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Survival model induced by discrete frailty for modeling of lifetime data with long-term survivors and change-point. (English) Zbl 07532941

Summary: Frailty models are used for modeling heterogeneity in the data analysis of lifetimes. Analysis that ignore frailty when it is present leads to incorrect inferences. In survival analysis, the distribution of frailty is generally assumed to be continuous and, in some cases, it may be appropriate to consider a discrete frailty distribution. Survival models induced by frailty with a continuous distribution are not appropriate for situations in which survival data contain experimental units where the event of interest has not happened even after a long period of observation (survival data with cure fraction), that is, situations with units having zero frailty. In this paper, we propose a new survival model induced by discrete frailty for modeling survival data in the presence of a proportion of long-term survivors and a single change point. We use the maximum likelihood method to estimate the model parameters and evaluate their performance by a Monte Carlo simulation study. The proposed approach is illustrated by analyzing a kidney infection recurrence data set.

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62-XX Statistics
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[1] Ata, N.; Özel, G., Survival functions for the frailty models based on the discrete compound Poisson process, Journal of Statistical Computation and Simulation, 83, 11, 2105-2116 (2013) · Zbl 1453.62660 · doi:10.1080/00949655.2012.679943
[2] Balakrishnan, N.; Peng, Y., Generalized gamma frailty model, Statistics in Medicine, 25, 16, 2797-2816 (2006) · doi:10.1002/sim.2375
[3] Cancho, V. G.; Rodrigues, J.; de Castro, M., A flexible model for survival data with a cure rate: A Bayesian approach, Journal of Applied Statistics, 38, 1, 57-70 (2011) · Zbl 1511.62315 · doi:10.1080/02664760903254052
[4] Caroni, C.; Crowder, M.; Kimber, A., Proportional hazards models with discrete frailty, Lifetime Data Analysis, 16, 3, 374-384 (2010) · Zbl 1322.62261 · doi:10.1007/s10985-010-9151-3
[5] dos Santos, D. M.; Davies, R. B.; Francis, B., Nonparametric hazard versus nonparametric frailty distribution in modelling recurrence of breast cancer, Journal of Statistical Planning and Inference, 47, 1-2, 111-127 (1995) · Zbl 0825.62902 · doi:10.1016/0378-3758(94)00125-F
[6] Hougaard, P., Life table methods for heterogeneous populations: Distributions describing the heterogeneity, Biometrika, 71, 1, 75-84 (1984) · Zbl 0553.92013 · doi:10.1093/biomet/71.1.75
[7] Hougaard, P., A class of multivanate failure time distributions, Biometrika, 73, 671-678 (1986) · Zbl 0613.62121 · doi:10.1093/biomet/73.3.671
[8] Lancaster, T., Econometric methods for the duration of unemployment, Econometrica, 47, 4, 939-956 (1979) · Zbl 0412.90018 · doi:10.2307/1914140
[9] Li, Y.; Qian, L.; Zhang, W., Estimation in a change-point hazard regression model with long-term survivors, Statistics & Probability Letters, 83, 7, 1683-1691 (2013) · Zbl 1277.62114 · doi:10.1016/j.spl.2013.03.026
[10] Liu, M.; Lu, W.; Shao, Y., A Monte Carlo approach for change-point detection in the Cox proportional hazards model, Statistics in Medicine, 27, 19, 3894-3909 (2008) · doi:10.1002/sim.3214
[11] Matthews, D. E.; Farewell, V. T., On testing for a constant hazard against a change-point alternative, Biometrics, 38, 2, 463-468 (1982) · doi:10.2307/2530460
[12] Matthews, D. E.; Farewell, V. T.; Pyke, R., Asymptotic score-statistic processes and tests for constant hazard against a change-point alternative, The Annals of Statistics, 13, 2, 583-591 (1985) · Zbl 0576.62032 · doi:10.1214/aos/1176349540
[13] Patra, K.; Dey, D. K., A general class of change point and change curve modeling for life time data, Annals of the Institute of Statistical Mathematics, 54, 3, 517-530 (2002) · Zbl 1015.62102 · doi:10.1023/A:1022454909407
[14] R-Team, R: A Language and Environment for Statistical Computing. (2017), Vienna, Austria: R Foundation for Statistical Computing, Vienna, Austria
[15] Rodrigues, J.; Cancho, V. G.; de Castro, M.; Louzada, F., On the unification of long-term survival models, Statistics & Probability Letters, 79, 6, 753-759 (2009) · Zbl 1349.62485 · doi:10.1016/j.spl.2008.10.029
[16] Rodrigues, J.; de Castro, M.; Cancho, V. G.; Balakrishnan, N., COM-Poisson cure rate survival models and an application to a cutaneous melanoma data, Journal of Statistical Planning and Inference, 139, 10, 3605-3611 (2009) · Zbl 1173.62074 · doi:10.1016/j.jspi.2009.04.014
[17] Taweab, Fauzia; Akma Ibrah, Noor, Cure rate models: A review of recent progress with a study of change-point cure models when cured is partially known, Journal of Applied Sciences, 14, 7, 609-616 (2014) · doi:10.3923/jas.2014.609.616
[18] Tsodikov, A. D.; Ibrahim, J. G.; Yakovlev, A. Y., Estimating cure rates from survival data: An alternative to two-component mixture models, Journal of the American Statistical Association, 98, 464, 1063-1078 (2003) · doi:10.1198/01622145030000001007
[19] Vaupel, J.; Manton, K.; Stallard, E., The impact of heterogeneity in individual frailty on the dynamics of mortality, Demography, 16, 3, 439-454 (1979)
[20] Zhang, W.; Qian, L.; Li, Y., Semiparametric sequential testing for multiple change points in piecewise constant hazard functions with long-term survivors, Communications in Statistics - Simulation and Computation, 43, 7, 1685-1699 (2014) · Zbl 1333.62235 · doi:10.1080/03610918.2012.742106
[21] Zhao, X.; Wu, X.; Zhou, X., A change-point model for survival data with long-term survivors, Statistica Sinica, 19, 377-390 (2009) · Zbl 1153.62077
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