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Frailty Models and Heterogeneity

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Modeling Discrete Time-to-Event Data

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Abstract

The regression modeling techniques considered in the previous chapters are based on the assumption that all relevant covariates are known and included in the analysis set. In practice, however, typically only a limited number of potentially influential variables are known, and it often happens that part of the heterogeneity in the population remains unobserved. In survival modeling, this “unobserved heterogeneity,” when ignored, may cause severe artifacts. This chapter presents various approaches to account for unobserved heterogeneity in discrete time-to-event models. We first consider the discrete hazard frailty model, which incorporates random intercept terms to account for subject-specific variations caused by unobserved covariate information (Sects. 9.1 and 9.2). In Sect. 9.3 discrete hazard frailty models are extended to the case where covariate effects are allowed to be smooth and nonlinear. The model class that is considered is the discrete additive hazard frailty model. Because model misspecification is a critical issue in random-effects models, Sect. 9.4 presents data-driven strategies for variable selection in discrete hazard frailty models. Alternative approaches to incorporate unobserved heterogeneity in discrete time-to-event models are presented in Sects. 9.5 and 9.6, which deal with penalized fixed-effects and finite mixture modeling, respectively. Finally, the connection between discrete hazard frailty models and sequential models in item response theory is investigated (Sect. 9.7).

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Authors and Affiliations

  1. LMU Munich, Munich, Germany

    Gerhard Tutz

  2. University of Bonn, Bonn, Germany

    Matthias Schmid

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  1. Gerhard Tutz
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  2. Matthias Schmid
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Tutz, G., Schmid, M. (2016). Frailty Models and Heterogeneity. In: Modeling Discrete Time-to-Event Data. Springer Series in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-28158-2_9

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