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The frailty mode

Luc Duchateau and Palul Janssen
11 Dec 2013-Iss: 1
About: The article was published on 2013-12-11 and is currently open access. It has received 58 citations till now. The article focuses on the topics: Mode (statistics).
Citations
More filters
Journal Article•DOI•
The analysis of multivariate longitudinal data: a review.

[...]

Geert Verbeke1, Steffen Fieuws1, Geert Molenberghs2, Geert Molenberghs1, Marie Davidian3 •
Katholieke Universiteit Leuven1, University of Hasselt2, North Carolina State University3
01 Feb 2014-Statistical Methods in Medical Research
TL;DR: This article will present a review of the many approaches proposed in the statistical literature, and four main model families will be presented, discussed and compared.
Abstract: Longitudinal experiments often involve multiple outcomes measured repeatedly within a set of study participants. While many questions can be answered by modeling the various outcomes separately, some questions can only be answered in a joint analysis of all of them. In this article, we will present a review of the many approaches proposed in the statistical literature. Four main model families will be presented, discussed and compared. Focus will be on presenting advantages and disadvantages of the different models rather than on the mathematical or computational details.

241 citations

Cites background from "The frailty mode"

  • ...Note that the same two approaches are sometimes used in the analysis of correlated time-to-event outcomes, leading to so-called shared frailty models and correlated frailty models.(41)...

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Journal Article•DOI•
parfm: Parametric Frailty Models in R

[...]

Marco Munda, Federico Rotolo, Catherine Legrand
13 Nov 2012-Journal of Statistical Software
TL;DR: The new parfm package remedies that lack by providing a wide range of parametric frailty models in R by maximising the marginal log-likelihood, with right-censored and possibly left-truncated data.
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.

145 citations

Cites background or methods from "The frailty mode"

  • ...Lots of examples of clustered survival data arise from large-scale clinical trials in which patients are recruited at several hospital centres (Duchateau, Janssen, Lindsey, Legrand, Nguti, and Sylvester 2002; Glidden and Vittinghoff 2004). Another classical example is the analysis of lifetimes of matched human organs such as eyes or kidneys. The frailty model, introduced in the biostatistical literature by Vaupel, Manton, and Stallard (1979), and discussed in details by Hougaard (2000), Duchateau and Janssen (2008), and by Wienke (2010), accounts for this heterogeneity in baseline....

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  • ...The frailty model, introduced in the biostatistical literature by Vaupel, Manton, and Stallard (1979), and discussed in details by Hougaard (2000), Duchateau and Janssen (2008), and by Wienke (2010), accounts for this heterogeneity in baseline....

    [...]

  • ...…number of subjects ni is 1 for all groups, then the univariate frailty model is obtained (Wienke 2010, Chapter 3), otherwise the model is called the shared frailty model (Hougaard 2000, Chapter 7; Duchateau and Janssen 2008) because all subjects in the same cluster share the same frailty value ui....

    [...]

  • ...If the number of subjects ni is 1 for all groups, then the univariate frailty model is obtained (Wienke 2010, Chapter 3), otherwise the model is called the shared frailty model (Hougaard 2000, Chapter 7; Duchateau and Janssen 2008) because all subjects in the same cluster share the same frailty value ui....

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  • ..., Duchateau and Janssen (2008, Example 6.4). For a deeper overview of who supports what, and for a comparison of some of the aforementioned functions, see Hirsch and Wienke (2012). Hereinbelow, we illustrate parfm (Rotolo and Munda 2012), a new R package that fits the gamma, the positive stable, the inverse Gaussian, and lognormal proportional hazards frailty models with either exponential, Weibull, inverse Weibull (Fréchet), Gompertz, lognormal, log-skewNormal, or loglogistic baseline....

    [...]

Journal Article•DOI•
Stereotactic body radiotherapy for oligo-metastatic liver disease - Influence of pre-treatment chemotherapy and histology on local tumor control.

[...]

Rainer J. Klement, M. Guckenberger1, H. Alheid, Michael Allgäuer, Gerhild Becker, Oliver Blanck, Judit Boda-Heggemann2, Thomas B. Brunner, Marciana Nona Duma3, Sabine Gerum4, Daniel Habermehl5, Guido Hildebrandt, V. Lewitzki, C. Ostheimer, Alexandros Papachristofilou6, Cordula Petersen7, Thomas Schneider, Robert Semrau, Stefan Wachter, Nicolaus Andratschke1 •
University of Zurich1, Heidelberg University2, Technische Universität München3, Ludwig Maximilian University of Munich4, University Hospital Heidelberg5, University Hospital of Basel6, University of Hamburg7
05 Mar 2017-Radiotherapy and Oncology
TL;DR: Besides dose, histology and pretreatment chemotherapy were important factors influencing local TCP in this large cohort of liver metastases, adding to the emerging evidence that breast cancer metastases do respond better to hypofractionated SBRT compared to other histologies.

78 citations

Cites background from "The frailty mode"

  • ...Because there are many different metastases subtypes, we did not include histology as a fixed effect in a Cox proportional hazards model as this could require too many parameters to be estimated, leading to a breakdown of asymptotic assumptions and possibly overestimating the effects of certain histological subtypes [4]....

    [...]

  • ...These associations are known as ‘‘frailties” or ‘‘random effects” and modeled as random variables drawn from a parametric probability distribution [4,6]....

    [...]

Journal Article•DOI•
Unobserved population heterogeneity: A review of formal relationships

[...]

James W. Vaupel, Trifon I. Missov
17 Sep 2014-Demographic Research
TL;DR: In this paper, the authors present a list of important mathematical relationships that govern populations in which individuals differ from each other in unobserved ways, and for some relationships they present proofs that, albeit formal, tend to be simple and intuitive.
Abstract: Background: Survival models accounting for unobserved heterogeneity (frailty models) play an important role in mortality research, yet there is no article that concisely summarizes useful relationships. Objective: We present a list of important mathematical relationships that govern populations in which individuals differ from each other in unobserved ways. For some relationships we present proofs that, albeit formal, tend to be simple and intuitive. Methods: We organize the article in a progression, starting with general relationships and then turning to models with stronger and stronger assumptions. Results: We start with the general case, in which we do not assume any structure of the underlying baseline hazard, the frailty distribution, or their link to one another. Then we sequentially assume, first, a relative-risk model; second, a gamma distribution for frailty; and, finally, a Gompertz and Gompertz-Makeham specification for baseline mortality. Comments: The article might serve as a handy overall reference to frailty models, especially for mortality research.

49 citations

Journal Article•DOI•
Introduction to the special issue on joint modelling techniques

[...]

Dimitris Rizopoulos1, Emmanuel Lesaffre2, Emmanuel Lesaffre1•
Erasmus University Medical Center1, Katholieke Universiteit Leuven2
01 Feb 2014-Statistical Methods in Medical Research
TL;DR: This special issue of Statistical Methods in Medical Research presents some recent developments from this field of joint modelling techniques and highlights the contents of the contributions.
Abstract: Joint modelling techniques have seen great advances in the recent years, with several types of joint models having been developed in literature that can handle a wide range of applications. This special issue of Statistical Methods in Medical Research presents some recent developments from this field. This introductory article contains some background material and highlights the contents of the contributions.

35 citations

References
More filters
Journal Article•DOI•
The analysis of multivariate longitudinal data: a review.

[...]

Geert Verbeke1, Steffen Fieuws1, Geert Molenberghs2, Geert Molenberghs1, Marie Davidian3 •
Katholieke Universiteit Leuven1, University of Hasselt2, North Carolina State University3
01 Feb 2014-Statistical Methods in Medical Research
TL;DR: This article will present a review of the many approaches proposed in the statistical literature, and four main model families will be presented, discussed and compared.
Abstract: Longitudinal experiments often involve multiple outcomes measured repeatedly within a set of study participants. While many questions can be answered by modeling the various outcomes separately, some questions can only be answered in a joint analysis of all of them. In this article, we will present a review of the many approaches proposed in the statistical literature. Four main model families will be presented, discussed and compared. Focus will be on presenting advantages and disadvantages of the different models rather than on the mathematical or computational details.

241 citations

Journal Article•DOI•
parfm: Parametric Frailty Models in R

[...]

Marco Munda, Federico Rotolo, Catherine Legrand
13 Nov 2012-Journal of Statistical Software
TL;DR: The new parfm package remedies that lack by providing a wide range of parametric frailty models in R by maximising the marginal log-likelihood, with right-censored and possibly left-truncated data.
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.

145 citations

Journal Article•DOI•
Stereotactic body radiotherapy for oligo-metastatic liver disease - Influence of pre-treatment chemotherapy and histology on local tumor control.

[...]

Rainer J. Klement, M. Guckenberger1, H. Alheid, Michael Allgäuer, Gerhild Becker, Oliver Blanck, Judit Boda-Heggemann2, Thomas B. Brunner, Marciana Nona Duma3, Sabine Gerum4, Daniel Habermehl5, Guido Hildebrandt, V. Lewitzki, C. Ostheimer, Alexandros Papachristofilou6, Cordula Petersen7, Thomas Schneider, Robert Semrau, Stefan Wachter, Nicolaus Andratschke1 •
University of Zurich1, Heidelberg University2, Technische Universität München3, Ludwig Maximilian University of Munich4, University Hospital Heidelberg5, University Hospital of Basel6, University of Hamburg7
05 Mar 2017-Radiotherapy and Oncology
TL;DR: Besides dose, histology and pretreatment chemotherapy were important factors influencing local TCP in this large cohort of liver metastases, adding to the emerging evidence that breast cancer metastases do respond better to hypofractionated SBRT compared to other histologies.

78 citations

Journal Article•DOI•
Unobserved population heterogeneity: A review of formal relationships

[...]

James W. Vaupel, Trifon I. Missov
17 Sep 2014-Demographic Research
TL;DR: In this paper, the authors present a list of important mathematical relationships that govern populations in which individuals differ from each other in unobserved ways, and for some relationships they present proofs that, albeit formal, tend to be simple and intuitive.
Abstract: Background: Survival models accounting for unobserved heterogeneity (frailty models) play an important role in mortality research, yet there is no article that concisely summarizes useful relationships. Objective: We present a list of important mathematical relationships that govern populations in which individuals differ from each other in unobserved ways. For some relationships we present proofs that, albeit formal, tend to be simple and intuitive. Methods: We organize the article in a progression, starting with general relationships and then turning to models with stronger and stronger assumptions. Results: We start with the general case, in which we do not assume any structure of the underlying baseline hazard, the frailty distribution, or their link to one another. Then we sequentially assume, first, a relative-risk model; second, a gamma distribution for frailty; and, finally, a Gompertz and Gompertz-Makeham specification for baseline mortality. Comments: The article might serve as a handy overall reference to frailty models, especially for mortality research.

49 citations

Journal Article•DOI•
The use of permutation tests for the analysis of parallel and stepped-wedge cluster-randomized trials

[...]

Rui Wang1, Victor De Gruttola1•
Harvard University1
15 Aug 2017-Statistics in Medicine
TL;DR: This work considers a class of test statistics formed by a weighted average of pair-specific treatment effect estimates and offers practical guidance on the choice of weights to improve efficiency and proposes a permutation test for stepped-wedge designs and compares its performance with mixed-effect modeling.
Abstract: We investigate the use of permutation tests for the analysis of parallel and stepped-wedge cluster-randomized trials. Permutation tests for parallel designs with exponential family endpoints have been extensively studied. The optimal permutation tests developed for exponential family alternatives require information on intraclass correlation, a quantity not yet defined for time-to-event endpoints. Therefore, it is unclear how efficient permutation tests can be constructed for cluster-randomized trials with such endpoints. We consider a class of test statistics formed by a weighted average of pair-specific treatment effect estimates and offer practical guidance on the choice of weights to improve efficiency. We apply the permutation tests to a cluster-randomized trial evaluating the effect of an intervention to reduce the incidence of hospital-acquired infection. In some settings, outcomes from different clusters may be correlated, and we evaluate the validity and efficiency of permutation test in such settings. Lastly, we propose a permutation test for stepped-wedge designs and compare its performance with mixed-effect modeling and illustrate its superiority when sample sizes are small, the underlying distribution is skewed, or there is correlation across clusters. Copyright © 2017 John Wiley & Sons, Ltd.

41 citations

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