Cox's Proportional Hazards Model is extended to encompass latent class variables as predictors of time to event in the parametric part of the semi-parametric model.
Information about the latent class variable is available indirectly via a number of items (answers to questions in a questionnaire), which are assumed to be conditionally independent given the latent class variable. The items are assumed to be ordered and categorical.
The joint distribution of the items and the survival time is modeled, and the EM algorithm is used to obtain maximum likelihood estimates. When doing so, the latent class variable is treated as missing data, and the items and survival information are treated as observed data.
Results from analyses on data from the Women's Health and Aging Study (Johns Hopkins, NIA) are presented and used to illustrate the applicability of the model, and different methods for model checking are illustrated by using this data.
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