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http://dx.doi.org/10.29220/CSAM.2018.25.5.523

The Bivariate Kumaraswamy Weibull regression model: a complete classical and Bayesian analysis  

Fachini-Gomes, Juliana B. (Department of Statistics, University of Brasilia)
Ortega, Edwin M.M. (Department of Exact Sciences, University of Sao Paulo)
Cordeiro, Gauss M. (Department of Statistics, Federal University of Pernambuco)
Suzuki, Adriano K. (Department of Applied Mathematics and Statistics, University of Sao Paulo)
Publication Information
Communications for Statistical Applications and Methods / v.25, no.5, 2018 , pp. 523-544 More about this Journal
Abstract
Bivariate distributions play a fundamental role in survival and reliability studies. We consider a regression model for bivariate survival times under right-censored based on the bivariate Kumaraswamy Weibull (Cordeiro et al., Journal of the Franklin Institute, 347, 1399-1429, 2010) distribution to model the dependence of bivariate survival data. We describe some structural properties of the marginal distributions. The method of maximum likelihood and a Bayesian procedure are adopted to estimate the model parameters. We use diagnostic measures based on the local influence and Bayesian case influence diagnostics to detect influential observations in the new model. We also show that the estimates in the bivariate Kumaraswamy Weibull regression model are robust to deal with the presence of outliers in the data. In addition, we use some measures of goodness-of-fit to evaluate the bivariate Kumaraswamy Weibull regression model. The methodology is illustrated by means of a real lifetime data set for kidney patients.
Keywords
Bayesian inference; bivariate failure time; censored data; diagnostics; survival analysis;
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1 Barriga GDC, Louzada-Neto F, Ortega EMM, and Cancho VG (2010). A bivariate regression model for matched paired survival data: local influence and residual analysis, Statistics Methods and Applications, 19, 477-496.   DOI
2 Brooks SP (2002). Discussion on the paper by Spiegelhalter, Best, Carlin, and van der Linde, Journal of the Royal Statistical Society Series B, 64, 616-618.
3 Carlin BP and Louis TA (2001). Bayes and Empirical Bayes Methods for Data Analysis (2nd ed), Chapman & Hall/CRC, Boca Raton.
4 Cook RD (1977). Detection of influential observations in linear regression, Technometrics, 19, 15-18.
5 Cook RD (1986). Assessment of local influence (with discussion), Journal of the Royal Statistical Society B, 48, 133-169.
6 Cordeiro GM and de Castro M (2011). A new family of generalized distributions, Journal of Statistical Computation and Simulation, 81, 883-898.   DOI
7 Cordeiro GM, Ortega EMM, and Nadarajah S (2010). The Kumaraswamy Weibull distribution with application to failure data, Journal of the Franklin Institute, 347, 1399-1429.   DOI
8 da Cruz JN, Ortega EMM, and Cordeiro GM (2016). The log-odd log-logistic Weibull regression model: modelling, estimation, influence diagnostics and residual analysis, Journal of Statistical Computation and Simulation, 86, 1516-1538.   DOI
9 Dey D and Birmiwal L (1994). Robust Bayesian analysis using divergence measures, Statistics and Probability Letters, 20, 287-294.   DOI
10 Geweke J (1992). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: Bernardo JM, Berger JO, Dawid AP, Smith AFM (eds), Bayesian Statistics (4th ed), Oxford University Press, 169-188.
11 Hashimoto EM, Ortega EMM, Cancho VG, and Cordeiro GM (2013). On estimation and diagnostics analysis in log-generalized gamma regression model for interval-censored data, Statistics, 47, 379-398.   DOI
12 He W and Lawless JF (2005). Bivariate location-scale models for regression analysis, with applications to lifetime data, Journal of the Royal Statistical Society, 67, 63-78.   DOI
13 Hougaard, P. (1986). A class of multivariate failure time distributions, Biometrika, 73, 671-678.
14 Ibrahim JG, Chen MH, and Sinha D (2001). Bayesian Survival Analysis, Springer, New York.
15 Lange K (1999). Numerical Analysis for Statisticians, Springer, New York.
16 Lawless JF (2003). Statistical Models and Methods for Lifetime Data, Wiley, New York.
17 McGilchrist CA and Aisbett CW (1991). Regression with frailty in survival analysis, Biometrics, 47, 461-466.   DOI
18 Mudholkar GS, Srivastava DK, and Friemer M (1995). The exponentiated Weibull family: a reanalysis of the bus-motor-failure data, Technometrics, 37, 436-445.   DOI
19 Ortega EMM, Cordeiro GM, and Kattan MW (2013). The log-beta Weibull regression model with application to predict recurrence of prostate cancer, Statistical Papers, 54, 113-132.   DOI
20 Ortega EMM, Cordeiro GM, Campelo AK, Kattan MW, and Cancho VG (2015). A power series beta Weibull regression model for predicting breast carcinoma, Statistics in Medicine, 34, 1366-1388.   DOI
21 Peng F and Dey D (1995). Bayesian analysis of outlier problems using divergence measures, Canadian Journal of Statistics, 23, 199-213.   DOI
22 R Core Team (2016). R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org
23 Spiegelhalter DJ, Best NG, Carlin BP, and van der Linde A (2002). Bayesian measures of model complexity and fit, Journal of the Royal Statistical Society Series B, 64, 583-639.   DOI
24 Silva GO, Ortega EMM, and Cordeiro GM (2010). The beta modified Weibull distribution, Lifetime Data Analysis, 16, 409-430.   DOI