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Parametric survival densities from phase-type models

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Abstract

After a brief historical survey of parametric survival models, from actuarial, biomedical, demographical and engineering sources, this paper discusses the persistent reasons why parametric models still play an important role in exploratory statistical research. The phase-type models are advanced as a flexible family of latent-class models with interpretable components. These models are now supported by computational statistical methods that make numerical calculation of likelihoods and statistical estimation of parameters feasible in theory for quite complicated settings. However, consideration of Fisher Information and likelihood-ratio type tests to discriminate between model families indicates that only the simplest phase-type model topologies can be stably estimated in practice, even on rather large datasets. An example of a parametric model with features of mixtures, multiple stages or ‘hits’, and a trapping-state is given to illustrate simple computational tools in R, both on simulated data and on a large SEER 1992–2002 breast-cancer dataset.

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Acknowledgments

We are grateful to Drs. Philip Rosenberg and William Anderson for an introduction to the breast cancer dataset and research questions of Anderson et al. (2006), and for their encouragement on this project.

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Authors and Affiliations

  1. Census Bureau CSRM, Washington, DC, USA

    Eric V. Slud

  2. University of Maryland, College park, MD, USA

    Eric V. Slud

  3. Chulalongkorn University, Bangkok, Thailand

    Jiraphan Suntornchost

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  1. Eric V. Slud
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  2. Jiraphan Suntornchost
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Correspondence to Jiraphan Suntornchost.

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Disclaimer This paper describes research of its authors, and is released to inform interested parties and encourage discussion. Results and conclusions are the authors’ and have not been endorsed by the Census Bureau.

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Slud, E.V., Suntornchost, J. Parametric survival densities from phase-type models. Lifetime Data Anal 20, 459–480 (2014). https://doi.org/10.1007/s10985-013-9278-0

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