A Bayesian normal mixture accelerated failure time spatial model and its application to prostate cancer

In the United States, prostate cancer is the third most common cause of death from cancer in males of all ages, and the most common cause of death from cancer in males over age 75. It has been recognized that the incidence of the prostate cancer is high in African Americans, and its occurrence and progression may be impacted by geographical factors. In order to investigate the spatial effects and racial disparities for prostate cancer in Louisiana, in this article we propose a normal mixture accelerated failure time spatial model, which does not require the proportional hazards assumption and allows the multi-model distribution to be modeled. The proposed model is estimated with a Bayesian approach and it can be easily implemented in WinBUGS. Extensive simulations show that the proposed model provides decent flexibility for a variety of parametric error distributions. The proposed method is applied to 2000–2007 Louisiana prostate cancer data set from the Surveillance, Epidemiology and End Results Program. The results reveal the possible spatial pattern and racial disparities for prostate cancer in Louisiana.

[1]  C. Robert,et al.  Deviance information criteria for missing data models , 2006 .

[2]  L. Wasserman,et al.  Practical Bayesian Density Estimation Using Mixtures of Normals , 1997 .

[3]  Arnošt Komárek,et al.  Bayesian semi-parametric accelerated failure time model for paired doubly interval-censored data , 2006 .

[4]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[5]  David A. Schoenfeld,et al.  Partial residuals for the proportional hazards regression model , 1982 .

[6]  R. Henderson,et al.  Modeling Spatial Variation in Leukemia Survival Data , 2002 .

[7]  D. Blackwell,et al.  Ferguson Distributions Via Polya Urn Schemes , 1973 .

[8]  A. Gelfand,et al.  Bayesian analysis of proportional hazards models built from monotone functions. , 1995, Biometrics.

[9]  David Darmofal,et al.  Bayesian Spatial Survival Models for Political Event Processes , 2009 .

[10]  Carl E. Rasmussen,et al.  The Infinite Gaussian Mixture Model , 1999, NIPS.

[11]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[12]  O. Aalen,et al.  Spatial smoothing of cancer survival: a Bayesian approach. , 1999, Statistics in medicine.

[13]  C. Antoniak.  Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems , 1974 .

[14]  Lynn Kuo,et al.  Bayesian semiparametric inference for the accelerated failure‐time model , 1997 .

[15]  Ronald Christensen,et al.  Modelling accelerated failure time with a Dirichlet process , 1988 .

[16]  Emmanuel Lesaffre,et al.  BAYESIAN ACCELERATED FAILURE TIME MODEL FOR CORRELATED INTERVAL-CENSORED DATA WITH A NORMAL MIXTURE AS ERROR DISTRIBUTION , 2007 .

[17]  Dipak K. Dey,et al.  Semiparametric Proportional Odds Models for Spatially Correlated Survival Data , 2005, Lifetime data analysis.

[18]  L. Fahrmeir,et al.  Geoadditive Survival Models , 2006 .

[19]  E. Lesaffre,et al.  Accelerated Failure Time Model for Arbitrarily Censored Data With Smoothed Error Distribution , 2005 .

[20]  J. Besag,et al.  Bayesian image restoration, with two applications in spatial statistics , 1991 .

[21]  B. Carlin,et al.  Frailty modeling for spatially correlated survival data, with application to infant mortality in Minnesota. , 2003, Biostatistics.

[22]  Louise Ryan,et al.  Modeling Spatial Survival Data Using Semiparametric Frailty Models , 2002, Biometrics.

[23]  David J. Lunn,et al.  Generic reversible jump MCMC using graphical models , 2009, Stat. Comput..

[24]  P. Green,et al.  On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion) , 1997 .

[25]  Andrew B Lawson,et al.  Bayesian parametric accelerated failure time spatial model and its application to prostate cancer , 2011, Journal of applied statistics.

[26]  Bradley P. Carlin,et al.  Mixtures of Polya trees for flexible spatial frailty survival modelling , 2009, Biometrika.

[27]  S. Geisser,et al.  A Predictive Approach to Model Selection , 1979 .

[28]  D. Dey,et al.  Semiparametric Bayesian analysis of survival data , 1997 .

[29]  E. Martin,et al.  Probability density estimation via an infinite Gaussian mixture model: application to statistical process monitoring , 2006 .

[30]  E. Bedrick,et al.  Hypothesis Tests on Mixture Model Components with Applications in Ecology and Agriculture , 2010 .

[31]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .