Analysis of incomplete event history data

Abstract

Event history data rise in studies where a collection of individuals, each experience certain events or moving among a finite number of states, is followed over a period of time. The data consist of the number, time, type and sequence of events experienced by individuals, although the data are often incompletely observed. One example of such data comes from classical survival analysis, where individuals move from one state to the other, such as rom alive to dead, or from healthy to diseased. The general event history data may contain information on events of multiple types or repeated occurrences of the same event (recurrent events).

The purpose of this thesis is to present methods using piecewise constant rate, intensity or hazard functions for event history data when events are interval-censored. These methods do not rely too heavily on parametric assumptions, and they are easier to implement than the nonparametric methods. In particular, we discuss the methods using piecewise constant rate, intensity or hazard functions for two types of event history data; one is interval-grouped recurrent events, the other is current status data and doubly-censored data.

Interval-grouped recurrent event data arise in longitudinal studies where subjects repeatedly experience a specific event and the events are observed only in the form of counts for intervals which can vary across subjects. We present two approaches for estimating the mean and rate functions of the recurrent event processes. One is mixed Poisson process estimation. Another is a robust method that requires only specification of the mean structure and covariance structure among recurrent event counts. Piecewise constant rate functions are incorporated in both approaches. The two approaches are compared in a simulation study and in an example involving superficial bladder tumors in humans.

In many studies, interest focuses on the time between two successive events, the initiating event and the subsequent event. Current status data arise when the time of the initiating event is observed, but the only information for the subsequent event is whether it has occurred sometime between the initiating event and a single subsequent monitoring time. Doubly-censored data refer to data where both events are not observed directly, but are both interval-censored, or the initiating event is interval-censored and the subsequent event is right censored. We discuss methods with piecewise constant parametrization to estimate the survival function of the time between the two events for current status data and doubly-censored data. Different regression models are also developed. Simulation results show that our methods are robust to model misspecification. These methods are also applied to a data set from an AIDS study.

Finally, we explore the issue of getting smoother estimates of intensity, rate or hazard functions. A penalized likelihood approach is applied to the piecewise constant models. It is shown in a simulation study that this approach provides satisfactory estimates of the intensity, rate or hazard functions when events are interval-censored.