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The log-beta Weibull regression model with application to predict recurrence of prostate cancer

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Abstract

We study the properties of the called log-beta Weibull distribution defined by the logarithm of the beta Weibull random variable (Famoye et al. in J Stat Theory Appl 4:121–136, 2005; Lee et al. in J Mod Appl Stat Methods 6:173–186, 2007). An advantage of the new distribution is that it includes as special sub-models classical distributions reported in the lifetime literature. We obtain formal expressions for the moments, moment generating function, quantile function and mean deviations. We construct a regression model based on the new distribution to predict recurrence of prostate cancer for patients with clinically localized prostate cancer treated by open radical prostatectomy. It can be applied to censored data since it represents a parametric family of models that includes as special sub-models several widely-known regression models. The regression model was fitted to a data set of 1,324 eligible prostate cancer patients. We can predict recurrence free probability after the radical prostatectomy in terms of highly significant clinical and pathological explanatory variables associated with the recurrence of the disease. The predicted probabilities of remaining free of cancer progression are calculated under two nested models.

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References

  • Cancho VG, Bolfarine H, Achcar JA (1999) A Bayesian analysis for the exponentiated-Weibull distribution. J Appl Stat 8: 227–242

    MathSciNet  MATH  Google Scholar 

  • Cancho VG, Ortega EMM, Bolfarine H (2009) The log-exponentiated-Weibull regression models with cure rate: local influence and residual analysis. J Data Sci 7: 433–458

    Google Scholar 

  • Carrasco JMF, Ortega EMM, Cordeiro MG (2008) A generalized modified Weibull distribution for lifetime modeling. Comput Stat Data Anal 53: 450–462

    Article  MathSciNet  MATH  Google Scholar 

  • Cordeiro GM, de Castro M (2011) A new family of generalized distributions. J Stat Comput Simul 81: 883–898

    Article  MathSciNet  MATH  Google Scholar 

  • Cordeiro GM, Silva GO, Ortega EMM (2011) The beta-Weibull geometric distribution. Statistics. doi:10.1080/02331888.2011.577897

  • Cox DR (1972) Regression models and life tables (with discussion). J R Stat Soc Ser B (Stat Methodol) 34: 187–220

    MATH  Google Scholar 

  • Famoye F, Lee C, Olumolade O (2005) The beta-Weibull distribution. J Stat Theory Appl 4: 121–136

    MathSciNet  Google Scholar 

  • Gradshteyn IS, Ryzhik IM (2000) In: Jeffrey A, Zwillinger D (eds) Table of integrals, series, and products, 6th edn. Academic Press, New York

  • Gupta RD, Kundu D (1999) Generalized exponential distributions. Austral N Z J Stat 41: 173–188

    Article  MathSciNet  MATH  Google Scholar 

  • Hashimoto EM, Ortega EMM, Cancho VG, Cordeiro GM (2010) The log-exponentiated Weibull regression model for interval-censored data. Comput Stat Data Anal 54: 1017–1035

    Article  MathSciNet  MATH  Google Scholar 

  • Hjorth U (1980) A realibility distributions with increasing, decreasing, constant and bathtub failure rates. Technometrics 22: 99–107

    Article  MathSciNet  MATH  Google Scholar 

  • Kattan MW, Wheeler TM, Scardino PT (1999) Postoperative nomogram for disease recurrence after radical prostatectomy for prostate cancer. J Clin Oncol 17: 1499–1507

    Google Scholar 

  • Kundu D, Raqab MZ (2005) Generalized Rayleigh distribution: different methods of estimation. Comput Stat Data Anal 49: 187–200

    Article  MathSciNet  MATH  Google Scholar 

  • Lai CD, Xie M, Murthy DNP (2003) A modified Weibull distribution. Trans Reliab 52: 33–37

    Article  Google Scholar 

  • Lawless JF (2003) Statistical models and methods for lifetime data. Wiley, New York

    MATH  Google Scholar 

  • Lee C, Famoye F, Olumolade O (2007) Beta-Weibull distribution: some properties and applications to censored data. J Mod Appl Stat Methods 6: 173–186

    Google Scholar 

  • Mudholkar GS, Srivastava DK, Friemer M (1995) The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics 37: 436–445

    Article  MATH  Google Scholar 

  • Ortega EMM, Cancho VG, Bolfarine H (2006) Influence diagnostics in exponentiated-Weibull regression models with censored data. Stat Oper Res Trans 30: 172–192

    MathSciNet  Google Scholar 

  • Prudnikov AP, Brychkov YA, Marichev OI (1986) Integrals and series, vol 1. Gordon and Breach Science Publishers, Amsterdam

    MATH  Google Scholar 

  • Rajarshi S, Rajarshi MB (1988) Bathtub distributions. Commun Stat Theory Methods 17: 2521–2597

    MathSciNet  Google Scholar 

  • Smith RM, Bain LJ (1975) An exponential power life testing distributions. Commun Stat Theory Methods 4: 469–481

    Article  MATH  Google Scholar 

  • Stacy EW (1962) A generalization of the gamma distribution. Ann Math Stat 33: 1187–1192

    Article  MathSciNet  MATH  Google Scholar 

  • Stephenson AJ, Scardino PT, Eastham JA, Bianco FJ Jr, Dotan ZA, DiBlasio CJ, Reuther A, Klein EA, Kattan MW (2005) Postoperative nomogram predicting the 10-year probability of prostate cancer recurrence after radical prostatectomy. J Clin Oncol 23: 7005–7012

    Article  Google Scholar 

  • Xie M, Lai CD (1995) Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function. Reliab Eng Syst Saf 52: 87–93

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Departamento de Ciências Exatas, Universidade de São Paulo, Piracicaba, SP, 13418-900, Brazil

    Edwin M. M. Ortega

  2. Departamento de Estatística, Universidade Federal de Pernambuco, Recife, PE, 50740–540, Brazil

    Gauss M. Cordeiro

  3. Department of Quantitative Health Sciences, Cleveland Clinic, Desk JJN3-01, 9500 Euclid Avenue, Cleveland, OH, 44195, USA

    Michael W. Kattan

Authors
  1. Edwin M. M. Ortega
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  2. Gauss M. Cordeiro
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  3. Michael W. Kattan
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Correspondence to Edwin M. M. Ortega.

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Ortega, E.M.M., Cordeiro, G.M. & Kattan, M.W. The log-beta Weibull regression model with application to predict recurrence of prostate cancer. Stat Papers 54, 113–132 (2013). https://doi.org/10.1007/s00362-011-0414-1

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  • DOI: https://doi.org/10.1007/s00362-011-0414-1

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