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Discrete and continuous bivariate lifetime models in presence of cure rate: a comparative study under Bayesian approach. (English) Zbl 1516.62243

J. Appl. Stat. 46, No. 3, 449-467 (2019); corrigendum ibid. 46, No. 3, 577-579 (2019).
Summary: The modeling and analysis of lifetime data in which the main endpoints are the times when an event of interest occurs is of great interest in medical studies. In these studies, it is common that two or more lifetimes associated with the same unit such as the times to deterioration levels or the times to reaction to a treatment in pairs of organs like lungs, kidneys, eyes or ears. In medical applications, it is also possible that a cure rate is present and needed to be modeled with lifetime data with long-term survivors. This paper presented a comparative study under a Bayesian approach among some existing continuous and discrete bivariate distributions such as the bivariate exponential distributions and the bivariate geometric distributions in presence of cure rate, censored data and covariates. In presence of lifetimes related to cured patients, it is assumed standard mixture cure rate models in the data analysis. The posterior summaries of interest are obtained using Markov Chain Monte Carlo methods. To illustrate the proposed methodology two real medical data sets are considered.

MSC:

62-XX Statistics

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[1] Achcar, J. A.; Leandro, R. A., Use of Markov Chain Monte Carlo methods in a Bayesian analysis of the Block and Basu bivariate exponential distribution, Ann. Inst. Statist. Math., 50, 403-416 (1998) · Zbl 0912.62037 · doi:10.1023/A:1003582409664
[2] Achcar, J. A.; Coelho-Barros, E. A.; Mazucheli, J., Cure fraction models using mixture and non-mixture models, Tatra. Mt. Math. Publ., 51, 1-9 (2012) · Zbl 1313.62137
[3] Achcar, J. A.; Coelho-Barros, E. A.; Mazucheli, J., Block and Basu bivariate lifetime distribution in the presence of cure fraction, J. Appl. Stat., 40, 1864-1874 (2013) · Zbl 1514.62377 · doi:10.1080/02664763.2013.798630
[4] Achcar, J. A.; Davarzani, N.; Souza, R., Basu-Dhar bivariate geometric distribution in the presence of covariates and censored data: A Bayesian approach, J. Appl. Stat., 43, 1636-1648 (2016) · Zbl 1514.62376 · doi:10.1080/02664763.2015.1117589
[5] Arnold, B. C., A characterization of the exponential distribution by multivariate geometric compounding, Sankhyā, 37, 164-173 (1975) · Zbl 0358.60025
[6] Basu, A. P.; Dhar, S., Bivariate geometric distribution, J. Appl. Statist. Sci., 2, 33-44 (1995) · Zbl 0823.62079
[7] Block, H. W.; Basu, A., A continuous bivariate exponential extension, J. Amer. Statist. Assoc., 69, 1031-1037 (1974) · Zbl 0299.62027
[8] Box, G. E.; Tiao, G. C., Bayesian Inference in Statistical Analysis, 40 (2011), John Wiley & Sons
[9] Cancho, V. G.; Bolfarine, H., Modeling the presence of immunes by using the exponentiated-Weibull model, J. Appl. Stat., 28, 659-671 (2001) · Zbl 0991.62084 · doi:10.1080/02664760120059200
[10] Chib, S.; Greenberg, E., Understanding the Metropolis-Hastings algorithm, Am. Stat., 49, 327-335 (1995)
[11] Cox, D. R., Regression models and life tables (with discussion), J. R. Stat. Soc. Ser. B, 34, 187-220 (1972) · Zbl 0243.62041
[12] Davarzani, N.; Acgcar, J. A.; Smirno, E. N.; Peeters, R., Bivariate lifetime geometric distribution in presence of cure fractions, J. Data Sci., 13, 755-770 (2015)
[13] De Angelis, R.; Capocaccia, R.; Hakulinen, T.; Soderman, B.; Verdecchia, A., Mixture models for cancer survival analysis: Application to population-based data with covariates, Stat. Med., 18, 441-454 (1999) · doi:10.1002/(SICI)1097-0258(19990228)18:4<441::AID-SIM23>3.0.CO;2-M
[14] Gelfand, A. E.; Smith, A. F.M., Sampling-based approaches to calculating marginal densities, J. Amer. Statist. Assoc., 85, 398-409 (1990) · Zbl 0702.62020 · doi:10.1080/01621459.1990.10476213
[15] Gumbel, E. J., Bivariate exponential distributions, J. Amer. Statist. Assoc., 55, 698-707 (1960) · Zbl 0099.14501 · doi:10.1080/01621459.1960.10483368
[16] Huster, W. J.; Brookmeyer, R.; Self, S. G., Modelling paired survival data with covariates, Biometrics, 45, 145-156 (1989) · Zbl 0715.62224 · doi:10.2307/2532041
[17] Ibrahim, J. G.; Chen, M. H.; Sinha, D., Bayesian Survival Analysis (2005), Wiley Online Library
[18] John, G., Louis, C., Berner, A., and Genné, D., Data from: Tobacco stained fingers and its association with death and hospital admission: A retrospective cohort study (2015). Available at doi:10.5061/dryad.4478v.
[19] John, G.; Louis, C.; Berner, A.; Genné, D., Tobacco stained fingers and its association with death and hospital admission: A retrospective cohort study, PLoS ONE, 10, e0138211 (2015) · doi:10.1371/journal.pone.0138211
[20] John, G.; Pasche, S.; Rothen, N.; Charmoy, A.; Delhumeau-Cartier, C.; Genné, D., Tobacco-stained fingers: A clue for smoking-related disease or harmful alcohol use? A case-control study, BMJ Open, 3, e003304 (2013) · doi:10.1136/bmjopen-2013-003304
[21] Kaplan, E. L.; Meier, P., Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc., 53, 457-481 (1958) · Zbl 0089.14801 · doi:10.1080/01621459.1958.10501452
[22] Lambert, P. C.; Thompson, J. R.; Weston, C. L.; Dickman, P. W., Estimating and modeling the cure fraction in population-based cancer survival analysis, Biostatistics, 8, 576-594 (2007) · Zbl 1121.62096 · doi:10.1093/biostatistics/kxl030
[23] Lu, W., Efficient estimation for an accelerated failure time model with a cure fraction, Statist. Sinica, 20, 661 (2010) · Zbl 1187.62069
[24] Maller, R. A.; Zhou, X., Survival Analysis with Long-term Survivors (1996), Wiley: Wiley, New York · Zbl 1151.62350
[25] Othus, M.; Barlogie, B.; LeBlanc, M. L.; Crowley, J. J., Cure models as a useful statistical tool for analyzing survival, Clin. Cancer Res., 18, 3731-3736 (2012) · doi:10.1158/1078-0432.CCR-11-2859
[26] Price, D. L.; Manatunga, A. K., Modelling survival data with a cured fraction using frailty models, Stat. Med., 20, 1515-1527 (2001) · doi:10.1002/sim.687
[27] R CoreTeam, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria (2016). Available at https://www.R-project.org/.
[28] Schemper, M.; Kaider, A.; Wakounig, S.; Heinze, G., Estimating the correlation of bivariate failure times under censoring, Stat. Med., 32, 4781-4790 (2013) · doi:10.1002/sim.5874
[29] Spiegelhalter, D.; Thomas, A.; Best, N.; Lunn, D., OpenBUGS User Manual, Version 3.0. 2 (2007), MRC Biostatistics Unit: MRC Biostatistics Unit, Cambridge
[30] Sun, K.; Basu, A. P., A characterization of a bivariate geometric distribution, Statist. Probab. Lett., 23, 307-311 (1995) · Zbl 0830.62016 · doi:10.1016/0167-7152(94)00129-V
[31] Tsodikov, A.; Ibrahim, J.; Yakovlev, A., Estimating cure rates from survival data: An alternative to two-component mixture models, J. Amer. Statist. Assoc., 98, 1063-1078 (2003) · doi:10.1198/01622145030000001007
[32] Vahidpour, M., Cure rate models, Ph.D. diss., École Polytechnique de Montréal, 2016.
[33] Wienke, A.; Lichtenstein, P.; Yashin, A. I., A bivariate frailty model with a cure fraction for modeling familial correlations in diseases, Biometrics, 59, 1178-1183 (2003) · Zbl 1274.62903 · doi:10.1111/j.0006-341X.2003.00135.x
[34] Wienke, A.; Locatelli, I.; Yashin, A. I., The modelling of a cure fraction in bivariate time-to-event data, Austrian J. Statist., 35, 67-76 (2006) · doi:10.17713/ajs.v35i1.349
[35] Yin, G.; Ibrahim, J. G., Cure rate models: A unified approach, Canad. J. Statist., 33, 559-570 (2005) · Zbl 1098.62127 · doi:10.1002/cjs.5550330407
[36] Yu, B.; Tiwari, R. C.; Cronin, K. A.; Feuer, E. J., Cure fraction estimation from the mixture cure models for grouped survival data, Stat. Med., 23, 1733-1747 (2004) · doi:10.1002/sim.1774
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