Statistical methods for frailty models: studies on old-age mortality and recurrent events

Böhnstedt, M.
VIII, 195 pages. Leiden, Leiden University (2021)


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 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.

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