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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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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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