Abstract
Correlated survival times may be modelled by introducing a random effect, or frailty component, into the hazard function. For multivariate survival data we extend a non-PH model, the generalized time-dependent logistic (GTDL) survival model (MacKenzie, J R Stat Soc 45:21–34, 1996; MacKenzie, Stat Med 16:1831–1843, 1997), to include random effects. The extension leads to two different, but related, non-PH models according to the method of incorporating the random effects in the hazard function. The h-likelihood procedures of Ha et al. (Biometrika 88:233–243, 2001) and Ha and Lee (J Comput Graph Stat 12:663–681, 2003), which obviate the need for marginalization (over the random effect distribution) are derived for these extended models and their properties discussed. The new models are used to analyze two practical examples in the survival literature and the results are compared with those obtained from fitting PH and PH frailty models.
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Acknowledgements
The work in this paper was supported by the Science Foundation Ireland’s (SFI, www.sfi.ie) project grant number 07/MI/012 (BIO-SI project, www3.ul.ie/bio-si) and by KOSEF, Daejeon, South Korea.
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MacKenzie, G., Ha, I. (2014). Multivariate Survival Models Based on the GTDL. In: MacKenzie, G., Peng, D. (eds) Statistical Modelling in Biostatistics and Bioinformatics. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-04579-5_3
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DOI: https://doi.org/10.1007/978-3-319-04579-5_3
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