A hierarchical Bayesian analysis for bivariate Weibull distribution under left-censoring scheme

References

• O. Aalen, O. Borgan, and H. Gjessing, Survival and Event History Analysis: a Process Point of View, Springer Science & Business Media, 2008.
   Google Scholar
• J.A. Achcar, E.A. Coelho-Barros, and J. Mazucheli, Cure fraction models using mixture and non-mixture models, Tatra Mt. Math. Publ. 51 (2012), pp. 1–9.
   Google Scholar
• M. Aitkin, Posterior Bayes factors, J. R. Stat. Soc. B Methodol. 53 (1991), pp. 111–128.
   Google Scholar
• E.M. Almetwally, H.Z. Muhammed, and E.S.A. El-Sherpieny, Bivariate Weibull distribution: properties and different methods of estimation, Ann. Data Sci. 7 (2020), pp. 163–193.
   Google Scholar
• B.C. Arnold and D. Strauss, Bivariate distributions with exponential conditionals, J. Am. Stat. Assoc. 83 (1988), pp. 522–527.
   Web of Science ®Google Scholar
• N. Best, A. Mason, and S. Richardson, Two-pronged strategy for using dic to compare selection models with non-ignorable missing responses, Bayesian Anal. 7 (2012), pp. 109–146.
   Web of Science ®Google Scholar
• H.W. Block and A. Basu, A continuous, bivariate exponential extension, J. Am. Stat. Assoc. 69 (1974), pp. 1031–1037.
   Web of Science ®Google Scholar
• J. Buckley and I. James, Linear regression with censored data, Biometrika 66 (1979), pp. 429–436.
   Web of Science ®Google Scholar
• G. Celeux, F. Forbes, C.P. Robert, and D.M. Titterington, Deviance information criteria for missing data models, Bayesian Anal. 1 (2006), pp. 651–673.
   Web of Science ®Google Scholar
• S. Chib and E. Greenberg, Understanding the Metropolis-Hastings algorithm, Am. Stat. 49 (1995), pp. 327–335.
   Web of Science ®Google Scholar
• C. Chiosi, Fundamentals of stellar evolution theory: Understanding the hrd, Stellar astrophysics for the local group: VIII Canary Islands Winter School of Astrophysics, 1998, p. 1.
   Google Scholar
• D. Clayton and J. Cuzick, Multivariate generalizations of the proportional hazards model, J. R. Stat. Soc. A General. 148 (1985), pp. 82–108.
   Web of Science ®Google Scholar
• D. Collett, Modelling Survival Data in Medical Research, 2nd ed., Chapman and Hall, New York, 2003.
   Google Scholar
• G.W. Collins, The fundamentals of stellar astrophysics, WH Freeman and Co., New York, 1989, p. 512 .
   Google Scholar
• D.R. Cox, Regression models and life tables, J. R. Stat. Soc. B 34 (1972), pp. 187–220.
   Google Scholar
• D.R. Cox and D. Oakes, Analysis of Survival Data, Chapman & Hall, London, 1984.
   Google Scholar
• R.P. de Oliveira, J.A. Achcar, D. Peralta, and J. Mazucheli, Discrete and continuous bivariate lifetime models in presence of cure rate: a comparative study under bayesian approach, J. Appl. Stat. 46 (2019), pp. 449–467.
   Web of Science ®Google Scholar
• R.P. de Oliveira, A.F. Menezes, J. Mazucheli, and J.A. Achcar, Mixture and nonmixture cure fraction models assuming discrete lifetimes: application to a pelvic sarcoma dataset, Biom. J. 61 (2019), pp. 813–826.
   PubMed Web of Science ®Google Scholar
• R.P. de Oliveira, Multivariate lifetime models to evaluate long-term survivors in medical studies, Ph.D. diss., University of São Paulo, 2019.
   Google Scholar
• R.P. de Oliveira, M.V. de Oliveira Peres, J.A. Achcar, and N. Davarzani, Inference for the trivariate Marshall-Olkin-Weibull distribution in presence of right-censored data., Chil. J. Stat. 11 (2020), pp. 95–116.
   Web of Science ®Google Scholar
• R.P. de Oliveira, J.A. Achcar, J. Mazucheli, and W. Bertoli, A new class of bivariate Lindley distributions based on stress and shock models and some of their reliability properties, Reliab. Eng. Syst. Saf. 211 (2021), pp. 107528.
   Web of Science ®Google Scholar
• F. Del Greco M, C. Pattaro, C. Minelli, and J.R. Thompson, Bayesian analysis of censored response data in family-based genetic association studies, Biom. J. 58 (2016), pp. 1039–1053.
   PubMed Web of Science ®Google Scholar
• G.E. Dinse, T.A. Jusko, L.A. Ho, K. Annam, B.I. Graubard, I. Hertz-Picciotto, F.W. Miller, B.W. Gillespie, and C.R. Weinberg, Accommodating measurements below a limit of detection: a novel application of cox regression, Am. J. Epidemiol. 179 (2014), pp. 1018–1024.
   PubMed Web of Science ®Google Scholar
• C.A. dos Santos and J.A. Achcar, A bayesian analysis for the block and basu bivariate exponential distribution in the presence of covariates and censored data, J. Appl. Stat. 38 (2011), pp. 2213–2223.
   Web of Science ®Google Scholar
• F. Downton, Bivariate exponential distributions in reliability theory, J. R. Stat. Soc. B Methodol. 32 (1970), pp. 408–417.
   Google Scholar
• P.H. Eilers, E. Röder, H.F. Savelkoul, and R.G. van Wijk, Quantile regression for the statistical analysis of immunological data with many non-detects, BMC. Immunol. 13 (2012), pp. 1–8.
   PubMed Web of Science ®Google Scholar
• A.Q. Flores, Testing copula functions as a method to derive bivariate Weibull distributions, in American Political Science Association (APSA), Annual Meeting. Citeseer, 2009, pp. 1–19.
   Google Scholar
• A.E. Gelfand and A.F. Smith, Sampling-based approaches to calculating marginal densities, J. Am. Stat. Assoc. 85 (1990), pp. 398–409.
   Web of Science ®Google Scholar
• A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari, and D.B. Rubin, Bayesian Data Analysis, CRC press, 2013.
   Google Scholar
• W. Gilks, S. Richardson, and D. Spieglhalter, Markov chain monte carlo in practice, 1996, p. 520.
   Google Scholar
• B.W. Gillespie, Q. Chen, H. Reichert, A. Franzblau, E. Hedgeman, J. Lepkowski, P. Adriaens, A. Demond, W. Luksemburg, and D.H. Garabrant, Estimating population distributions when some data are below a limit of detection by using a reverse kaplan-meier estimator, Epidemiology (2010), pp. S64–S70.
   PubMed Web of Science ®Google Scholar
• E.J. Gumbel, Bivariate exponential distributions, J. Am. Stat. Assoc. 55 (1960), pp. 698–707.
   Web of Science ®Google Scholar
• A.G. Hawkes, A bivariate exponential distribution with applications to reliability, J. R. Stat. Soc. B Methodol. 34 (1972), pp. 129–131.
   Google Scholar
• D.R. Helsel, More than obvious: better methods for interpreting nondetect data, Environ. Sci. Technol. 39 (2005), pp. 419A–423A.
   PubMed Web of Science ®Google Scholar
• P. Hougaard, A class of multivariate failure time distributions, Biometrika 73 (1986), pp. 671–678.
   Web of Science ®Google Scholar
• J.P. Hughes, Mixed effects models with censored data with application to hiv rna levels, Biometrics 55 (1999), pp. 625–629.
   PubMed Web of Science ®Google Scholar
• H. Jacqmin-Gadda, R. Thiébaut, G. Chêne, and D. Commenges, Analysis of left-censored longitudinal data with application to viral load in hiv infection, Biostatistics 1 (2000), pp. 355–368.
   PubMedGoogle Scholar
• J.D. Kalbfleisch and R.L. Prentice, The Statistical Analysis of Failure Time Data, 2nd ed., Wiley, New York, NY, 2002.
   Google Scholar
• J.P. Klein and M.L. Moeschberger, Survival Analysis: Techniques for Censored and Truncated Data, Springer-Verlag, New York, 1997.
   Google Scholar
• D. Kundu and A.K. Dey, Estimating the parameters of the Marshall–Olkin bivariate Weibull distribution by EM algorithm, Comput. Stat. Data. Anal. 53 (2009), pp. 956–965.
   Web of Science ®Google Scholar
• D. Kundu and A.K. Gupta, Bayes estimation for the Marshall–Olkin bivariate Weibull distribution, Comput. Stat. Data. Anal. 57 (2013), pp. 271–281.
   Web of Science ®Google Scholar
• J.F. Lawless, Statistical Models and Methods for Lifetime Data, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1982.
   Google Scholar
• E.T. Lee and J.W. Wang, Statistical Methods for Survival Data Analysis, 3rd ed., Wiley Series in Probability and Statistics, Wiley-Interscience [John Wiley & Sons], Hoboken, NJ, 2003.
   Google Scholar
• M. Lee, L. Kong, and L. Weissfeld, Multiple imputation for left-censored biomarker data based on gibbs sampling method, Stat. Med. 31 (2012), pp. 1838–1848.
   PubMed Web of Science ®Google Scholar
• H.S. Lynn, Maximum likelihood inference for left-censored hiv rna data, Stat. Med. 20 (2001), pp. 33–45.
   PubMed Web of Science ®Google Scholar
• R.A. Maller and X. Zhou, Survival Analysis with Long-Term Survivors, Wiley, New York, 1996.
   Google Scholar
• I.C. Marschner, R.A. Betensky, V. DeGruttola, S.M. Hammer, and D.R. Kuritzkes, Clinical trials using hiv-1 rna-based primary endpoints: statistical analysis and potential biases., J. Acquir. Immune Defic. Syndr. Hum. Retrovirol. Offic. Publ. Int. Retrovirol. Assoc. 20 (1999), pp. 220–227.
   PubMed Web of Science ®Google Scholar
• A.W. Marshall and I. Olkin, A multivariate exponential distribution, J. Am. Stat. Assoc. 62 (1967), pp. 30–44.
   Web of Science ®Google Scholar
• A.W. Marshall and I. Olkin, A family of bivariate distributions generated by the bivariate bernoulli distribution, J. Am. Stat. Assoc. 80 (1985), pp. 332–338.
   Web of Science ®Google Scholar
• G. Martínez-Flórez, H. Bolfarine, and H.W. Gómez, The alpha-power Tobit model, Commun. Stat. Theory Methods. 42 (2013), pp. 633–643.
   Web of Science ®Google Scholar
• C. McGilchrist and C. Aisbett, Regression with frailty in survival analysis, Biometrics 47 (1991), pp. 461–466.
   PubMed Web of Science ®Google Scholar
• M. Mills, Introducing Survival and Event History Analysis, Sage, 2010.
   Google Scholar
• L. Nie, H. Chu, C. Liu, S.R. Cole, A. Vexler, and E.F. Schisterman, Linear regression with an independent variable subject to a detection limit, Epidemiology (Cambridge, Mass.) 21 (2010), pp. S17–S24.
   PubMed Web of Science ®Google Scholar
• D. Oakes, Semiparametric inference in a model for association in bivanate survival data, Biometrika 73 (1986), pp. 353–361.
   Web of Science ®Google Scholar
• D. Oakes, Bivariate survival models induced by frailties, J. Am. Stat. Assoc. 84 (1989), pp. 487–493.
   Web of Science ®Google Scholar
• W.B. Paxton, R.W. Coombs, M.J. McElrath, M.C. Keefer, J. Hughes, F. Sinangil, D. Chernoff, L. Demeter, B. Williams, and L. Corey, et al. Longitudinal analysis of quantitative virologic measures in human immunodeficiency virus-infected subjects with ≥ 400 cd4 lymphocytes: implications for applying measurements to individual patients, J. Infect. Dis. 175 (1997), pp. 247–254.
   PubMed Web of Science ®Google Scholar
• J.L. Powell, Least absolute deviations estimation for the censored regression model, J. Econom. 25 (1984), pp. 303–325.
   Web of Science ®Google Scholar
• J.L. Powell, Censored regression quantiles, J. Econom. 32 (1986), pp. 143–155.
   Web of Science ®Google Scholar
• C.A. Santos and J.A. Achcar, A Bayesian analysis in the presence of covariates for multivariate survival data: an example of application, Rev. Colomb. Estad. 34 (2011), pp. 111–131.
   Google Scholar
• N. Santos, G. Israelian, R.G. López, M. Mayor, R. Rebolo, S. Randich, A. Ecuvillon, and C.D. Cerdeña, Are beryllium abundances anomalous in stars with giant planets?, Astron. Astrophys. 427 (2004), pp. 1085–1096.
   Web of Science ®Google Scholar
• J.H. Shih, Models and analysis for multivariate failure time data 1992.
   Google Scholar
• J.D. Singer, J.B. Willett, and J.B. Willett, et al. Applied Longitudinal Data Analysis: modeling change and event occurrence, Oxford University Press, 2003.
   Google Scholar
• P. Soret, M. Avalos, L. Wittkop, D. Commenges, and R. Thiébaut, Lasso regularization for left-censored gaussian outcome and high-dimensional predictors, BMC. Med. Res. Methodol. 18 (2018), pp. 1–13.
   PubMed Web of Science ®Google Scholar
• D.J. Spiegelhalter, N.G. Best, B.P. Carlin, and A. Van Der Linde, Bayesian measures of model complexity and fit, J. R. Stat. Soc. B Stat. Methodol. 64 (2002), pp. 583–639.
   Google Scholar
• D. Spiegelhalter, A. Thomas, N. Best, and D. Lunn, Winbugs user manual 2003.
   Google Scholar
• T.M. Therneau and P.M. Grambsch, Modeling Survival Data: Extending the Cox Model, Springer, 2000.
   Google Scholar
• J. Tobin, Estimation of relationships for limited dependent variables, Econom. J. Econom. Soc. 26 (1958), pp. 24–36.
   Web of Science ®Google Scholar
• J.W. Vaupel, How change in age-specific mortality affects life expectancy, Popul. Stud. (Camb). 40 (1986), pp. 147–157.
   PubMed Web of Science ®Google Scholar
• H.J. Wang, Z. Zhu, and J. Zhou, Quantile regression in partially linear varying coefficient models, Ann. Stat. 37 (2009), pp. 3841–3866.
   Web of Science ®Google Scholar
• W. Weibull, Wide applicability, J. Appl. Mech. 103 (1951), pp. 293–297.
   Google Scholar
• R.E. Wiegand, C.E. Rose, and J.M. Karon, Comparison of models for analyzing two-group, cross-sectional data with a gaussian outcome subject to a detection limit, Stat. Methods. Med. Res. 25 (2016), pp. 2733–2749.
   PubMed Web of Science ®Google Scholar