Statistical Methods for Joint Modeling of Disease Processes under Intermittent Observation

Abstract

In studies of life history data, individuals often experience multiple events of interest that may be associated with one another. In such settings, joint models of event processes are essential for valid inferences. Data used for statistical inference are typically obtained through various sources, including observational data from registries or clinics and administrative records. These observation processes frequently result in incomplete histories of the event processes of interest. In settings where interest lies in the development of conditions or complications that are not self-evident, data become available only at periodic clinic visits. This thesis focuses on developing statistical methods for the joint analysis of disease processes involving incomplete data due to intermittent observation. Many disease processes involve recurrent adverse events and an event which terminates the process. Death, for example, terminates the event process of interest and precludes the occurrence of further events. In Chapter 2, we present a joint model for such processes which has appealing properties due to its construction using copula functions. Covariates have a multiplicative effect on the recurrent event intensity function given a random effect, which is in turn associated with the failure time through a copula function. This permits dependence modeling while retaining a marginal Cox model for the terminal event process. When these processes are subject to right-censoring, simultaneous and two-stage estimation strategies are developed based on the observed data likelihood, which can be implemented by direct maximization or via an expectation-maximization algorithm - the latter facilitates semi-parametric modeling for the terminal event process. Variance estimates are derived based on the missing information principle. Simulation studies demonstrate good finite sample performance of proposed methods and high efficiency of the two-stage procedure. An application to a study of effect of pamidronate on reducing skeletal complications in patient with skeletal metastases illustrates the use of this model. Interval-censored recurrent event data can occur when the events of interest are only evident through intermittent clinical examination. Chapter 3 addresses such scenarios and extends the copula-based joint model for recurrent and terminal events proposed in Chapter 2 to accommodate interval-censored recurrent event data resulting from intermittent observation. Conditional on a random effect, the intensity for the recurrent event process has a multiplicative form with a weak parametric piecewise constant baseline rate, and a Cox model is formulated for the terminal event process. The two processes are then linked via a copula function, which defines a joint model for the random effect and the terminal event. The observed data likelihood can be maximized directly or via an EM algorithm; the latter facilitates a semi-parametric terminal event process. A computationally convenient two-stage estimation procedure is also investigated. Variance estimates are derived and validated by simulation studies. We apply this method to investigate the association between a biomarker (HLA-B27) and joint damage in patients with psoriatic arthritis. Databases of electronic medical records offer an unprecedented opportunity to study chronic disease processes. In survival analysis, interest may lie in studying the effects of time-dependent biomarkers on a failure time through Cox regression models. Often however, it is too labour intensive to collect and clean data on all covariates at all times, and in such settings it is common to select a single clinic visit at which variables are measured. In Chapter 4, we consider several cost-effective ad hoc strategies for inference, consisting of: 1) selecting either the last or the first visit for a measurement of the marker value, and 2) using the measured value with or without left-truncation. The asymptotic bias of estimators based on these strategies arising from misspecified Cox models is investigated via a multistate model constructed for the joint modeling of the marker and failure processes. An alternative selection method for efficient selection of individuals is discussed under budgetary constraint, and the corresponding observed data likelihood is derived. The asymptotic relative efficiency of regression coefficients obtained from Fisher information is explored and an optimal design is provided under this selection scheme.