The Pareto type I joint frailty-copula model for clustered bivariate survival data

References

• Aggarwal, A., and S. Pant. 2020. Beyond Newton: A new root-finding fixed-point iteration for nonlinear equations. Algorithms 13 (4):78. doi:10.3390/a13040078.
   Web of Science ®Google Scholar
• Amin, Z. H. 2008. Bayesian inference for the Pareto lifetime model under progressive censoring with binomial removals. Journal of Applied Statistics 35 (11):1203–17. doi:10.1080/09537280802187634.
   Web of Science ®Google Scholar
• Arnold, B. C. 2014. Pareto distribution. In Wiley StatsRef: Statistics Reference Online. Hoboken, NJ: Wiley. doi:10.1002/9781118445112.
   Google Scholar
• Böhnstedt, M. J. Gampe, A. Monique, A. Caljouw, and H. Putter. 2021. Incorporating delayed entry into the joint frailty model for recurrent events and a terminal event. https://arxiv.org/abs/2103.14368.
   Google Scholar
• Clayton, D. G. 1978. A model for association in bivariate life tables and its application to epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65 (1):141–51. doi:10.1093/biomet/65.1.141.
   Web of Science ®Google Scholar
• Chesneau, C. 2022. Theoretical study of some angle parameter trigonometric copulas. Modelling 3 (1):140–63. doi:10.3390/modelling3010010.
   Google Scholar
• Chiou, S. H., J. Qian, E. Mormino, R. A. Betensky, L. F. S. Aging, and H. A. B. Study. 2018. Permutation tests for general dependent truncation. Computational Statistics & Data Analysis 128:308–24. doi:10.1016/j.csda.2018.07.012.
   PubMed Web of Science ®Google Scholar
• Chiou, S. H., M. D. Austin, J. Qian, and R. A. Betensky. 2019. Transformation model estimation of survival under dependent truncation and independent censoring. Statistical Methods in Medical Research 28 (12):3785–98. doi:10.1177/0962280218817573.
   PubMed Web of Science ®Google Scholar
• Cohen, A. 1991. Truncated and censored samples: Theory and applications. New York, NY: CRC Press.
   Google Scholar
• Crowder, M. J. 2012. Multivariate survival analysis and competing risks. New York, NY: CRC Press.
   Google Scholar
• Deresa, N. W., and I. Van Keilegom. 2020. A multivariate normal regression model for survival data subject to different types of dependent censoring. Computational Statistics & Data Analysis 144:106879. doi:10.1016/j.csda.2019.106879.
   Web of Science ®Google Scholar
• de Uña-Álvarez, J. 2012. On the Markov three-state progressive model. In Recent advances in system reliability, 269–81. London, UK: Springer.
   Google Scholar
• de Uña-Álvarez, J., and N. Veraverbeke. 2013. Generalized copula-graphic estimator. TEST 22 (2):343–60. doi:10.1007/s11749-012-0314-2.
   Web of Science ®Google Scholar
• de Uña-Álvarez, J., and N. Veraverbeke. 2017. Copula-graphic estimation with left-truncated and right-censored data. Statistics 51 (2):387–403. doi:10.1080/02331888.2016.1274898.
   Web of Science ®Google Scholar
• Duchateau, L, and P. Janssen. 2008. The frailty model. Berlin, Germany: Springer.
   Google Scholar
• Duchateau, L., P. Janssen, P. Lindsey, C. Legrand, R. Nguti, and R. Sylvester. 2002. The shared frailty model and the power for heterogeneity tests in multicenter trials. Computational Statistics & Data Analysis 40 (3):603–20. doi:10.1016/S0167-9473(02)00057-9.
   Web of Science ®Google Scholar
• Dörre, A. 2021. Semiparametric likelihood inference for heterogeneous survival data under double truncation based on a Poisson birth process. Japanese Journal of Statistics and Data Science 4 (2):1203–26. doi:10.1007/s42081-021-00128-w.
   Google Scholar
• Emura, T., and Y. H. Chen. 2016. Gene selection for survival data under dependent censoring: A copula-based approach. Statistical Methods in Medical Research 25 (6):2840–57. doi:10.1177/0962280214533378.
   PubMed Web of Science ®Google Scholar
• Emura, T., and J. H. Hsu. 2020. Estimation of the Mann-Whitney effect in the two-sample problem under dependent censoring. Computational Statistics & Data Analysis 150:106990. doi:10.1016/j.csda.2020.106990.
   Web of Science ®Google Scholar
• Emura, T. S. Matsui, and V. Rondeau. 2019. Survival analysis with correlated endpoints, joint Frailty-Copula models, JSS Research Series in Statistics. Singapore: Springer.
   Google Scholar
• Emura, T. H. Michimae, and S. Matsui. 2022. Dynamic risk prediction via a joint frailty-copula model and IPD meta-analysis: Building web applications, Entropy 24 (5):589. doi:10.3390/e24050589.
   Google Scholar
• Emura, T., M. Nakatochi, K. Murotani, and V. Rondeau. 2017. A joint frailty-copula model between tumour progression and death for meta-analysis. Statistical Methods in Medical Research 26 (6):2649–66. doi:10.1177/0962280215604510.
   PubMed Web of Science ®Google Scholar
• Emura, T., M. Nakatochi, S. Matsui, H. Michimae, and V. Rondeau. 2018. Personalized dynamic prediction of death according to tumour progression and high-dimensional genetic factors: Meta-analysis with a joint model. Statistical Methods in Medical Research 27 (9):2842–58. doi:10.1177/0962280216688032.
   PubMed Web of Science ®Google Scholar
• Emura, T., and C. H. Pan. 2020. Parametric maximum likelihood inference and goodness-of-fit tests for dependently left-truncated data, a copula-based approach. Statistical Papers 61 (1):479–501. doi:10.1007/s00362-017-0947-z.
   Web of Science ®Google Scholar
• Emura, T., C. Sofeu, and V. Rondeau. 2021. Conditional copula models for correlated survival endpoints: Individual patient data meta-analysis of randomized controlled trials. Statistical Methods in Medical Research 30 (12):2634–50. doi:10.1177/09622802211046390.
   PubMed Web of Science ®Google Scholar
• Emura, T., and W. Wang. 2010. Testing quasi-independence for truncation data. Journal of Multivariate Analysis 101 (1):223–39. doi:10.1016/j.jmva.2009.07.006.
   Web of Science ®Google Scholar
• Emura, T., and W. Wang. 2016. Semiparametric inference for an accelerated failure time model with dependent truncation. Annals of the Institute of Statistical Mathematics 68 (5):1073–94. doi:10.1007/s10463-015-0526-9.
   Web of Science ®Google Scholar
• Emura, T., J. H. Shih, I. D. Ha, and R. A. Wilke. 2020. Comparison of the marginal hazard model and the sub-distribution hazard model for competing risks under an assumed copula. Statistical Methods in Medical Research 29 (8):2307–27. doi:10.1177/0962280219892295.
   PubMed Web of Science ®Google Scholar
• Escarela, G., and J. F. Carriere. 2003. Fitting competing risks with an assumed copula. Statistical Methods in Medical Research 12 (4):333–49. doi:10.1191/0962280203sm335ra.
   PubMed Web of Science ®Google Scholar
• Everitt, B. 2003. Modern medical statistics: A practical guide. Hoboken, NJ: Wiley.
   Google Scholar
• Fine, J. P., H. Jiang, and R. Chappell. 2001. On semi-competing risks data. Biometrika 88 (4):907–19. doi:10.1093/biomet/88.4.907.
   Web of Science ®Google Scholar
• Ghosh, I. 2021. On the asymptotic properties of the likelihood estimates and some inferential issues related to hidden truncated Pareto (type II) model. Communications in Statistics - Theory and Methods 2021:1–12. doi:10.1080/03610926.2021.2004422.
   Google Scholar
• Gumbel, E. J. 1960. Distributions de valeurs extremes en plusieurs dimensions. PubL Inst Stat. Pari 9:171–3.
   Google Scholar
• Ha, I. D., J. H. Jeong, and Y. Lee. 2017. Statistical modelling of survival data with random effects: H-likelihood approach. Singapore: Springer.
   Google Scholar
• Ha, I. D., J. M. Kim, and T. Emura. 2019. Profile likelihood approaches for semiparametric copula and frailty models for clustered survival data. Journal of Applied Statistics 46 (14):2553–71. doi:10.1080/02664763.2019.1601688.
   Web of Science ®Google Scholar
• Kwon, S., I. D. Ha, J.-H. Shih, and T. Emura. 2022. A flexible parametric copula modeling approach for clustered survival data. Pharmaceutical Statistics 21 (1):69–88.
   PubMed Web of Science ®Google Scholar
• Ha, I. D., and Y. Lee. 2021. A review of h-likelihood for survival analysis. Japanese Journal of Statistics and Data Science 4 (2):1157–78. doi:10.1007/s42081-021-00125-z.
   Google Scholar
• Hougaard, P. 1995. Frailty models for survival data. Lifetime Data Analysis 1 (3):255–73. doi:10.1007/BF00985760.
   PubMedGoogle Scholar
• Huang, X., W. Wang, and T. Emura. 2021. A copula-based Markov chain model for serially dependent event times with a dependent terminal event. Japanese Journal of Statistics and Data Science 4 (2):917–51. doi:10.1007/s42081-020-00087-8.
   Google Scholar
• Jenkins, S. P. 2017. Pareto models, top incomes and recent trends in UK income inequality. Economica 84 (334):261–89. doi:10.1111/ecca.12217.
   Web of Science ®Google Scholar
• Kawakami, R., H. Michimae, and Y. H. Lin. 2021. Assessing the numerical integration of dynamic prediction formulas using the exact expressions under the joint frailty-copula model. Japanese Journal of Statistics and Data Science 4 (2):1293–321. doi:10.1007/s42081-021-00133-z.
   Google Scholar
• Klein, J. P, and M. L. Moeschberger. 2003. Survival analysis: Techniques for censored and truncated data, 2nd ed. New York, NY: Springer.
   Google Scholar
• Kundu, D., N. Balakrishnan, and A. Jamalizadeh. 2010. Bivariate Birnbaum–Saunders distribution and associated inference. Journal of Multivariate Analysis 101 (1):113–25. doi:10.1016/j.jmva.2009.05.005.
   Web of Science ®Google Scholar
• Kundu, D., D. Mitra, and A. Ganguly. 2017. Analysis of left truncated and right censored competing risks data. Computational Statistics & Data Analysis 108:12–26. doi:10.1016/j.csda.2016.10.020.
   Web of Science ®Google Scholar
• Langberg, N. A., and M. Shaked. 1982. On the identifiability of multivariate life distribution functions. The Annals of Probability 10 (3):773–9. doi:10.1214/aop/1176993785.
   Web of Science ®Google Scholar
• Mardia, K. V. 1962. Multivariate pareto distributions. The Annals of Mathematical Statistics 33 (3):1008–15. doi:10.1214/aoms/1177704468.
   Google Scholar
• MacDonald, I. L. 2014. Does Newton–Raphson really fail? Statistical Methods in Medical Research 23 (3):308–11. doi:10.1177/0962280213497329.
   PubMed Web of Science ®Google Scholar
• MacKenzie, G., M. Blagojevic-Bucknall, Y. Al-Tawarah, and D. Peng. 2021. The XGTDL family of survival distributions. Japanese Journal of Statistics and Data Science 4 (2):1227–45. doi:10.1007/s42081-021-00129-9.
   Google Scholar
• Mitra, D., D. Kundu, and N. Balakrishnan. 2021. Likelihood analysis and stochastic EM algorithm for left truncated right censored data and associated model selection from the Lehmann family of life distributions. Japanese Journal of Statistics and Data Science 4 (2):1019–48. doi:10.1007/s42081-021-00115-1.
   Google Scholar
• Nagatsuka, H., and N. Balakrishnan. 2021. Efficient likelihood-based inference for the generalized Pareto distribution. Annals of the Institute of Statistical Mathematics 73 (6):1153–85. doi:10.1007/s10463-020-00782-z.
   Web of Science ®Google Scholar
• Nelsen, R. B. 2006. An introduction to copulas, 2nd ed. New York, NY: Springer.
   Google Scholar
• Ning, J., D. Pak, H. Zhu, and J. Qin. 2021. Conditional independence test of failure and truncation times: Essential tool for method selection. Computational Statistics & Data Analysis 2021:107402.
   Google Scholar
• de Oliveira, R. P., M. V. de Oliveira Peres, and M. R. dos Santos. 2021. A Bayesian inference approach for bivariate Weibull distributions derived from Roy and Morgenstern methods. Statistics, Optimization & Information Computing 9 (3):529–54.
   Google Scholar
• Peng, M., L. Xiang, and S. Wang. 2018. Semiparametric regression analysis of clustered survival data with semi-competing risks. Computational Statistics & Data Analysis 124:53–70. doi:10.1016/j.csda.2018.02.003.
   Web of Science ®Google Scholar
• Piancastelli, L. S., W. Barreto-Souza, and V. D. Mayrink. 2021. Generalized inverse-Gaussian frailty models with application to TARGET neuroblastoma data. Annals of the Institute of Statistical Mathematics 73 (5):979–1010. doi:10.1007/s10463-020-00774-z.
   Web of Science ®Google Scholar
• Prenen, L., R. Braekers, and L. Duchateau. 2018. Investigating the correlation structure of quadrivariate udder infection times through hierarchical Archimedean copulas. Lifetime Data Analysis 24 (4):719–42. doi:10.1007/s10985-017-9411-6.
   PubMed Web of Science ®Google Scholar
• Rivest, L. P., and M. T. Wells. 2001. A martingale approach to the copula-graphic estimator for the survival function under dependent censoring. Journal of Multivariate Analysis 79 (1):138–55. doi:10.1006/jmva.2000.1959.
   Web of Science ®Google Scholar
• Rondeau, V., J. P. Pignon, and S. Michiels. 2015. A joint model for the dependence between clustered times to tumour progression and deaths: A meta-analysis of chemotherapy in head and neck cancer. Statistical Methods in Medical Research 24 (6):711–29.
   PubMed Web of Science ®Google Scholar
• Rotolo, F., X. Paoletti, T. Burzykowski, M. Buyse, and S. Michiels. 2019. A Poisson approach to the validation of failure time surrogate endpoints in individual patient data meta-analyses. Statistical Methods in Medical Research 28 (1):170–83. doi:10.1177/0962280217718582.
   PubMed Web of Science ®Google Scholar
• Sahu, S. K., and D. K. Dey. 2000. A comparison of frailty and other models for bivariate survival data. Lifetime Data Analysis 6 (3):207–28. doi:10.1023/a:1009633524403.
   PubMed Web of Science ®Google Scholar
• Saïd, M., N. Ghazzali, and L. P. Rivest. 2009. Score tests for independence in semiparametric competing risks models. Lifetime Data Analysis 15 (4):413–40. doi:10.1007/s10985-009-9123-7.
   PubMed Web of Science ®Google Scholar
• Saldaña-Zepeda, D. P., H. Vaquera-Huerta, and B. C. Arnold. 2010. A goodness of fit test for the Pareto distribution in the presence of type II censoring, based on the cumulative hazard function. Computational Statistics & Data Analysis 54 (4):833–42. doi:10.1016/j.csda.2009.11.004.
   Web of Science ®Google Scholar
• Sankaran, P. G., and D. Kundu. 2014. A bivariate Pareto model. Statistics 48 (2):241–55. doi:10.1080/02331888.2012.719521.
   Web of Science ®Google Scholar
• Schneider, S., F. N. Demarqui, E. A. Colosimo, and V. D. Mayrink. 2020. An approach to model clustered survival data with dependent censoring. Biometrical Journal 62 (1):157–74. doi:10.1002/bimj.201800391.
   PubMed Web of Science ®Google Scholar
• Šeliga, A., M. Kauers, S. Saminger-Platz, R. Mesiar, A. Kolesárová, and E. P. Klement. 2021. Polynomial bivariate copulas of degree five: Characterization and some particular inequalities. Dependence Modeling 9 (1):13–42. doi:10.1515/demo-2021-0101.
   Web of Science ®Google Scholar
• Shih, J. H. 2014. Copula models. In Handbook of survival analysis, Chapter 24, 489–510. Boca Raton, FL: CRC Press.
   Google Scholar
• Shih, J. H., and T. Emura. 2018. Likelihood-based inference for bivariate latent failure time models with competing risks under the generalized FGM copula. Computational Statistics 33 (3):1293–323. doi:10.1007/s00180-018-0804-0.
   Web of Science ®Google Scholar
• Shih, J. H., and T. Emura. 2020. Penalized Cox regression with a five-parameter spline model. Communications in Statistics - Theory and Methods 50 (16):1–20. doi:10.1080/03610926.2020.1772305.
   Web of Science ®Google Scholar
• Shih, J. H., W. Lee, L. H. Sun, and T. Emura. 2019. Fitting competing risks data to bivariate Pareto models. Communications in Statistics - Theory and Methods 48 (5):1193–220. doi:10.1080/03610926.2018.1425450.
   Web of Science ®Google Scholar
• Shih, J. H., Y. Konno, Y. T. Chang, and T. Emura. 2022. Copula-based estimation methods for a common mean vector for bivariate meta-analyses. Symmetry 14 (2):186. doi:10.3390/sym14020186.
   Google Scholar
• Shinohara, S., Y. H. Lin, H. Michimae, and T. Emura. 2020. Dynamic lifetime prediction using a Weibull-based bivariate failure time model: A meta-analysis of individual-patient data. Communications in Statistics - Simulation and Computation 2020:1–20. doi:10.1080/03610918.2020.1855449.
   Google Scholar
• Susam, S. O. 2022. A multi-parameter Generalized Farlie-Gumbel-Morgenstern bivariate copula family via Bernstein polynomial. Hacettepe Journal of Mathematics and Statistics 2022:1–14. doi:10.15672/hujms.993698.
   Google Scholar
• Wang, L., Y. Lio, Y. M. Tripathi, S. Dey, and F. Zhang. 2022. Inference of dependent left-truncated and right-censored competing risks data from a general bivariate class of inverse exponentiated distributions. Statistics 2022:1–28. doi:10.1080/02331888.2022.2047680.
   Google Scholar
• Wang, Y. C., T. Emura, T. H. Fan, S. M. Lo, and R. A. Wilke. 2020. Likelihood-based inference for a frailty-copula model based on competing risks failure time data. Quality and Reliability Engineering International 36 (5):1622–38. doi:10.1002/qre.2650.
   Web of Science ®Google Scholar
• Wang, Y. C., and T. Emura. 2021. Multivariate failure time distributions derived from shared frailty and copulas. Japanese Journal of Statistics and Data Science 4 (2):1105–31. doi:10.1007/s42081-021-00123-1.
   Google Scholar
• Wu, B. H., H. Michimae, and T. Emura. 2020. Meta-analysis of individual patient data with semi-competing risks under the Weibull joint frailty-copula model. Computational Statistics 35 (4):1525–52. doi:10.1007/s00180-020-00977-1.
   Web of Science ®Google Scholar
• Yeh, H. C. 2007. Three general multivariate semi-Pareto distributions and their characterizations. Journal of Multivariate Analysis 98 (6):1305–19. doi:10.1016/j.jmva.2006.08.002.
   Web of Science ®Google Scholar