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978-3-8439-1781-0, Reihe Statistik
Regularization in Discrete Survival Models
173 Seiten, Dissertation Ludwig-Maximilians-Universität München (2014), Softcover, A5
In the framework of analyzing failure time or time to event data, time is often considered to be continuously observed. However, in many studies it is only known that the event occurs between a pair of consecutive follow-ups or time is truly discrete. Hence, these ties cause problems when likelihood methods for continuous-time models are used. To account for the issue of tied observations, in this thesis discrete-time survival models are considered. After a restructuring of the typical form of time-to-event data, survival models for discrete duration time can be understood as generalized linear models. This complex data restructuring process results in a large number of observations that are only rarely observed, especially when there are many time periods. This data situation becomes even more difficult when time-varying covariate effects are incorporated. Ordinary Maximum-Likelihood methods cannot be applied as the ML-estimates are deteriorated or even do not exist. To obtain stable and reliable estimates, the application of regularization methods is necessary. Thereby, this thesis focuses on penalization methods.
It is of great interest to incorporate time-varying covariate effects in survival models. To regularize discrete survival regression models, different penalty terms that cope with this special case are proposed. For example, these penalty terms allow for smooth time-varying coefficients or provide a variable selection. The latter means that covariates can be completely removed from the model. The strength of penalization is steered by tuning parameters. In this thesis, it is systematically investigated, how these tuning parameters have to be chosen.
The underlying data in survival models deal with repeated measurements leading to certain heterogeneity in the data. To control for unobserved heterogeneity, frailty models are considered and a corresponding penalty term is introduced. That is, the described penalization methods are combined with the incorporation of frailty effects.
In many applications concerning survival analysis, the investigation of k, that is greater than one, terminating events (competing risks) is of interest. Discrete competing risks models can be embedded into the framework of multinomial regression models. To provide variable selection and to account for the large amount of parameters that arise with the use of this model type, a penalization technique for discrete-time competing risks models is introduced.