×

zbMATH — the first resource for mathematics

Approximate Bayesian inference for mixture cure models. (English) Zbl 1458.62225
Summary: Cure models in survival analysis deal with populations in which a part of the individuals cannot experience the event of interest. Mixture cure models consider the target population as a mixture of susceptible and non-susceptible individuals. The statistical analysis of these models focuses on examining the probability of cure (incidence model) and inferring on the time to event in the susceptible subpopulation (latency model). Bayesian inference for mixture cure models has typically relied upon Markov chain Monte Carlo (MCMC) methods. The integrated nested Laplace approximation (INLA) is a recent and attractive approach for doing Bayesian inference but in its natural definition cannot fit mixture models. This paper focuses on the implementation of a feasible INLA extension for fitting standard mixture cure models. Our proposal is based on an iterative algorithm which combines the use of INLA for estimating the process of interest in each of the subpopulations in the study, and Gibbs sampling for computing the posterior distribution of the cure latent indicator variable which classifies individuals to the susceptible or non-susceptible subpopulations. We illustrated our approach by means of the analysis of two paradigmatic datasets in the framework of clinical trials. Outputs provide closing estimates and a substantial reduction of computational time in relation to those using MCMC.
MSC:
62N05 Reliability and life testing
62F15 Bayesian inference
62N02 Estimation in survival analysis and censored data
62P10 Applications of statistics to biology and medical sciences; meta analysis
Software:
R; JAGS; GMRFLib; R-INLA; Smcure
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Akerkar, R.; Martino, S.; Rue, H., Implementing approximate bayesian inference for survival analysis using integrated nested laplace approximations, Prepr Stat Nor Univ Sci Technol, 1, 1-38 (2010)
[2] Bivand, RS; Gómez-Rubio, V.; Rue, H., Approximate bayesian inference for spatial econometrics models, Spat Stat, 9, 146-165 (2014)
[3] Cai, C.; Zoua, Y.; Pengb, Y.; Zhanga, J., smcure: An r-package for estimating semiparametric mixture cure models, Comput Meth Prog Biomed, 108, 1255-1260 (2012)
[4] Christensen, R.; Wesley, J.; Branscum, A.; Hanson, TE, Bayesian ideas and data analysis: an introduction for scientists and statisticians (2011), Boca Raton: Chapman & Hall/CRC Press, Boca Raton
[5] Cox, DR, Regression models and life-tables, J R Stat Soc: Sei B (Methodol), 34, 2, 187-220 (1972)
[6] Diebolt J, Robert CP (1994) Estimation of finite mixture distributions through bayesian sampling. J R Stat Soc: Ser B (Methodol) 363-375 · Zbl 0796.62028
[7] Gelman, A.; Rubin, DB, Inference from iterative simulation using multiple sequences, Stat Sci, 7, 4, 457-472 (1992) · Zbl 1386.65060
[8] Gómez-Rubio V (2018) Mixture model fitting using conditional models and modal Gibbs sampling. arXiv:1712.09566 pp 1-37
[9] Gómez-Rubio, V.; Rue, H., Markov chain monte carlo with the integrated nested laplace approximation, Stat Comput, 28, 5, 1033-1051 (2018) · Zbl 1405.62078
[10] Hennerfeind, A.; Brezger, A.; Fahrmeir, L., Geoadditive survival models, J Am Stat Assoc, 101, 475, 1065-1075 (2006) · Zbl 1120.62331
[11] Hurtado Rúa, SM; Dey, DK, A transformation class for spatio-temporal survival data with a cure fraction, Stat Methods Med Res, 25, 167-187 (2016)
[12] Ibrahim, JG; Chen, MH; Sinha, D., Bayesian survival analysis (2001), New York: Springer, New York
[13] Kersey, JH; Weisdorf, D.; Nesbit, ME; LeBien, TW; Woods, WG; McGlave, PB; Kim, T.; Vallera, DA; Goldman, AI; Bostrom, B., Comparison of autologous and allogeneic bone marrow transplantation for treatment of high-risk refractory acute lymphoblastic leukemia, New Engl J Med, 317, 8, 461-467 (1987)
[14] Kirkwood, JM; Strawderman, MH; Ernstoff, MS; Smith, TJ; Borden, EC; Blum, RH, Interferon alfa-2b adjuvant therapy of high-risk resected cutaneous melanoma: the Eastern Cooperative Oncology Group Trial EST 1684, J Clin Oncol, 14, 1, 7-17 (1996)
[15] Lambert, PC; Thompson, JR; Weston, CL; Dickman, PW, Estimating and modeling the cure fraction in population-based cancer survival analysis, Biostatistics, 8, 3, 576-594 (2007) · Zbl 1121.62096
[16] Lázaro E, Armero C, Alvares D (2018) Bayesian regularization for flexible baseline hazard functions in Cox survival models (submitted)
[17] Loredo, TJ; Fougère, PF, From laplace to supernova sn 1987a: Bayesian inference in astrophysics, Maximum entropy and Bayesian methods, 81-142 (1989), Dordrecht: Kluwer Academic publishers, Dordrecht · Zbl 0736.62025
[18] Loredo, TJ; Feigelson, E.; Babu, G., Promise of Bayesian inference for astrophysics, Statistical challenges in modern astronomy, 275-297 (1992), New York: Springer, New York
[19] Marin, JM; Mengersen, K.; Robert, CP; Dey, D.; Rao, C., Bayesian modelling and inference on mixtures of distributions, Bayesian thinking, handbook of statistics, 459-507 (2005), Amsterdam: Elsevier, Amsterdam
[20] Martino, S.; Akerkar, R.; Rue, H., Approximate bayesian inference for survival models, Scand J Stat, 38, 3, 514-528 (2011) · Zbl 1246.62059
[21] Meeker, WQ, Limited failure population life tests: application to integrated circuit reliability, Technometrics, 29, 1, 51-65 (1987) · Zbl 0608.62125
[22] Peng, Y.; Taylor, J.; Klein, J.; van Houwelingen, H.; Ibrahim, JG; Scheike, TH, Cure models, Handbook of survival analysis, 113-134 (2014), Boca Raton: Chapman and Hall, Boca Raton
[23] Plummer M (2003) JAGS: a program for analysis of bayesian graphical models using Gibbs sampling. In: Proceedings of the 3rd international workshop on distributed statistical computing, vol 124, Vienna, Austria
[24] R: A language and environment for statistical computing (2014), Vienna: R Foundation for Statistical Computing, Vienna
[25] Robinson M (2014) Mixture cure models: simulation comparisons of methods in R and SAS. Ph.D. thesis, University of South Carolina, USA
[26] Rondeau, V.; Schaffner, E.; Corbière, F.; González, JR; Mathoulin-Pélissier, S., Cure frailty models for survival data: application to recurrences for breast cancer and to hospital readmissions for colorectal cancer, Stat Methods Med Res, 22, 243-260 (2013)
[27] Rue, H.; Held, L., Gaussian Markov random fields: theory and applications (2005), Boca Raton: Chapman & Hall/CRC Press, Boca Raton · Zbl 1093.60003
[28] Rue, H.; Martino, S.; Chopin, N., Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations, J R Stat Soc: Ser B (Methodol), 71, 2, 319-392 (2009) · Zbl 1248.62156
[29] Rue, H.; Riebler, A.; Sørbye, SH; Illian, JB; Simpson, DP; Lindgren, FK, Bayesian computing with INLA: a review, Annu Rev Stat Appl, 4, 395-421 (2017)
[30] Schmidt, P.; Witte, AD, Predicting criminal recidivism using ‘split population’ survival time models, J Econom, 40, 1, 141-159 (1989)
[31] Sposto, R., Cure model analysis in cancer: an application to data from the children’s cancer group, Stat Med, 21, 293-312 (2002)
[32] Stephens, M., Dealing with label switching in mixture models, J R Stat Soc: Ser B (Methodol), 62, 4, 795-809 (2000) · Zbl 0957.62020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.