A7: Essays on inference in multi-state models

PhD student: Holger Reulen
Thesis Committee: Prof. Thomas Kneib, Prof. Tatyana Krivobokova, Prof. Helmut Herwartz
Graduation Date: 3/2015

Competing risk and multi-state models play an increasingly important role in the analysis of time to event data. Competing risk models generalize the analysis of time to a single event (duration analysis) to analyze the timing of distinct terminal events. Multi-state models extend competing risk models to the analysis of what happens beyond some first event, by allowing individuals to progress through different states in continuous time.
Examples are disease progression and changes in marital status or labor force participation over the life-course.
Multi-state models are described by a continuous time state multi-state process. The most general setting is a process with irreducible state space where all states are mutually accessible.

Two exemplary scaling problems in the analysis of multi state models are:
(1) For estimation of multi-state models, the transition probabilities and their underlying covariate mechanism, observation of complete event-histories in the categorical scaled state space on a continuous time scale is ideal. However in many situations, e.g. courses of diseases, the status of subjects is observed only at a finite number of visits on a discrete time scale. This leads to interval-censored observations of transition times.
(2) Modeling progressive K state multi state processes can be performed using a combined modeling of K-1 single event processes by a common likelihood, however without using the full information given by the ordinal scale of the state space.

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