In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events... Show moreIn studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence parameter have been studied for cases in which individuals are observed from the start of the event processes. However, samples are often selected at a later time, which results in delayed entry so that only individuals who have not yet experienced the terminal event will be included. In joint frailty models such left truncation has effects on the frailty distribution that need to be accounted for in both the recurrence process and the terminal event process, if the two are associated. We demonstrate, in a comprehensive simulation study, the effects that not adjusting for late entry can have and derive the correctly adjusted marginal likelihood, which can be expressed as a ratio of two integrals over the frailty distribution. We extend the estimation method of Liu and Huang (Stat Med 27:2665-2683, 2008.) to include potential left truncation. Numerical integration is performed by Gaussian quadrature, the baseline intensities are specified as piecewise constant functions, potential covariates are assumed to have multiplicative effects on the intensities. We apply the method to estimate age-specific intensities of recurrent urinary tract infections and mortality in an older population. Show less
This thesis develops and investigates statistical methods for two frailty models in the analysis of time-to-event data.The first part of the thesis deals with the statistical assessment of the... Show moreThis thesis develops and investigates statistical methods for two frailty models in the analysis of time-to-event data.The first part of the thesis deals with the statistical assessment of the slowing down of human death rates at advanced ages. Such mortality deceleration can be described through the gamma-Gompertz model as an effect of selection in heterogeneous populations. As the frailty variance of this proportional hazards frailty model may lie on the boundary of the parameter space, statistical techniques have to be adjusted to this non-standard condition. Chapter 2 presents the asymptotic properties of likelihood inference in this model. In Chapter 3, aspects of study design are discussed, such as the information loss if samples are restricted to cover only survivors beyond some high age. Chapter 4 introduces focused model selection as a new approach to assessing mortality deceleration.The second part of the thesis is concerned with inference in a joint frailty model for recurrent events and a terminal event in two different observational settings. Chapter 5 considers the situation of intermittent observation of the recurrence process, such that only interval counts of recurrent events are available. Chapter 6 examines the situation of delayed entry, in which individuals can only be included in the recurrent event study if they have not yet experienced the terminal event. Show less
