Communications for Statistical Applications and Methods

  • 제24권3호
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  • Pages.271-290
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  • 2017
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Bivariate odd-log-logistic-Weibull regression model for oral health-related quality of life

  • Cruz, Jose N. da (Department of Exact Sciences, ESALQ-USP) ;
  • Ortega, Edwin M.M. (Department of Exact Sciences, ESALQ-USP) ;
  • Cordeiro, Gauss M. (Department of Statistics, UFPE) ;
  • Suzuki, Adriano K. (Department of Applied Mathematics and Statistics, ICMC-USP) ;
  • Mialhe, Fabio L. (Department of Community Dentistry, Division of Health Education and Health Promotion, UNICAMP)
  • 투고 : 2017.02.11
  • 심사 : 2017.05.08
  • 발행 : 2017.05.31
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초록

We study a bivariate response regression model with arbitrary marginal distributions and joint distributions using Frank and Clayton's families of copulas. The proposed model is used for fitting dependent bivariate data with explanatory variables using the log-odd log-logistic Weibull distribution. We consider likelihood inferential procedures based on constrained parameters. For different parameter settings and sample sizes, various simulation studies are performed and compared to the performance of the bivariate odd-log-logistic-Weibull regression model. Sensitivity analysis methods (such as local and total influence) are investigated under three perturbation schemes. The methodology is illustrated in a study to assess changes on schoolchildren's oral health-related quality of life (OHRQoL) in a follow-up exam after three years and to evaluate the impact of caries incidence on the OHRQoL of adolescents.

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참고문헌

  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, Statistical Methods and Applications, 19, 477-495. https://doi.org/10.1007/s10260-010-0140-1
  2. Chatterjee N and Shih J (2001). A bivariate cure-mixture approach for modeling familial association in diseases, Biometrics, 57, 779-786. https://doi.org/10.1111/j.0006-341X.2001.00779.x
  3. Cook RD (1986). Assessment of local influence, Journal of the Royal Statistical Society Series B (Methodological), 48, 133-169. https://doi.org/10.1111/j.2517-6161.1986.tb01398.x
  4. Cordeiro GM, Alizadeh M, Pescim RR, and Ortega EMM (2017a). The odd log-logistic generalized half-normal lifetime distribution: properties and applications, Communications in Statistics - Theory and Methods, 46, 4195-4214. https://doi.org/10.1080/03610926.2015.1080841
  5. Cordeiro GM, Alizadeh M, Ramires TG, and Ortega EMM (2017b). The generalized odd half-Cauchy family of distributions: properties and applications, Communications in Statistics - Theory and Methods, 46, 5685-5705. https://doi.org/10.1080/03610926.2015.1109665
  6. Cameron AC and Trivedi PK (1998). Regression Analysis of Count Data, Cambridge University Press, New York.
  7. Clayton DG (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence, Biometrika, 65, 141-151. https://doi.org/10.1093/biomet/65.1.141
  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. https://doi.org/10.1080/00949655.2015.1071376
  9. Da Silva Braga A, Cordeiro GM, Ortega EMM, and da Cruz JN (2016). The odd log-logistic normal distribution: theory and applications in analysis of experiments, Journal of Statistical Theory and Practice, 10, 311-335. https://doi.org/10.1080/15598608.2016.1141127
  10. De Paula JS, de Oliveira M, Soares MRSP, Chaves MGAM, and Mialhe FL (2012). Perfil epidemiologico dos pacientes atendidos no pronto atendimento da Faculdade de Odontologia da Universidade Federal de Juiz de Fora. Arquivos em Odontologia (UFMG), 48, 257-262.
  11. Doornik JA (2007). An Object-Oriented Matrix Language: Ox 5, Timberlake Consultants Press, London.
  12. Escobar LA and Meeker Jr WQ (1992). Assessing influence in regression analysis with censored data, Biometrics, 48, 507-528. https://doi.org/10.2307/2532306
  13. Eugene N, Lee C, and Famoye F (2002). Beta-normal distribution and its applications, Communications in Statistics - Theory and Methods, 31, 497-512. https://doi.org/10.1081/STA-120003130
  14. Fachini JB, Ortega EMM, and Cordeiro GM (2014). A bivariate regression model with cure fraction, Journal of Statistical Computation and Simulation, 84, 1580-1595. https://doi.org/10.1080/00949655.2012.755531
  15. Frank MJ (1979). On the simultaneous associativity of F(x, y) and x + y - F(x, y), Aequationes Mathematicae, 19, 194-226. https://doi.org/10.1007/BF02189866
  16. Genest C (1987). Frank's family of bivariate distributions, Biometrika, 74, 549-555. https://doi.org/10.1093/biomet/74.3.549
  17. 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. https://doi.org/10.1080/02331888.2011.605888
  18. Hashimoto EM, Ortega EMM, Cordeiro GM, and Cancho VG (2015). A new long-term survival model with interval-censored data, Sankhya B, 77, 207-239. https://doi.org/10.1007/s13571-015-0102-6
  19. He W and Lawless JF (2005). Bivariate location-scale models for regression analysis, with applications to lifetime data, Journal of the Royal Statistical Society Series B (Statistical Methodological), 67, 63-78. https://doi.org/10.1111/j.1467-9868.2005.00488.x
  20. Lesaffre E and Verbeke G (1998). Local influence in linear mixed models, Biometrics, 54, 570-582. https://doi.org/10.2307/3109764
  21. Nelsen RB (2006). An Introduction to Copulas (2nd ed), Springer, New York.
  22. Nunez JSR (2005). Modelagem Bayesiana para Dados de Sobrevivencia Bivariados Atraves de Copulas (Doctoral dissertation), University of Sao Paulo, Brasil (in Portuguese).
  23. 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. https://doi.org/10.1007/s00362-011-0414-1
  24. 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. https://doi.org/10.1002/sim.6416
  25. Ortega EMM, Cordeiro GM, Hashimoto EM, and Suzuki AK (2017). Regression models generated by gamma random variables with long-term survivors, Communications for Statistical Applications and Methods, 24, 43-65. https://doi.org/10.5351/CSAM.2017.24.1.043
  26. Ortega EMM, Lemonte AJ, Cordeiro GM, and da Cruz JN (2016). The odd Birnbaum-Saunders regression model with applications to lifetime data, Journal of Statistical Theory and Practice, 10, 780-804. https://doi.org/10.1080/15598608.2016.1224746
  27. Pettitt AN and Bin Daud I (1989). Case-weight measures of influence for proportional hazards regression, Journal of the Royal Statistical Society. Series C (Applied Statistics), 38, 51-67.
  28. Silva GO, Ortega EMM, and Cancho VG (2010). Log-Weibull extended regression model: estimation, sensitivity and residual analysis. Statistical Methodology, 7, 614-631. https://doi.org/10.1016/j.stamet.2010.05.004

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