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Published in: BMC Medical Research Methodology 1/2009

Open Access 01-12-2009 | Research article

A semiparametric Bayesian proportional hazards model for interval censored data with frailty effects

Authors: Volkmar Henschel, Jutta Engel, Dieter Hölzel, Ulrich Mansmann

Published in: BMC Medical Research Methodology | Issue 1/2009

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Abstract

Background

Multivariate analysis of interval censored event data based on classical likelihood methods is notoriously cumbersome. Likelihood inference for models which additionally include random effects are not available at all. Developed algorithms bear problems for practical users like: matrix inversion, slow convergence, no assessment of statistical uncertainty.

Methods

MCMC procedures combined with imputation are used to implement hierarchical models for interval censored data within a Bayesian framework.

Results

Two examples from clinical practice demonstrate the handling of clustered interval censored event times as well as multilayer random effects for inter-institutional quality assessment. The software developed is called survBayes and is freely available at CRAN.

Conclusion

The proposed software supports the solution of complex analyses in many fields of clinical epidemiology as well as health services research.
Appendix
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Literature
1.
go back to reference Finkelstein D: A proportional hazards model for interval-censored failure time data. Biometrics. 1986, 42: 845-854.CrossRefPubMed Finkelstein D: A proportional hazards model for interval-censored failure time data. Biometrics. 1986, 42: 845-854.CrossRefPubMed
2.
go back to reference Huang J: Efficient Estimation for the Cox Model with Interval Censoring. The Annals of Statistics. 1996, 24: 540-568.CrossRef Huang J: Efficient Estimation for the Cox Model with Interval Censoring. The Annals of Statistics. 1996, 24: 540-568.CrossRef
3.
go back to reference Huang J, Wellner J: Efficient Estimation for the Cox Model with Case 2 Interval Censoring. Tech Rep 290. 1995, Department of Statistics, University of Washington Huang J, Wellner J: Efficient Estimation for the Cox Model with Case 2 Interval Censoring. Tech Rep 290. 1995, Department of Statistics, University of Washington
4.
go back to reference Lin D, Oakes D, Ying Z: Additive Hazards regression with Current Status Data. Biometrika. 1998, 85: 289-298.CrossRef Lin D, Oakes D, Ying Z: Additive Hazards regression with Current Status Data. Biometrika. 1998, 85: 289-298.CrossRef
5.
go back to reference Pan W: Extending the Iterative convex Minorant Algorithm to the Cox Model for Interval-Censored Data. Journal of Computational and Graphical Statistics. 1999, 78: 109-120. Pan W: Extending the Iterative convex Minorant Algorithm to the Cox Model for Interval-Censored Data. Journal of Computational and Graphical Statistics. 1999, 78: 109-120.
6.
go back to reference Satten G: Rank-based inference in the proportional hazards model for interval censored data. Biometrika. 1996, 83: 355-370.CrossRef Satten G: Rank-based inference in the proportional hazards model for interval censored data. Biometrika. 1996, 83: 355-370.CrossRef
7.
go back to reference Huber C, Solev V, Vonta F: Estimation of Density for Arbitrarily Censored And Truncated Data. Probability, statistics and modelling in public health. Edited by: Nikulin MS. 2006, New York: Springer, 246-265.CrossRef Huber C, Solev V, Vonta F: Estimation of Density for Arbitrarily Censored And Truncated Data. Probability, statistics and modelling in public health. Edited by: Nikulin MS. 2006, New York: Springer, 246-265.CrossRef
8.
go back to reference Bellamy S, Li Y, Ryan L, Lipsitz S, Canner M, Wright R: Analysis of clustered and interval censored data from a community based study in asthma. Statistics in Medicine. 2004, 23: 3607-3621.CrossRefPubMed Bellamy S, Li Y, Ryan L, Lipsitz S, Canner M, Wright R: Analysis of clustered and interval censored data from a community based study in asthma. Statistics in Medicine. 2004, 23: 3607-3621.CrossRefPubMed
10.
go back to reference Cox DR: Regression models and life tables (with discussion). Journal of the Royal Statistical Society (B). 1972, 34: 187-220. Cox DR: Regression models and life tables (with discussion). Journal of the Royal Statistical Society (B). 1972, 34: 187-220.
11.
go back to reference Ferguson T: A Bayesian Analysis of some non-parametric problems. Annals of Statistics. 1973, 1: 209-230.CrossRef Ferguson T: A Bayesian Analysis of some non-parametric problems. Annals of Statistics. 1973, 1: 209-230.CrossRef
12.
go back to reference Kalbfleisch J: Nonparametric Bayesian analysis of survival time data. Journal of the Royal Statistical Society (B). 1978, 40: 214-221. Kalbfleisch J: Nonparametric Bayesian analysis of survival time data. Journal of the Royal Statistical Society (B). 1978, 40: 214-221.
13.
go back to reference Dey D, Müller P, Sinha D: Practical Nonparametric and Semiparametric Bayesian Statistics. 1998, New York: SpringerCrossRef Dey D, Müller P, Sinha D: Practical Nonparametric and Semiparametric Bayesian Statistics. 1998, New York: SpringerCrossRef
14.
go back to reference Ibrahim J, Chen M, Sinha D: Bayesian Survival Analysis. 2001, New York, Berlin, Heidelberg: SpringerCrossRef Ibrahim J, Chen M, Sinha D: Bayesian Survival Analysis. 2001, New York, Berlin, Heidelberg: SpringerCrossRef
15.
go back to reference Härkänen T, Virtanen J, Arjas E: Caries on permanent teeth: A nonparametric Bayesian analysis. Scandinavian Journal of Statistics. 2000, 27: 577-588.CrossRef Härkänen T, Virtanen J, Arjas E: Caries on permanent teeth: A nonparametric Bayesian analysis. Scandinavian Journal of Statistics. 2000, 27: 577-588.CrossRef
16.
go back to reference Härkänen T: BITE: A Bayesian intensity estimator. Computational Statistics. 2003, 18: 565-583.CrossRef Härkänen T: BITE: A Bayesian intensity estimator. Computational Statistics. 2003, 18: 565-583.CrossRef
17.
go back to reference Hennerfeind A, Brezger A, Fahrmeir L: Geoadditive survival models. Journal of the American Statistical Association. 2006, 101: 1065-1075.CrossRef Hennerfeind A, Brezger A, Fahrmeir L: Geoadditive survival models. Journal of the American Statistical Association. 2006, 101: 1065-1075.CrossRef
18.
go back to reference Kneib T: Mixed model based inference in geoadditive hazard regression for interval censored survival times. Computational Statistics and Data Analysis. 2006, 51: 777-792.CrossRef Kneib T: Mixed model based inference in geoadditive hazard regression for interval censored survival times. Computational Statistics and Data Analysis. 2006, 51: 777-792.CrossRef
19.
20.
go back to reference Gamerman D: Dynamic Bayesian Models for Survival Data. Applied Statistics. 1991, 40: 63-79.CrossRef Gamerman D: Dynamic Bayesian Models for Survival Data. Applied Statistics. 1991, 40: 63-79.CrossRef
21.
go back to reference Lang S, Brezger A: Bayesian P-Splines. Journal of Computational and Graphical Statistics. 2004, 13: 183-212.CrossRef Lang S, Brezger A: Bayesian P-Splines. Journal of Computational and Graphical Statistics. 2004, 13: 183-212.CrossRef
22.
go back to reference Aitkin M, Clayton D: The fitting of exponential, Weibull and extreme value distributions to complex censored survival data using GLIM. Applied Statistics. 1980, 29: 156-63.CrossRef Aitkin M, Clayton D: The fitting of exponential, Weibull and extreme value distributions to complex censored survival data using GLIM. Applied Statistics. 1980, 29: 156-63.CrossRef
23.
go back to reference Gamerman D: Sampling from the posterior distribution in generalized linear mixed models. Statistics and Computing. 1997, 7: 57-68.CrossRef Gamerman D: Sampling from the posterior distribution in generalized linear mixed models. Statistics and Computing. 1997, 7: 57-68.CrossRef
24.
go back to reference Knorr-Held L, Rue H: On block updating in Markov random field models for disease mapping. Scandinavian Journal of Statistics. 2002, 29: 597-614.CrossRef Knorr-Held L, Rue H: On block updating in Markov random field models for disease mapping. Scandinavian Journal of Statistics. 2002, 29: 597-614.CrossRef
25.
go back to reference Rue H: Fast sampling of Gaussian Markov random fields. Journal of the Royal Statistical Society (B). 2001, 63: 325-338.CrossRef Rue H: Fast sampling of Gaussian Markov random fields. Journal of the Royal Statistical Society (B). 2001, 63: 325-338.CrossRef
26.
27.
go back to reference Bebchuk JD, Betensky RA: Multiple Imputation for simple estimation of the Hazard function based on interval censored Data. Statistics in Medicine. 2000, 19: 405-419.CrossRefPubMed Bebchuk JD, Betensky RA: Multiple Imputation for simple estimation of the Hazard function based on interval censored Data. Statistics in Medicine. 2000, 19: 405-419.CrossRefPubMed
28.
go back to reference Hougaard P: Analysis of Multivariate Survival Data. 2000, New York, Berlin, Heidelberg: SpringerCrossRef Hougaard P: Analysis of Multivariate Survival Data. 2000, New York, Berlin, Heidelberg: SpringerCrossRef
29.
go back to reference Clayton D: A Monte Carlo method for Bayesian inference in frailty models. Biometrics. 1991, 47: 467-485.CrossRefPubMed Clayton D: A Monte Carlo method for Bayesian inference in frailty models. Biometrics. 1991, 47: 467-485.CrossRefPubMed
30.
go back to reference Feller W: An Introduction to Probability Theory and Its Applications. 1971, New York: John Wiley and Sons Feller W: An Introduction to Probability Theory and Its Applications. 1971, New York: John Wiley and Sons
31.
go back to reference Mansmann U: Convergence Diagnosis for Gibbs Sampling Output. Medical Infobahn for Europe. Edited by: Hasman A, Prokosch H, Blobel B, Dudeck J, Gell G, Engelbrecht R. 2000, IOC Press, 83-87. Mansmann U: Convergence Diagnosis for Gibbs Sampling Output. Medical Infobahn for Europe. Edited by: Hasman A, Prokosch H, Blobel B, Dudeck J, Gell G, Engelbrecht R. 2000, IOC Press, 83-87.
32.
go back to reference Zhang Y, Jamdhidian M: On Algorithms fo the Nonparametric Maximum Likelihood Estimator of the Failure Function With Censored Data. Journal of Computational and Graphical Statistics. 2004, 13: 123-140.CrossRef Zhang Y, Jamdhidian M: On Algorithms fo the Nonparametric Maximum Likelihood Estimator of the Failure Function With Censored Data. Journal of Computational and Graphical Statistics. 2004, 13: 123-140.CrossRef
33.
go back to reference Meisel HJ, Mansmann U, Alvarez H, Rodesch G, Brock M, Lasjaunias P: Cerebral Arteriovenous Malformations and Associated Aneurysms: Analysis of 305 Cases from a Series of 662 Patients. Neurosurgery. 2000, 46: 793-802.PubMed Meisel HJ, Mansmann U, Alvarez H, Rodesch G, Brock M, Lasjaunias P: Cerebral Arteriovenous Malformations and Associated Aneurysms: Analysis of 305 Cases from a Series of 662 Patients. Neurosurgery. 2000, 46: 793-802.PubMed
34.
go back to reference Klein J, Moeschberger M: Survival analysis. 2003, New York: Springer, 2 Klein J, Moeschberger M: Survival analysis. 2003, New York: Springer, 2
35.
go back to reference Engel J, Kerr J, Eckel R, Günther B, Heiss M, Heitland W, Siewert J, Jauch KW, Hölzel D: Influence of hospital volume on local recurrence and survival in a population sample of rectal cancer patients. European Journal of Surgical Oncology. 2005, 31: 512-520.CrossRefPubMed Engel J, Kerr J, Eckel R, Günther B, Heiss M, Heitland W, Siewert J, Jauch KW, Hölzel D: Influence of hospital volume on local recurrence and survival in a population sample of rectal cancer patients. European Journal of Surgical Oncology. 2005, 31: 512-520.CrossRefPubMed
36.
go back to reference Komarek A, Lesaffre E, Härkänen T, Declerck D, Virtanen J: A Bayesian analysis of multivariate doubly-interval-censored data. Biostatistics. 2005, 6: 145-155.CrossRefPubMed Komarek A, Lesaffre E, Härkänen T, Declerck D, Virtanen J: A Bayesian analysis of multivariate doubly-interval-censored data. Biostatistics. 2005, 6: 145-155.CrossRefPubMed
Metadata
Title
A semiparametric Bayesian proportional hazards model for interval censored data with frailty effects
Authors
Volkmar Henschel
Jutta Engel
Dieter Hölzel
Ulrich Mansmann
Publication date
01-12-2009
Publisher
BioMed Central
Published in
BMC Medical Research Methodology / Issue 1/2009
Electronic ISSN: 1471-2288
DOI
https://doi.org/10.1186/1471-2288-9-9

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