of specific interest is the consideration of cure fraction and multilevel structure in the presence of interval-censored recurrent event data. An investigation of the generalised linear mixed model methodology for estimation of semiparametric accelerated failure time frailty model is emphasised. The development of multistate frailty models for survival data from multimorbidity studies are also discussed.