Biometrika Advance Access originally published online on April 27, 2009
Biometrika 2009 96(2):263-276; doi:10.1093/biomet/asp014
Article |
Mixtures of Polya trees for flexible spatial frailty survival modelling
Eli Lilly & Company, Indianapolis, Indiana 46285, U.S.A. zhao0117{at}umn.edu
Division of Biostatistics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A. hans0058{at}umn.edu carli002{at}umn.edu
Received for publication 1 August 2007. Revision received 1 September 2008.
Mixtures of Polya trees offer a very flexible nonparametric approach for modelling time-to-event data. Many such settings also feature spatial association that requires further sophistication, either at the point level or at the lattice level. In this paper, we combine these two aspects within three competing survival models, obtaining a data analytic approach that remains computationally feasible in a fully hierarchical Bayesian framework using Markov chain Monte Carlo methods. We illustrate our proposed methods with an analysis of spatially oriented breast cancer survival data from the Surveillance, Epidemiology and End Results program of the National Cancer Institute. Our results indicate appreciable advantages for our approach over competing methods that impose unrealistic parametric assumptions, ignore spatial association or both.
Key Words: Areal data • Bayesian modelling • Breast cancer • Conditionally autoregressive model • Log pseudo marginal likelihood • Nonparametric modelling
References
-
Banerjee S., Carlin B. P. Spatial semiparametric proportional hazards models for analyzing infant mortality rates in Minnesota counties. In: Case Studies in Bayesian Statistics, Vol. VI—Gatsonis C., Kass R. E., Carriquiry A., Gelman A., Higdon D., Verdinelli D. K., Pauler I., eds. (2002) New York: Springer. 137–51.
Banerjee S., Carlin B. P. Semiparametric spatio-temporal frailty modelling. Environmetrics (2003) 14:523–35.[CrossRef][Web of Science]
Banerjee S., Carlin B. P., Gelfand A. E. Hierarchical Modeling and Analysis for Spatial Data (2004) Boca Raton, FL: Chapman and Hall/CRC Press.
Banerjee S., Dey D. K. Semi-parametric proportional odds models for spatially correlated survival data. Lifetime Data Anal. (2005) 11:175–91.[CrossRef][Web of Science][Medline]
Banerjee S., Wall M. M., Carlin B. P. Frailty modeling for spatially correlated survival data, with application to infant mortality in Minnesota. Biostatistics (2003) 4:123–42.[Abstract]
Barker P., Henderson R. Modelling converging hazards in survival analysis. Lifetime Data Anal. (2004) 10:263–81.[CrossRef][Web of Science][Medline]
Bedrick E. J., Christensen R., Johnson W. O. Bayesian accelerated failure time analysis with application to veterinary epidemiology. Statist. Med. (2000) 19:221–37.[CrossRef]
Besag J. Spatial interaction and the statistical analysis of lattice systems (with discussion. J. R. Statist. Soc. (1974) B 36:192–236.
Besag J., York J. C., Mollié A. Bayesian image restoration, with two applications in spatial statistics (with discussion). Ann. Inst. Statist. Math. (1991) 43:1–59.[CrossRef]
Carlin B. P., Louis T. A. Bayesian Methods for Data Analysis (2008) 3rd ed. Boca Raton, FL: Chapman and Hall/CRC Press.
Chen Y. Q., Jewell N. P. On a general class of semiparametric hazards regression models. Biometrika (2001) 88:687–702.
Clayton D., Cuzick J. Multivariate generalizations of the proportional hazards model. J. R. Statist. Soc. (1985) A 148:82–117.
Ferguson T. S. Prior distributions on spaces of probability measures. Ann. Statist. (1974) 2:615–29.[CrossRef]
Geisser S., Eddy W. F. A predictive approach to model selection. J. Am. Statist. Assoc. (1979) 74:153–60.[CrossRef][Web of Science]
Gore S. M., Pocock S. J., Kerr G. R. Regression models and non-proportional hazards in the analysis of breast cancer survival. Appl. Statist. (1984) 33:176–95.[CrossRef]
Gustafson P. On robustness and model flexibility in survival analysis: transformed hazards models and average effects. Biometrics (2007) 63:69–77.[CrossRef][Web of Science][Medline]
Hanson T. E. Inference for mixtures of finite Polya tree models. J. Am. Statist. Assoc. (2006) 101:1548–65.[CrossRef][Web of Science]
Hanson T. E., Johnson W. O. Modeling regression error with a mixture of Polya trees. J. Am. Statist. Assoc. (2002) 97:1020–33.[CrossRef][Web of Science]
Hanson T. E., Yang M. Bayesian semiparametric proportional odds models. Biometrics (2007) 63:88–95.[CrossRef][Web of Science][Medline]
Hennerfeind A., Brezger A., Fahrmeir L. Geoadditive survival models. J. Am. Statist. Assoc. (2006) 101:1065–75.[CrossRef][Web of Science]
Huzurbazar A. V. A censored data histogram. Commun. Statist. Simul. (2005) 34:113–20.[CrossRef]
Jeong J.-H., Jung S.-H., Wieand S. A parametric model for long-term follow-up data from phase III breast cancer clinical trials. Statist. Med. (2003) 22:339–52.[CrossRef]
Jin X., Carlin B. P. Multivariate parametric spatio-temporal models for county level breast cancer survival data. Lifetime Data Anal. (2005) 11:5–27.[CrossRef][Web of Science][Medline]
Lavine M. Some aspects of Polya tree distributions for statistical modeling. Ann. Statist. (1992) 20:1222–35.[CrossRef]
Li Y., Lin X. Semiparametric normal transformation models for spatially correlated survival data. J. Am. Statist. Assoc. (2006) 101:591–603.[CrossRef][Web of Science]
Li Y., Ryan L. Modeling spatial survival data using semiparametric frailty models. Biometrics (2002) 58:287–97.[CrossRef][Web of Science][Medline]
Mallick B. K., Walker S. G. A Bayesian semiparametric transformation model incorporating frailties. J. Statist. Plan. Infer. (2003) 112:159–74.[CrossRef]
Martinussen T., Scheike T. H. Dynamic Regression Models for Survival Data (2006) New York: Springer.
Scharfstein D. O., Tsiatis A. A., Gilbert P. B. Efficient estimation in the generalized odds-rate class of regression models for right-censored time-to-event data. Lifetime Data Anal. (1998) 4:355–91.[CrossRef][Web of Science][Medline]
Spiegelhalter D. J., Best N., Carlin B. P., van der Linde A. Bayesian measures of model complexity and fit (with discussion). J. R. Statist. Soc. (2002) B 64:583–639.[CrossRef]
Vaupel J. W., Manton K. G., Stallard E. The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography (1979) 16:439–54.[Web of Science][Medline]
Walker S. G., Mallick B. K. Hierarchical generalized linear models and frailty models with Bayesian nonparametric mixing. J. R. Statist. Soc. (1997) B 59:845–60.[CrossRef]
Walker S. G., Mallick B. K. Semiparametric accelerated life time model. Biometrics (1999) 55:477–83.[CrossRef][Web of Science][Medline]
Yakovlev A. Y., Tsodikov A. D., Boucher K., Kerber R. The shape of the hazard function in breast carcinoma: curability of the disease revisited. Cancer (1999) 85:1789–98.[CrossRef][Web of Science][Medline]
Yin G., Ibrahim J. G. A class of Bayesian shared gamma frailty models with multivariate failure time data. Biometrics (2005) 61:208–16.[CrossRef][Web of Science][Medline]
Zhang M., Davidian M. "Smooth" semiparametric regression analysis for arbitrarily censored time-to-event data. Biometrics (2008) 64:567–76.[CrossRef][Web of Science][Medline]
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