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parfm: Parametric Frailty Models in R

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  • Munda, Marco
  • Rotolo, Federico
  • Legrand, Catherine

Abstract

Frailty models are getting more and more popular to account for overdispersion and/or clustering in survival data. When the form of the baseline hazard is somehow known in advance, the parametric estimation approach can be used advantageously. Nonetheless, there is no unified widely available software that deals with the parametric frailty model. The new parfm package remedies that lack by providing a wide range of parametric frailty models in R. The gamma, inverse Gaussian, and positive stable frailty distributions can be specified, together with five different baseline hazards. Parameter estimation is done by maximising the marginal log-likelihood, with right-censored and possibly left-truncated data. In the multivariate setting, the inverse Gaussian may encounter numerical difficulties with a huge number of events in at least one cluster. The positive stable model shows analogous difficulties but an ad-hoc solution is implemented, whereas the gamma model is very resistant due to the simplicity of its Laplace transform.

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  • Munda, Marco & Rotolo, Federico & Legrand, Catherine, 2012. "parfm: Parametric Frailty Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i11).
    • Handle: RePEc:jss:jstsof:v:051:i11
    DOI: http://hdl.handle.net/10.18637/jss.v051.i11
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    References listed on IDEAS

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    1. Duchateau, Luc & Janssen, Paul & Lindsey, Patrick & Legrand, Catherine & Nguti, Rosemary & Sylvester, Richard, 2002. "The shared frailty model and the power for heterogeneity tests in multicenter trials," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 603-620, September.
    2. Munda, Marco & Rotolo, Federico & Legrand, Catherine, 2012. "parfm: Parametric Frailty Models in R," LIDAM Discussion Papers ISBA 2012005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Abrahantes, Jose Cortinas & Legrand, Catherine & Burzykowski, Tomasz & Janssen, Paul & Ducrocq, Vincent & Duchateau, Luc, 2007. "Comparison of different estimation procedures for proportional hazards model with random effects," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3913-3930, May.
    4. Gerda Claeskens & Rosemary Nguti & Paul Janssen, 2008. "One-sided tests in shared frailty models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 69-82, May.
    5. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    Cited by:

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    2. Bodunrin Brown & Bin Liu & Stuart McIntyre & Matthew Revie, 2023. "Reliability evaluation of repairable systems considering component heterogeneity using frailty model," Journal of Risk and Reliability, , vol. 237(4), pages 654-670, August.
    3. Harttgen, Kenneth & Lang, Stefan & Seiler, Johannes, 2019. "Selective mortality and the anthropometric status of children in low- and middle-income countries," Economics & Human Biology, Elsevier, vol. 34(C), pages 257-273.
    4. Giuliana Cortese & Nicola Sartori, 2016. "Integrated likelihoods in parametric survival models for highly clustered censored data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 382-404, July.
    5. Wagner Barreto-Souza & Vinícius Diniz Mayrink, 2019. "Semiparametric generalized exponential frailty model for clustered survival data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 679-701, June.
    6. Sujatro Chakladar & Samuel Rosin & Michael G. Hudgens & M. Elizabeth Halloran & John D. Clemens & Mohammad Ali & Michael E. Emch, 2022. "Inverse probability weighted estimators of vaccine effects accommodating partial interference and censoring," Biometrics, The International Biometric Society, vol. 78(2), pages 777-788, June.
    7. Munda, Marco & Rotolo, Federico & Legrand, Catherine, 2012. "parfm: Parametric Frailty Models in R," LIDAM Discussion Papers ISBA 2012005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Niels Keiding & Katrine Lykke Albertsen & Helene Charlotte Rytgaard & Anne Lyngholm Sørensen, 2019. "Prevalent cohort studies and unobserved heterogeneity," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 712-738, October.
    9. Kenneth Harttgen & Stefan Lang & Johannes Seiler, 2017. "Selective mortality and undernutrition in low- and middle-income countries," Working Papers 2017-27, Faculty of Economics and Statistics, Universität Innsbruck, revised Aug 2018.

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