Abstract
Many recent survival studies propose modeling data with a cure fraction, i.e., data in which part of the population is not susceptible to the event of interest. This event may occur more than once for the same individual (recurrent event). We then have a scenario of recurrent event data in the presence of a cure fraction, which may appear in various areas such as oncology, finance, industries, among others. This paper proposes a multiple time scale survival model to analyze recurrent events using a cure fraction. The objective is analyzing the efficiency of certain interventions so that the studied event will not happen again in terms of covariates and censoring. All estimates were obtained using a sampling-based approach, which allows information to be input beforehand with lower computational effort. Simulations were done based on a clinical scenario in order to observe some frequentist properties of the estimation procedure in the presence of small and moderate sample sizes. An application of a well-known set of real mammary tumor data is provided.
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References
Berkson J, Gage RP (1952) Survival curve for cancer patients following treatment. J Am Stat Assoc 42:501–515
Boag J (1949) Maximum likelihood estimates of the proportion of patients cured by cancer therapy. J R Stat Soc B 11:15–44
Chib S, Greenberg E (1995) Understanding the Metropolis–Hastings algorithm. Am Stat 49:327–335
Cobre J, Louzada-Neto F (2009) A sampling-based approach for a hybrid scale intensity model. J Stat, Adv Theory Appl 1:159–168
Cowless MK, Carlin BP (1996) Markov chain Monte Carlo convergence diagnostics: a comparative review. J Am Stat Assoc 91(434):883–904
Cox DR (1972) The statistical analysis of dependencies in point process. Stoch Point Process, Stat Anal Theory Appl, 55–66
Cox DR, Oakes D (1984) Analysis of Survival Data. Chapman and Hall, London
Farewell VT (1982) The use of mixture models for the analysis of survival data with long term survivors. Biometrics 38:1041–1046
Gail MH, Santner TJ, Brown CC (1980) An analysis of comparative carcinogenesis experiments based on multiple times to tumor. Biometrics 36:255–266
Gelfand AE, Smith AFM (1990) Sampling based approaches to calculating marginal densities. J Am Stat Assoc 85:398–409
Gelman A, Rubin BD (1992) Inference from iterative simulation using multiple sequences. Stat Sci 4:457–511
Geweke J (1992) Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. Bayesian Stat 4:169–193
Ghitany M, Maller R (1992) Asymptotic results for exponential mixture models with long-term survivors. Statistics 23:321–336
Ghitany M, Maller R, Zhou S (1994) Exponential mixture models with long-term survivors and covariates. J Multivar Anal 49:218–241
Goldman AI (1984) Survivorship analysis when cure is a possibility: a Monte Carlo study. Stat Med 3:153–163
Ibrahim JG, Chen MH, Sinha D (2001) Bayesian survival analysis. Springer, New York
Kuk AYC, Chen C-H (1992) A mixture model combining logistic regression with proportional hazards regression. Biometrika 79:531–541
Lawless J, Thiagarajah K (1996) A point-process model incorporating renewals and time trends, with application to repairable systems. Technometrics 38:131–138
Lawless JF (2003) Statistical models and methods for lifetime data. Jonh Wiley and Sons, New York
Louzada-Neto F (2004) A hybrid scale intensity model for recurrent event dada. Commun Stat 33:119–133
Louzada-Neto F (2008) Intensity models for parametric analysis of recurrent events data. Braz J Probab Stat 22(1):23–33
Louzada-Neto F, Cobre J. (2010) A multiple time scale survival model. Adv Appl Stat 14:1–15
Maller R, Zhou X (1996) Survival analysis with long-term survivors. Wiley Series, Chichester
Massey WA, Parker GA, Whitt W (1996) Estimating the parameters of a nonhomogeneous Poisson process with linear rate. Telecommun Syst 5(2):361–388
McDonald JW, Rosina A (2001) Mixture modelling of recurrent events times with long-term survivors: Analysis of Hutterite birth intervals. Stat Methods Appl 10:257–272
McShane B, Adrian M, Bradlow E, Fader P (2008) Count models based on Weibull interarrival times. J Bus Econ Stat 26(3):369–378
Ng SK, McLachlan G, Yau K, Lee A (2004) Modelling the distribution of ischaemic stroke-specific survival time using an em-based mixture approach with random effects adjustment. Stat Med 23:2729–2744
Paulino CD, Turkman MAA, Murteira B (2003) Estatísitca Bayesiana Fundação Calouste, Gulbenkian
Peng Y, Dear KBG, Denham JW (1998) A generalized f mixture model for cure rate estimation. Stat Med 17:813–830
Prentice RL, Willians BJ, Peterson AV (1981) On the regression analysis of multivariate failure time data. Biometrika 68:373–379
R Development Core Team (2006) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna
Spiegelhalter DJ, Thomas A, Best NG, Gilks WR (1999) WinBugs: Bayesian Inference Using Gibbs Sampling. MRC Biostatistics Unit, Cambridge
Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A (2002) Bayesian measures of model complexity and fit (with discussion). J R Stat Soc B 64:583–639
Sy JP, Taylor JMG (2000) Estimation in a proportional hazards cure model. Biometrics 56:227–336
Yannaros N (1994) Weibull renewal process. Ann Inst Stat Math 46(4):641–648
Yu B (2008) A frailty mixture cure model with application to hospital readmission data. Biom J 50(3):386–394
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Communicated by: Domingo Morales.
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Louzada, F., Cobre, J. A multiple time scale survival model with a cure fraction. TEST 21, 355–368 (2012). https://doi.org/10.1007/s11749-011-0247-1
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DOI: https://doi.org/10.1007/s11749-011-0247-1