Semiparametric spatio‐temporal frailty modeling

Recent developments in GIS have encouraged health science databases to incorporate geographical information about the subjects under study. Such databases have in turn generated interest among statisticians to develop and analyze models that account for spatial clustering and variation. In this article we develop a semiparametric (Cox) hierarchical Bayesian frailty model for capturing spatio‐temporal heterogeneity in the survival patterns of women diagnosed with breast cancer in Iowa. In the absence of appropriate surrogates for standards of treatments and health care for cancer patients in the different counties, epidemiologists and health‐care professionals are interested in discerning spatial patterns in survival from breast cancer that might be present among the counties. In addition, it is naturally of interest to see if the counties show discernible temporal trends over the years. The SEER (Surveillance Epidemiology and End Results) database from the National Cancer Institute (NCI) provides data on a cohort of breast cancer patients observed progressively through time, spanning 26 years. We implement our hierarchical spatio‐temporal models on data extracted from the database for the 99 counties of Iowa. Our results suggest log‐relative hazards that are generally flat initially, but steadily decrease for more recent years. Copyright © 2003 John Wiley & Sons, Ltd.

[1]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[2]  D. Cox,et al.  Analysis of Survival Data. , 1985 .

[3]  K. Mardia.  Multi-dimensional multivariate Gaussian Markov random fields with application to image processing , 1988 .

[4]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

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

[6]  D G Clayton,et al.  A Monte Carlo method for Bayesian inference in frailty models. , 1991, Biometrics.

[7]  L Bernardinelli,et al.  Empirical Bayes versus fully Bayesian analysis of geographical variation in disease risk. , 1992, Statistics in medicine.

[8]  W. Gilks,et al.  Adaptive Rejection Sampling for Gibbs Sampling , 1992 .

[9]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[10]  Bradley P. Carlin,et al.  Bayesian approaches for monitoring clinical trials with an application to toxoplasmic encephalitis prophylaxis , 1993 .

[11]  D. Clayton.  Some approaches to the analysis of recurrent event data , 1994, Statistical methods in medical research.

[12]  Kerrie Mengersen,et al.  [Bayesian Computation and Stochastic Systems]: Rejoinder , 1995 .

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

[14]  J. Besag,et al.  Bayesian Computation and Stochastic Systems , 1995 .

[15]  David B. Dunson,et al.  Bayesian Data Analysis , 2010 .

[16]  Bradley P. Carlin,et al.  BAYES AND EMPIRICAL BAYES METHODS FOR DATA ANALYSIS , 1996, Stat. Comput..

[17]  Bradley P. Carlin,et al.  Hierarchical Spatio-Temporal Mapping of Disease Rates , 1997 .

[18]  R. Kass,et al.  Nonconjugate Bayesian Estimation of Covariance Matrices and its Use in Hierarchical Models , 1999 .

[19]  P. Speckman,et al.  Posterior distribution of hierarchical models using CAR(1) distributions , 1999 .

[20]  B. Carlin,et al.  Hierarchical Proportional Hazards Regression Models for Highly Stratified Data , 1999, Biometrics.

[21]  B. Carlin,et al.  Identifiability and convergence issues for Markov chain Monte Carlo fitting of spatial models. , 2000, Statistics in medicine.

[22]  B. Carlin,et al.  Spatial Semiparametric Proportional Hazards Models for Analyzing Infant Mortality Rates in Minnesota Counties , 2002 .

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

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

[25]  A. Gelfand,et al.  Proper multivariate conditional autoregressive models for spatial data analysis. , 2003, Biostatistics.

[26]  B. Carlin,et al.  On the Precision of the Conditionally Autoregressive Prior in Spatial Models , 2003, Biometrics.