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Munezero P, Villani M, Kohn R. Dynamic Mixture of Experts Models for Online Prediction. Technometrics 2022. [DOI: 10.1080/00401706.2022.2146755] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Affiliation(s)
- Parfait Munezero
- Department of Statistics, Stockholm University
- Data Insights Support Team, Ericsson, Stockholm, Sweden
| | - Mattias Villani
- Department of Statistics, Stockholm University
- Department of Computer and Information Science, Linköping University
| | - Robert Kohn
- UNSW Business School, University of New South Wales
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2
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Gómez YM, Gallardo DI, Leão J, Calsavara VF. On a new piecewise regression model with cure rate: Diagnostics and application to medical data. Stat Med 2021; 40:6723-6742. [PMID: 34581460 DOI: 10.1002/sim.9208] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2020] [Revised: 08/26/2021] [Accepted: 09/11/2021] [Indexed: 12/27/2022]
Abstract
In this article, we discuss an extension of the classical negative binomial cure rate model with piecewise exponential distribution of the time to event for concurrent causes, which enables the modeling of monotonic and non-monotonic hazard functions (ie, the shape of the hazard function is not assumed as in traditional parametric models). This approach produces a flexible cure rate model, depending on the choice of time partition. We discuss local influence on this negative binomial power piecewise exponential model. We report on Monte Carlo simulation studies and application of the model to real melanoma and leukemia datasets.
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Affiliation(s)
- Yolanda M Gómez
- Facultad de Medicina, Universidad de Atacama, Copiapó, Chile.,Departamento de Matemática, Universidad de Atacama, Copiapó, Chile
| | - Diego I Gallardo
- Departamento de Matemática, Universidad de Atacama, Copiapó, Chile
| | - Jeremias Leão
- Department of Statistics, Federal University of Amazonas, Manaus, Brazil
| | - Vinicius F Calsavara
- Department of Epidemiology and Statistics, A.C. Camargo Cancer Center, São Paulo, Brazil.,Biostatistics and Bioinformatics Research Center, Cedars-Sinai Medical Center, Los Angeles, California, USA
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3
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Affiliation(s)
- Ismaël Castillo
- Laboratoire de Probabilités, Statistique et Modélisation, Sorbonne Université & Institut Universitaire de France
| | - Stéphanie van der Pas
- Department of Epidemiology and Data Science, Amsterdam UMC, Vrije Universiteit Amsterdam
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4
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5
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Demarqui FN, Mayrink VD. Yang and Prentice model with piecewise exponential baseline distribution for modeling lifetime data with crossing survival curves. BRAZ J PROBAB STAT 2021. [DOI: 10.1214/20-bjps471] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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6
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Munezero P, Ghilagaber G. Dynamic Bayesian adjustment of anticipatory covariates in retrospective data: application to the effect of education on divorce risk. J Appl Stat 2020; 49:1382-1401. [PMID: 35707119 PMCID: PMC9041697 DOI: 10.1080/02664763.2020.1864812] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
We address a problem in inference from retrospective studies where the value of a variable is measured at the date of the survey but is used as covariate to events that have occurred long before the survey. This causes problem because the value of the current-date (anticipatory) covariate does not follow the temporal order of events. We propose a dynamic Bayesian approach for modelling jointly the anticipatory covariate and the event of interest, and allowing the effects of the anticipatory covariate to vary over time. The issues are illustrated with data on the effects of education attained by the survey-time on divorce risks among Swedish men. The overall results show that failure to adjust for the anticipatory nature of education leads to elevated relative risks of divorce across educational levels. The results are partially in accordance with previous findings based on analyses of the same data set. More importantly, our findings provide new insights in that the bias due to anticipatory covariates varies over marriage duration.
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Affiliation(s)
- Parfait Munezero
- Department of Statistics, Stockholm University, Stockholm, Sweden
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7
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A Bayesian Cure Rate Model Based on the Power Piecewise Exponential Distribution. Methodol Comput Appl Probab 2019. [DOI: 10.1007/s11009-019-09728-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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8
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9
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Wilson KJ, Farrow M. Bayes linear kinematics in a dynamic survival model. Int J Approx Reason 2017. [DOI: 10.1016/j.ijar.2016.09.010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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10
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Perperoglou A. A special case of reduced rank models for identification and modelling of time varying effects in survival analysis. Stat Med 2016; 35:5135-5148. [DOI: 10.1002/sim.7088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/10/2015] [Revised: 08/01/2016] [Accepted: 08/04/2016] [Indexed: 11/06/2022]
Affiliation(s)
- Aris Perperoglou
- Department of Mathematical Sciences; University of Essex; CO4 3SQ Wivenhoe ParkColchester U.K
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11
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Murray TA, Hobbs BP, Sargent DJ, Carlin BP. Flexible Bayesian survival modeling with semiparametric time-dependent and shape-restricted covariate effects. BAYESIAN ANALYSIS 2016; 11:381-402. [PMID: 27042243 PMCID: PMC4811615 DOI: 10.1214/15-ba954] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Presently, there are few options with available software to perform a fully Bayesian analysis of time-to-event data wherein the hazard is estimated semi- or non-parametrically. One option is the piecewise exponential model, which requires an often unrealistic assumption that the hazard is piecewise constant over time. The primary aim of this paper is to construct a tractable semiparametric alternative to the piecewise exponential model that assumes the hazard is continuous, and to provide modifiable, user-friendly software that allows the use of these methods in a variety of settings. To accomplish this aim, we use a novel model formulation for the log-hazard based on a low-rank thin plate linear spline that readily facilitates adjustment for covariates with time-dependent and proportional hazards effects, possibly subject to shape restrictions. We investigate the performance of our model choices via simulation. We then analyze colorectal cancer data from a clinical trial comparing the effectiveness of two novel treatment regimes relative to the standard of care for overall survival. We estimate a time-dependent hazard ratio for each novel regime relative to the standard of care while adjusting for the effect of aspartate transaminase, a biomarker of liver function, that is subject to a non-decreasing shape restriction.
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Affiliation(s)
- Thomas A. Murray
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center
| | - Brian P. Hobbs
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center
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12
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13
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French JL, Thomas N, Wang C. Using Historical Data With Bayesian Methods in Early Clinical Trial Monitoring. Stat Biopharm Res 2012. [DOI: 10.1080/19466315.2012.707088] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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14
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Bian L, Gebraeel N. Stochastic methodology for prognostics under continuously varying environmental profiles. Stat Anal Data Min 2012. [DOI: 10.1002/sam.11154] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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15
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Demarqui FN, Loschi RH, Dey DK, Colosimo EA. A class of dynamic piecewise exponential models with random time grid. J Stat Plan Inference 2012. [DOI: 10.1016/j.jspi.2011.09.006] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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16
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He J, Mayo MS. Adjusted Interim Survival Analysis Under Nonproportional Hazards. COMMUN STAT-SIMUL C 2012. [DOI: 10.1080/03610918.2011.582562] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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17
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Yin G, Li H, Zeng D. Partially Linear Additive Hazards Regression With Varying Coefficients. J Am Stat Assoc 2012. [DOI: 10.1198/016214508000000463] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Affiliation(s)
- Guosheng Yin
- Guosheng Yin is Associate Professor, Department of Biostatistics, M. D. Anderson Cancer Center, University of Texas, Houston, TX 77030 . Hui Li is Assistant Professor, School of Mathematical Sciences, Beijing Normal University, Beijing, China. Donglin Zeng is Associate Professor, Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599. The authors thank the editor, associate editor, and three referees for their insightful comments, which led to substantial improvements in the
| | - Hui Li
- Guosheng Yin is Associate Professor, Department of Biostatistics, M. D. Anderson Cancer Center, University of Texas, Houston, TX 77030 . Hui Li is Assistant Professor, School of Mathematical Sciences, Beijing Normal University, Beijing, China. Donglin Zeng is Associate Professor, Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599. The authors thank the editor, associate editor, and three referees for their insightful comments, which led to substantial improvements in the
| | - Donglin Zeng
- Guosheng Yin is Associate Professor, Department of Biostatistics, M. D. Anderson Cancer Center, University of Texas, Houston, TX 77030 . Hui Li is Assistant Professor, School of Mathematical Sciences, Beijing Normal University, Beijing, China. Donglin Zeng is Associate Professor, Department of Biostatistics, University of North Carolina, Chapel Hill, NC 27599. The authors thank the editor, associate editor, and three referees for their insightful comments, which led to substantial improvements in the
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18
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He J, McGee DL, Niu X. Application of the Bayesian dynamic survival model in medicine. Stat Med 2010; 29:347-60. [PMID: 20014356 DOI: 10.1002/sim.3795] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
The Bayesian dynamic survival model (BDSM), a time-varying coefficient survival model from the Bayesian prospective, was proposed in early 1990s but has not been widely used or discussed. In this paper, we describe the model structure of the BDSM and introduce two estimation approaches for BDSMs: the Markov Chain Monte Carlo (MCMC) approach and the linear Bayesian (LB) method. The MCMC approach estimates model parameters through sampling and is computationally intensive. With the newly developed geoadditive survival models and software BayesX, the BDSM is available for general applications. The LB approach is easier in terms of computations but it requires the prespecification of some unknown smoothing parameters. In a simulation study, we use the LB approach to show the effects of smoothing parameters on the performance of the BDSM and propose an ad hoc method for identifying appropriate values for those parameters. We also demonstrate the performance of the MCMC approach compared with the LB approach and a penalized partial likelihood method available in software R packages. A gastric cancer trial is utilized to illustrate the application of the BDSM.
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Affiliation(s)
- Jianghua He
- Department of Biostatistics, University of Kansas Medical Center, Kansas City, KS 66160, U.S.A.
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19
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Yin G, Li H. Least squares estimation of varying-coefficient hazard regression with application to breast cancer dose-intensity data. CAN J STAT 2009. [DOI: 10.1002/cjs.10036] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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20
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Triantafyllopoulos K. Inference of Dynamic Generalized Linear Models: On-Line Computation and Appraisal. Int Stat Rev 2009. [DOI: 10.1111/j.1751-5823.2009.00087.x] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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21
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Cheng YJ, Crainiceanu CM. Cox Models With Smooth Functional Effect of Covariates Measured With Error. J Am Stat Assoc 2009; 104:1144-1154. [PMID: 21818167 PMCID: PMC3148771 DOI: 10.1198/jasa.2009.tm08160] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We propose, develop, and implement a fully Bayesian inferential approach for the Cox model when the log hazard function contains unknown smooth functions of the variables measured with error. Our approach is to model nonparametrically both the log-baseline hazard and the smooth components of the log-hazard functions using low-rank penalized splines. Careful implementation of the Bayesian inferential machinery is shown to produce remarkably better results than the naive approach. Our methodology was motivated by and applied to the study of progression time to chronic kidney disease as a function of baseline kidney function and applied to the Atherosclerosis Risk in Communities study, a large epidemiological cohort study. This article has supplementary material online.
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Affiliation(s)
- Yu-Jen Cheng
- Department of Biostatistics, Johns Hopkins University, Baltimore, MD 21205 ()
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22
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Congdon P. Adaptive autoregressive priors for area and time structured mortality data. J Stat Plan Inference 2009. [DOI: 10.1016/j.jspi.2009.01.011] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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23
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24
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Natarajan L, Pu M, Parker BA, Thomson CA, Caan BJ, Flatt SW, Madlensky L, Hajek RA, Al-Delaimy WK, Saquib N, Gold EB, Pierce JP. Time-varying effects of prognostic factors associated with disease-free survival in breast cancer. Am J Epidemiol 2009; 169:1463-70. [PMID: 19403844 DOI: 10.1093/aje/kwp077] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
Early detection and effective treatments have dramatically improved breast cancer survivorship, yet the risk of relapse persists even 15 years after the initial diagnosis. It is important to identify prognostic factors for late breast cancer events. The authors investigated time-varying effects of tumor characteristics on breast-cancer-free survival using data on 3,088 breast cancer survivors from 4 US states who participated in a randomized dietary intervention trial in 1995-2006, with maximum follow-up through 15 years (median, 9 years). A piecewise constant penalized spline approach incorporating time-varying coefficients was adopted, allowing for deviations from the proportional hazards assumption. This method is more flexible than standard approaches, provides direct estimates of hazard ratios across time intervals, and is computationally tractable. Having a stage II or III tumor was associated with a 3-fold higher hazard of breast cancer than having a stage I tumor during the first 2.5 years after diagnosis; this hazard ratio decreased to 2.1 after 7.7 years, but higher tumor stage remained a significant risk factor. Similar diminishing effects were found for poorly differentiated tumors. Interestingly, having a positive estrogen receptor status was protective up to 4 years after diagnosis but detrimental after 7.7 years (hazard ratio = 1.5). These results emphasize the importance of careful statistical modeling allowing for possibly time-dependent effects in long-term survivorship studies.
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Affiliation(s)
- Loki Natarajan
- Rebecca and John Moores UCSD Cancer Center, School of Medicine, University of California, La Jolla, California 92093-0901, USA
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25
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Amorim LD, Cai J, Zeng D, Barreto ML. Regression splines in the time-dependent coefficient rates model for recurrent event data. Stat Med 2009; 27:5890-906. [PMID: 18696748 DOI: 10.1002/sim.3400] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Many epidemiologic studies involve the occurrence of recurrent events and much attention has been given for the development of modeling techniques that take into account the dependence structure of multiple event data. This paper presents a time-dependent coefficient rates model that incorporates regression splines in its estimation procedure. Such methods would be appropriate in situations where the effect of an exposure or covariates changes over time in recurrent event data settings. The finite sample properties of the estimators are studied via simulation. Using data from a randomized community trial that was designed to evaluate the effect of vitamin A supplementation on recurrent diarrheal episodes in small children, we model the functional form of the treatment effect on the time to the occurrence of diarrhea. The results describe how this effect varies over time. In summary, we observed a major impact of the vitamin A supplementation on diarrhea after 2 months of the dosage, with the effect diminishing after the third dosage. The proposed method can be viewed as a flexible alternative to the marginal rates model with constant effect in situations where the effect of interest may vary over time.
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Affiliation(s)
- Leila D Amorim
- Department of Statistics, Federal University of Bahia, Salvador, Brazil.
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26
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Henschel V, Engel J, Hölzel D, Mansmann U. A semiparametric Bayesian proportional hazards model for interval censored data with frailty effects. BMC Med Res Methodol 2009; 9:9. [PMID: 19208234 PMCID: PMC2679769 DOI: 10.1186/1471-2288-9-9] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2008] [Accepted: 02/10/2009] [Indexed: 11/10/2022] Open
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.
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Affiliation(s)
- Volkmar Henschel
- Institute for Medical Informatics, Biometry and Epidemiology, and Tumour Registry Munich, University of Munich, Marchioninistr, 15, D-81377 Munich, Germany.
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27
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ROCCA LUCALA. Bayesian Non-Parametric Estimation of Smooth Hazard Rates for Seismic Hazard Assessment. Scand Stat Theory Appl 2008. [DOI: 10.1111/j.1467-9469.2008.00595.x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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28
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Demarqui FN, Loschi RH, Colosimo EA. Estimating the grid of time-points for the piecewise exponential model. LIFETIME DATA ANALYSIS 2008; 14:333-356. [PMID: 18463801 DOI: 10.1007/s10985-008-9086-0] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2006] [Accepted: 04/15/2008] [Indexed: 05/26/2023]
Abstract
One of the greatest challenges related to the use of piecewise exponential models (PEMs) is to find an adequate grid of time-points needed in its construction. In general, the number of intervals in such a grid and the position of their endpoints are ad-hoc choices. We extend previous works by introducing a full Bayesian approach for the piecewise exponential model in which the grid of time-points (and, consequently, the endpoints and the number of intervals) is random. We estimate the failure rates using the proposed procedure and compare the results with the non-parametric piecewise exponential estimates. Estimates for the survival function using the most probable partition are compared with the Kaplan-Meier estimators (KMEs). A sensitivity analysis for the proposed model is provided considering different prior specifications for the failure rates and for the grid. We also evaluate the effect of different percentage of censoring observations in the estimates. An application to a real data set is also provided. We notice that the posteriors are strongly influenced by prior specifications, mainly for the failure rates parameters. Thus, the priors must be fairly built, say, really disclosing the expert prior opinion.
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Affiliation(s)
- Fabio N Demarqui
- Departamento de Estatistica, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6.627, Pampulha, 31270-010, Belo Horizonte, MG, Brazil
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Haneuse SJPA, Rudser KD, Gillen DL. The separation of timescales in Bayesian survival modeling of the time-varying effect of a time-dependent exposure. Biostatistics 2007; 9:400-10. [PMID: 18025072 DOI: 10.1093/biostatistics/kxm038] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, we apply flexible Bayesian survival analysis methods to investigate the risk of lymphoma associated with kidney transplantation among patients with end-stage renal disease. Of key interest is the potentially time-varying effect of a time-dependent exposure: transplant status. Bayesian modeling of the baseline hazard and the effect of transplant requires consideration of 2 timescales: time since study start and time since transplantation, respectively. Previous related work has not dealt with the separation of multiple timescales. Using a hierarchical model for the hazard function, both timescales are incorporated via conditionally independent stochastic processes; smoothing of each process is specified via intrinsic conditional Gaussian autoregressions. Features of the corresponding posterior distribution are evaluated from draws obtained via a Metropolis-Hastings-Green algorithm.
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Perperoglou A, Keramopoullos A, van Houwelingen HC. Approaches in modelling long-term survival: an application to breast cancer. Stat Med 2007; 26:2666-85. [PMID: 17072918 DOI: 10.1002/sim.2729] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
Several modelling techniques have been proposed for non-proportional hazards. In this work we consider different models which can be classified into three wide categories: models with time-varying effects of the covariates; frailty models and cure rate models. We present those different extensions of the proportional hazards model on an application of 2433 breast cancer patients with a long follow-up. We comment on the differences and similarities among the models and evaluate their performance using survival and hazard plots, Brier scores and pseudo-observations.
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Affiliation(s)
- Aris Perperoglou
- Leiden University Medical Center, University of Leiden, P.O. Box 9604, 2300 RC, The Netherlands.
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Abstract
Many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly, such as infection, hospitalization, recurrence of disease, or tumor onset. To analyze such data, it is necessary to account for within-subject dependency in the multiple event times. Motivated by data from studies of palpable tumors, this article proposes a dynamic frailty model and Bayesian semiparametric approach to inference. The widely used shared frailty proportional hazards model is generalized to allow subject-specific frailties to change dynamically with age while also accommodating nonproportional hazards. Parametric assumptions on the frailty distribution are avoided by using Dirichlet process priors for a shared frailty and for multiplicative innovations on this frailty. By centering the semiparametric model on a conditionally conjugate dynamic gamma model, we facilitate posterior computation and lack-of-fit assessments of the parametric model. Our proposed method is demonstrated using data from a cancer chemoprevention study.
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Affiliation(s)
- Michael L Pennell
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA.
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Kim S, Chen MH, Dey DK, Gamerman D. Bayesian dynamic models for survival data with a cure fraction. LIFETIME DATA ANALYSIS 2007; 13:17-35. [PMID: 17136621 DOI: 10.1007/s10985-006-9028-7] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2006] [Accepted: 09/28/2006] [Indexed: 05/12/2023]
Abstract
In this paper, we propose a new class of semi-parametric cure rate models. Specifically, we construct dynamic models for piecewise hazard functions over a finite partition of the time axis. Allowing the size of partition and the levels of baseline hazard to be random, our proposed models provide a great flexibility in controlling the degree of parametricity in the right tail of the survival distribution and the amount of correlations among the log-baseline hazard levels. Several properties of the proposed models are derived, and propriety of the implied posteriors with improper noninformative priors for regression coefficients based on the proposed models is established for the fixed partition of the time axis. In addition, an efficient reversible jump computational algorithm is developed for carrying out posterior computation. A real data set from a melanoma clinical trial is analyzed in detail to further demonstrate the proposed methodology.
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Affiliation(s)
- Sungduk Kim
- Department of Statistics, University of Connecticut, Storrs, CT 06269, USA.
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34
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Bastos LS, Gamerman D. Dynamic survival models with spatial frailty. LIFETIME DATA ANALYSIS 2006; 12:441-60. [PMID: 17031498 DOI: 10.1007/s10985-006-9020-2] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2006] [Accepted: 07/24/2006] [Indexed: 05/12/2023]
Abstract
In many survival studies, covariates effects are time-varying and there is presence of spatial effects. Dynamic models can be used to cope with the variations of the effects and spatial components are introduced to handle spatial variation. This paper proposes a methodology to simultaneously introduce these components into the model. A number of specifications for the spatial components are considered. Estimation is performed via a Bayesian approach through Markov chain Monte Carlo methods. Models are compared to assess relevance of their components. Analysis of a real data set is performed, showing the relevance of both time-varying covariate effects and spatial components. Extensions to the methodology are proposed along with concluding remarks.
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35
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Godolphin E, Triantafyllopoulos K. Decomposition of time series models in state-space form. Comput Stat Data Anal 2006. [DOI: 10.1016/j.csda.2004.12.012] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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36
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Perperoglou A, le Cessie S, van Houwelingen HC. Reduced-rank hazard regression for modelling non-proportional hazards. Stat Med 2006; 25:2831-45. [PMID: 16158396 DOI: 10.1002/sim.2360] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
The Cox proportional hazards model is the most common method to analyse survival data. However, the proportional hazards assumption might not hold. The natural extension of the Cox model is to introduce time-varying effects of the covariates. For some covariates such as (surgical)treatment non-proportionality could be expected beforehand. For some other covariates the non-proportionality only becomes apparent if the follow-up is long enough. It is often observed that all covariates show similar decaying effects over time. Such behaviour could be explained by the popular (gamma-) frailty model. However, the (marginal) effects of covariates in frailty models are not easy to interpret. In this paper we propose the reduced-rank model for time-varying effects of covariates. Starting point is a Cox model with p covariates and time-varying effects modelled by q time functions (constant included), leading to a pxq structure matrix that contains the regression coefficients for all covariate by time function interactions. By reducing the rank of this structure matrix a whole range of models is introduced, from the very flexible full-rank model (identical to a Cox model with time-varying effects) to the very rigid rank one model that mimics the structure of a gamma-frailty model, but is easier to interpret. We illustrate these models with an application to ovarian cancer patients.
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Affiliation(s)
- Aris Perperoglou
- Department of Medical Statistics, Leiden University Medical Center, University of Leiden, P.O. Box 9604, 2300 RC, Leiden, The Netherlands.
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CHANG ISHOU, HSIUNG CHAOA, WU YUHJENN, YANG CHECHI. Bayesian Survival Analysis Using Bernstein Polynomials. Scand Stat Theory Appl 2005. [DOI: 10.1111/j.1467-9469.2005.00451.x] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Abstract
A class of parametric dynamic survival models are explored in which only limited parametric assumptions are made, whilst avoiding the assumption of proportional hazards. Both the log-baseline hazard and covariate effects are modelled by piecewise constant and correlated processes. The method of estimation is to use Markov chain Monte Carlo simulations: Gibbs sampling with a Metropolis-Hastings step. In addition to standard right censored data sets, extensions to accommodate interval censoring and random effects are included. The model is applied to two well known and illustrative data sets, and the dynamic variability of covariate effects investigated.
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Affiliation(s)
- K Hemming
- Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
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40
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A bayesian semiparametric analysis for additive Hazard models with censored observations. TEST-SPAIN 2003. [DOI: 10.1007/bf02595719] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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41
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Albers M, Battistella VM, Romiti M, Rodrigues AAE, Pereira CAB. Meta-analysis of polytetrafluoroethylene bypass grafts to infrapopliteal arteries. J Vasc Surg 2003; 37:1263-9. [PMID: 12764274 DOI: 10.1016/s0741-5214(02)75332-9] [Citation(s) in RCA: 100] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
Abstract
CONTEXT Reports of polytetrafluoroethylene (PTFE) bypass grafting to the infrapopliteal arteries have often used survival analysis of acceptable quality to describe a wide range of long-term results. In theory, these results may be combined if variability between series and time intervals is considered. OBJECTIVE Meta-analysis was performed to gain insight into long-term graft patency and foot preservation after PTFE bypass grafting to infrapopliteal arteries. DATA SOURCE Studies published from 1982 through 2001 were identified from the PubMed database and pertinent original articles. STUDY SELECTION Three investigators selected 43 studies that used survival analysis, reported 2-year patency rates, and included at least 15 bypass procedures. Data extraction and transformation: Based on standard life-tables or survivor curves, an interval success rate was calculated for each month in each series. The monthly success rates were combined across series, enabling construction of pooled survivor curves. DATA SYNTHESIS Random-effects meta-analysis yielded 5-year pooled estimates (SE) of 30.5% (7.6%) for primary graft patency, 39.7% (5.5%) for secondary graft patency, and 55.7% (5.0%) for foot preservation. During the entire follow-up, pooled estimates were slightly higher for series of PTFE grafts with adjunctive procedures compared with series of PTFE grafts only. Sensitivity analysis: A simulation using only unfavorable assumptions showed a decrease of less than 5% at 5 years for all outcomes, and smaller differences at subgroup meta-analysis. Funnel plots suggested that publication bias was unlikely. CONCLUSION This meta-analysis indicated moderate success for PTFE bypass grafts to infrapopliteal arteries, but the role of adjunctive procedures at the distal anastomosis remains uncertain.
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Affiliation(s)
- Maximiano Albers
- Vascular Surgery Section, Department of Surgery, Health and Medical Sciences Sector, Lusiada University Center UNILUS, Lusiada Foundation, Santos and São Paulo, Brazil.
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Tighiouart M. Modeling Correlated Time-Varying Covariate Effects In A Cox-Type Regression Model. JOURNAL OF MODERN APPLIED STATISTICAL METHODS 2003. [DOI: 10.22237/jmasm/1051748040] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
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43
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Winnett A, Sasieni P. Iterated residuals and time-varying covariate effects in Cox regression. J R Stat Soc Series B Stat Methodol 2003. [DOI: 10.1111/1467-9868.00397] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Abstract
In epidemiologic studies, there is often interest in assessing the association between exposure history and disease incidence. For many diseases, incidence may depend not only on cumulative exposure, but also on the ages at which exposure occurred. This article proposes a flexible Bayesian approach for modeling age-varying and waning exposure effects. The Cox model is generalized to allow the hazard of disease to depend on an integral, across the exposed ages, of a piecewise polynomial function of age, multiplied by an exponential decay term. Linearity properties of the model facilitate posterior computation via a Gibbs sampler, which generalizes previous algorithms for Cox regression with time-dependent covariates. The approach is illustrated by an application to the study of protective effects of breastfeeding on incidence of childhood asthma.
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Affiliation(s)
- David B Dunson
- Biostatistics Branch, MD A3-03, National Institute of Environmental Health Sciences, P.O. Box 12233, Research Triangle Park, North Carolina 27709, USA.
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45
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CAI ZONGWU, SUN YANQING. Local Linear Estimation for Time-Dependent Coefficients in Cox's Regression Models. Scand Stat Theory Appl 2003. [DOI: 10.1111/1467-9469.00320] [Citation(s) in RCA: 103] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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46
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Abstract
The objective of a chronic rodent bioassay is to assess the impact of a chemical compound on the development of tumors. However, most tumor types are not observable prior to necropsy, making direct estimation of the tumor incidence rate problematic. In such cases, estimation can proceed only if the study incorporates multiple interim sacrifices or we make use of simplified parametric or nonparametric models. In addition, it is widely accepted that other factors, such as weight, can be related to both dose level and tumor onset, confounding the association of interest. However, there is not typically enough information in the current study to assess such effects. The addition of historical data can help alleviate this problem. In this article, we propose a novel Bayesian semiparametric model for the analysis of data from rodent carcinogenicity studies. We develop informative prior distributions for covariate effects through the use of historical control data and outline a Gibbs sampling scheme. We implement the model by analyzing data from a National Toxicology Program chronic rodent bioassay.
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Affiliation(s)
- Jonathan L French
- Biostatistics, Pfizer Global Research and Development, 50 Pequot Avenue, New London, Connecticut 06320, USA.
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Abstract
In the absence of longitudinal data, the current presence and severity of disease can be measured for a sample of individuals to investigate factors related to disease incidence and progression. In this article, Bayesian discrete-time stochastic models are developed for inference from cross-sectional data consisting of the age at first diagnosis, the current presence of disease, and one or more surrogates of disease severity. Semiparametric models are used for the age-specific hazards of onset and diagnosis, and a normal underlying variable approach is proposed for modeling of changes with latency time in disease severity. The model accommodates multiple surrogates of disease severity having different measurement scales and heterogeneity among individuals in disease progression. A Markov chain Monte Carlo algorithm is described for posterior computation, and the methods are applied to data from a study of uterine leiomyoma.
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Affiliation(s)
- B Dunson
- Biostatistics Branch, MD A3-03, National Institute of Environmental Health Sciences, P.O. Box 12233, Research Triangle Park, North Carolina 27709, USA.
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Hemming K, Shaw JEH. A parametric dynamic survival model applied to breast cancer survival times. J R Stat Soc Ser C Appl Stat 2002. [DOI: 10.1111/1467-9876.00278] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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49
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NIETO-BARAJAS LUISE, WALKER STEPHENG. Markov Beta and Gamma Processes for Modelling Hazard Rates. Scand Stat Theory Appl 2002. [DOI: 10.1111/1467-9469.00298] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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50
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Wainwright NWJ, Surtees PG. Time-varying exposure and the impact of stressful life events on onset of affective disorder. Stat Med 2002; 21:2077-91. [PMID: 12111888 DOI: 10.1002/sim.1159] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
Stressful life events are now established as risk factors for the onset of affective disorder but few studies have investigated time-varying exposure effects. Discrete (grouped) time survival methods provide a flexible framework for evaluating multiple time-dependent covariates and time-varying covariate effects. Here, we use these methods to investigate the time-varying influence of life events on the onset of affective disorder. Various straightforward time-varying exposure models are compared, involving one or more (stepped) time-dependent covariates and time-dependent covariates constructed or estimated according to exponential decay. These models are applied to data from two quite different studies. The first, a small scale interviewer-based longitudinal study (n = 180) concerned with affective disorder onset following loss (or threat of loss) event experiences. The second, a questionnaire assessment as part of an ongoing population study (n = 3353), provides a history of marital loss events and of depressive disorder onset. From the first study the initial impact of loss events was found to decay with a half-life of 5 weeks. Psychological coping strategy was found to modify vulnerability to the adverse effects of these events. The second study revealed that while men had a lower immediate risk of disorder onset following loss event experience their risk period was greater than for women. Time-varying exposure effects were well described by the appropriate use of simple time-dependent covariates.
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Affiliation(s)
- Nicholas W J Wainwright
- Medical Research Council Staff, Strangeways Research Laboratory, Worts Causeway, Cambridge, CB1 8RN, U.K.
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