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A new latent cure rate marker model for survival data. (English) Zbl 1196.62142

Summary: To address an important risk classification issue that arises in clinical practice, we propose a new mixture model via latent cure rate markers for survival data with a cure fraction. In the proposed model, the latent cure rate markers are modeled via a multinomial logistic regression and patients who share the same cure rate are classified into the same risk group. Compared to available cure rate models, the proposed model fits better to data from a prostate cancer clinical trial. In addition, the proposed model can be used to determine the number of risk groups and to develop a predictive classification algorithm.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62J12 Generalized linear models (logistic models)
92C50 Medical applications (general)
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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[1] Agresti, A. (2002). Categorical Data Analysis , 2nd ed. Wiley, New York. · Zbl 1018.62002
[2] Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In International Symposium on Information Theory (B. N. Petrov and F. Csaki, eds.) 267-281. Akademia Kiado, Budapest. · Zbl 0283.62006
[3] Banerjee, T., Chen, M.-H., Dey, D. K. and Kim, S. (2007). Bayesian analysis of generalized odds-rate hazards models for survival data. Lifetime Data Anal. 13 241-260. · Zbl 1162.62430
[4] Berkson, J. and Gage, R. P. (1952). Survival curve for cancer patients following treatment. J. Amer. Statist. Assoc. 47 501-515.
[5] Broet, P., Rycke, Y. D., Tubert-Bitter, P., Lellouch, J., Asselain, B. and Moreau, T. (2001). A semiparametric approach for the two-sample comparison of survival times with long-term survivors. Biometrics 57 844-852. · Zbl 1209.62230
[6] Chen, M.-H., Ibrahim, J. G. and Sinha, D. (1999). A new Bayesian model for survival data with a surviving fraction. J. Amer. Statist. Assoc. 94 909-919. · Zbl 0996.62019
[7] Cooner, F., Banerjee, S., Carlin, B. P. and Sinha, D. (2007). Flexible cure rate modelling under latent activation schemes. J. Amer. Statist. Assoc. 102 560-572. · Zbl 1172.62331
[8] Cox, D. R. (1972). Regression models and life tables. J. Roy. Statist. Soc. Ser. B 34 187-220. · Zbl 0243.62041
[9] Cowles, M. K. and Carlin, B. P. (1996). Markov chain Monte Carlo convergence diagnostics: A comparative review. J. Amer. Statist. Assoc. 91 883-904. · Zbl 0869.62066
[10] D’Amico, A. V., Whittington, R., Malkowicz, S. B., Cote, K., Loffredo, M., Schultz, D., Chen, M.-H., Tomaszewski, J. E., Renshaw, A. A., Wein, A. and Richie, J. P. (2002). Biochemical outcome following radical prostatectomy or external beam radiation therapy for clinically localized prostate cancer in the PSA era. Cancer 95 281-286.
[11] D’Amico, A. V., Whittington, R., Malkowicz, S. B., Schultz, D., Tomaszewski, J. E., Kaplan, I., Beard, C. and Wein, A. (1998). Biochemical outcome after radical prostatectomy, external beam radiation therapy, or interstitial radiation therapy for clinically localized prostate cancer. The Journal of the American Medical Association 280 969-974.
[12] Dayton, C. M. (1999). Latent Class Scaling Analysis . Sage, Thousand Oaks, CA.
[13] Etzioni, R., Penson, D. F., Legler, J. M., di Tommaso, D., Boer, R., Gann, P. H. and Feuer, E. J. (2002). Overdiagnosis due to prostate-specific antigen screening: Lessons from U.S. prostate cancer incidence trends. Journal of the National Cancer Institute 94 981-990.
[14] Gelfand, A. E. and Dey, D. K. (1994). Bayesian model choice: Asymptotics and exact calculations. J. Roy. Statist. Soc. Ser. B 56 501-514. · Zbl 0800.62170
[15] Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 711-732. · Zbl 0861.62023
[16] Ibrahim, J. G., Chen, M.-H. and Sinha, D. (2001). Bayesian Survival Analysis . Springer, New York. · Zbl 0978.62091
[17] Kaplan, E. L. and Meier, P. (1958). Non-parametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53 457-500. · Zbl 0089.14801
[18] Kim, S., Xi, Y. and Chen, M.-H. (2009). Supplement to “A new latent cure rate marker for survival data.” DOI: 10.1214/08-AOAS238SUPP. · Zbl 1196.62142
[19] Larsen K. (2004). Joint analysis of time-to-event and multiple binary indicators of latent classes. Biometrics 60 85-92. · Zbl 1130.62375
[20] Lin, H., Turnbull, B. W., McCulloch, C. E. and Slate, E. H. (2002). Latent class models for joint analysis of longitudinal biomarker and event process data: Application to longitudinal prostate-specific antigen readings and prostate cancer. J. Amer. Statist. Assoc. 97 53-65. · Zbl 1073.62582
[21] Liu, M., Lu, W. and Shao, Y. (2006). Interval mapping of quantitative trait loci for time-to-event data with the proportional hazards mixture cure model. Biometrics 62 1053-1061. · Zbl 1116.62123
[22] Lopes, H. F. and West, M. (2004). Bayesian model assessment in factor analysis. Statist. Sinica 14 41-67. · Zbl 1035.62060
[23] Maller, R. A. and Zhou, S. (1996). Survival Analysis With Long Term Survivors . Wiley, New York. · Zbl 1151.62350
[24] Martin, N. E., Chen, M.-H., Catalona, W. J., Loeb, S., Roehl, K. A. and D’Amico, A. V. (2008). The influence of serial prostate-specific antigen (PSA) screening on the PSA velocity at diagnosis. Cancer 113 717-722.
[25] Patterson, B. H., Dayton, C. M. and Graubard, B. I. (2002). Latent class analysis of complex sample survey data: Application to dietary data (with discussion). J. Amer. Statist. Assoc. 97 721-741. · Zbl 1073.62585
[26] Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit (with discussion). J. Roy. Statist. Soc. Ser. B 64 583-639. · Zbl 1067.62010
[27] Tsodikov, A. D. (2002). Semiparametric models of long- and short-term survival: An application to the analysis of breast cancer survival in Utah by age and stage. Statistics in Medicine 21 895-920.
[28] Tsodikov, A. D., Ibrahim, J. G. and Yakovlev, A. Y. (2003). Estimating cure rates from survival data: An alternative to two-component mixture models. J. Amer. Statist. Assoc. 98 1063-1078.
[29] Wang, L. and Arnold, K. (2002). Press release: Prostate cancer incidence trends reveal extent of screening-related overdiagnosis. Journal of the National Cancer Institute 94 957.
[30] Yakovlev, A. Y. and Tsodikov, A. D. (1996). Stochastic Models of Tumor Latency and Their Biostatistical Applications . World Scientific, River Edge, NJ. · Zbl 0919.92024
[31] Yakovlev, A. Y., Asselain, B., Bardou, V. J., Fourquet, A., Hoang, T., Rochefediere, A. and Tsodikov, A. D. (1993). A simple stochastic model of tumor recurrence and its applications to data on premenopausal breast cancer. In Biometrie et Analyse de Dormees Spatio-Temporelles 12 (B. Asselain, M. Boniface, C. Duby, C. Lopez, J. P. Masson and J. Tranchefort, eds.) 66-82. Société Francaise de Biométrie, ENSA Renned, France.
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