Full-text resources of CEJSH and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


2022 | 23 | 4 | 161-176

Article title

Generalised Lindley shared additive frailty regression model for bivariate survival data

Content

Title variants

Languages of publication

Abstracts

EN
Frailty models are the possible choice to counter the problem of the unobserved heterogeneity in individual risks of disease and death. Based on earlier studies, shared frailty models can be utilised in the analysis of bivariate data related to survival times (e.g. matched pairs experiments, twin or family data). In this article, we assume that frailty acts additively to the hazard rate. A new class of shared frailty models based on generalised Lindley distribution is established. By assuming generalised Weibull and generalised log-logistic baseline distributions, we propose a new class of shared frailty models based on the additive hazard rate. We estimate the parameters in these frailty models and use the Bayesian paradigm of the Markov Chain Monte Carlo (MCMC) technique. Model selection criteria have been applied for the comparison of models. We analyse kidney infection data and suggest the best model.

Year

Volume

23

Issue

4

Pages

161-176

Physical description

Dates

published
2022

Contributors

author
  • Department of Statistics, Central University of Rajasthan, Rajasthan, India
  • Department of Statistics, Savitribai Phule Pune University, Pune-411007, India
author
  • Department of Statistics, Central University of Rajasthan, Rajasthan, India

References

  • Bacon, R. W., (1993). A note on the use of the log-logistic functional form for modeling saturation effects. Oxford Bulletin of Economics and Statistics, 55, pp. 355–361.
  • Bin, H., (2010). Additive hazards model with time-varying regression coefficients. Acta Math. Sci., 30B(4), pp. 1318–1326.
  • Clayton’s, D. G., (1978). A model for association in bivariate life tables and its applications to epidemiological studies of familial tendency in chronic disease incidence. Biometrica, 65, pp. 141–151.
  • Cox, D. R., (1972). Regression Models and Life Tables (with Discussion). Journal of Royal Statistical Society, Series B, 34, pp. 187–220.
  • Deshpande, J. V., Purohit, S. G., (2005). Life Time Data: Statistical Models and Methods. World Scientific, New Jersey.
  • Elbatal, I., Merovci, F., & Elgarhy, M., (2013). A new generalized Lindley distribution. Mathematical theory and Modeling, 3(13), pp. 30–47.
  • Gelman, A., Rubin, D. B., (1992). A single series from the Gibbs sampler provides a false sense of security. In Bayesian Statistics 4 (J. M. Bernardo, J. 0. Berger, A. P. Dawid and A. F. M. Smith, eds.). Oxford University Press. pp. 625–632.
  • Geweke, J., (1992). Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments. In Bayesian Statistics 4 (eds. J. M. Bernardo, J. Berger, A. P. Dawid and A. F. M. Smith), Oxford University Press, pp. 169–193.
  • Gupta, P., Pandey, A., and Tyagi, S., (2022). Comparison of Multiplicative Frailty Models under Generalized Log-Logistic-II Baseline Distribution for Counter Heterogeneous Left Censored Data, 1, pp. 97–114.
  • Hanagal, D. D., (2008a). Frailty regression models in mixture distributions. Journal of Statistical Planning and Inference, 138(8), pp. 2462–68.
  • Hanagal, D. D. (2019). Modeling Survival Data Using Frailty Models. 2nd Edition. Springer, Singapore.
  • Hanagal, D. D., & Pandey, A., (2014a). Inverse Gaussian shared frailty for modeling kidney infection data. Advances in Reliability, 1, pp. 1–14.
  • Hanagal, D. D., & Pandey, A., (2015a). Gamma frailty models for bivariate survival data. Journal of Statistical Computation and Simulation, 85(15), pp. 3172–3189.
  • Hanagal, D. D., Pandey, A., & Ganguly, A., (2017). Correlated gamma frailty models for bivariate survival data. Communications in Statistics-Simulation and Computation, 46(5), pp. 3627–3644.
  • Hanagal, D. D., & Pandey, A., (2017a). Shared inverse Gaussian frailty models based on additive hazards. Communications in Statistics-Theory and Methods, 46(22), pp. 11143–11162.
  • Hosmer, D.W., Royston, P., (2002). Using Aalen’s linear hazards model to investigate time varying effects in the proportional hazards regression model. Stat Journal, 2(4), pp. 331–350.
  • Hougaard, P., (1985). Discussion of the paper by D.G. Clayton and J. Cuzick. Journal of the Royal Statistical Society, A, 148, pp. 113–14.
  • Hougaard, P., (1991). Modeling heterogeneity in survival data. Journal of Applied Probability, 28, pp. 695–701.
  • Hougaard, P., (2000). Analysis of Multivariate Survival Data. Springer, New York.
  • Ibrahim, J. G., Ming-Hui C. and Sinha, D., (2001). Bayesian Survival Analysis. Springer, Verlag.
  • Johnson, N. L., Kotz, S., (1975). A vector valued multivariate hazard rate. Journal of Multivariate Analysis, 5 (1), pp. 53–66. doi:10.1016/0047-259X(75)90055-X.
  • Lin, D. Y., Ying, Z., (1994). Semiparametric analysis of the additive risk model. Biometrika, 81(1), pp. 61–71.
  • Lindley, D. V., (1958). Fiducial distributions and Bayes’s theorem. Journal of the Royal Statistical Society, B, 20, pp. 102–107.
  • McGilchrist, C. A., Aisbett, C.W.,(1991): Regression with frailty in survival analysis. Biometrics, 47, pp. 461–466.
  • Oakes, D.,(1982). Bivariate Survival Models Induced by Frailties. Journal of the American Statistical Association, 84(406), pp. 487–493.
  • Pandey, A., Lalpawimawha, L., & Bhushan, S., (2018). Additive shared inverse Gaussian frailty model. Pak. J. Statist, 34(4), pp. 311–330.
  • Pandey, A., Bhushan, S., Pawimawha, L., and Tyagi, S., (2020a).Analysis of Bivariate Survival Data using Shared Inverse Gaussian Frailty Models: A Bayesian Approach, Predictive Analytics Using Statistics and Big Data: Concepts and Modeling, Bentham Books, 14, pp. 75–88.
  • Pandey, A., Hanagal, D. D., Gupta, P., & Tyagi, S., (2020b). Analysis of Australian Twin Data Using Generalized Inverse Gaussian Shared Frailty Models Based on Reversed Hazard Rate. International Journal of Statistics and Reliability Engineering, 7(2), pp. 219–235.
  • Pandey, A., & Tyagi, S., (2021). Comparison of Multiplicative Frailty Models Under Weibull Baseline Distribution. Lobachevskii Journal of Mathematics, 42(13), pp. 3184–3195.
  • Pandey, A., Hanagal, D. D., Tyagi, S., and Gupta, P., (2021a). Generalized Lindley Shared Frailty Based on Reversed Hazard Rate. International Journal of Reliability, Quality and Safety Engineering, 2150040.
  • Pandey, A., Hanagal, D. D., and Tyagi, S., (2021b). Generalized Lindley Shared Frailty Models. Statistics and Applications, 19(2), pp. 41–62.
  • Pandey, A., Hanagal, D. D., Tyagi, S., & Gupta, P., (2022). Modeling Australian Twin Data Using Generalized Lindley Shared Frailty Models. In Annual Conference of the Society of Statistics, Computer and Applications, pp. 143–169. Springer, Singapore.
  • Santos, C. A., Achcar, J. A.,(2010). A Bayesian analysis for multivariate survival data in the presence of covariates. Journal of Statistical Theory and Applications, 9, pp. 233– 253.
  • Shaked, M., Shantikumar, J. G. (1994). Stochastic Orders and Their Applications. Academic Press, New York.
  • Tyagi, S., Pandey, A., Hanagal, D. D., and Gupta, P.,(2021a). Bayesian inferences in generalized Lindley shared frailty model with left censored bivariate data. Advance Research Trends in Statistics and Data Science, pp. 137–157.
  • Tyagi, S., Pandey, A., Agiwal, V., and Chesneau, C.,(2021b). Weighted Lindley multiplicative regression frailty models under random censored data. Computational and Applied Mathematics, 40(8), pp. 1-24.
  • Tyagi, S., Pandey, A. & Chesneau, C., (2022a).Identifying the Effects of Observed and Unobserved Risk Factors Using Weighted Lindley Shared Regression Model. J Stat Theory Pract 16, 16, https://doi.org/10.1007/s42519-021-00241-9.
  • Tyagi, S., Pandey, A. & Chesneau, C.,(2022b). Weighted Lindley Shared Regression Model for Bivariate Left Censored Data. Sankhya B., https://doi.org/10.1007/s13571-022- 00278-1.
  • Vaupel, J. W., Manton, K. G. and Stallaed, E., (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16, pp. 439–454.
  • Xie, X., Strickler,H.D., Xue, X., (2013). Additive hazard regression models: An application to the natural history of human papillomavirus. Comput. Math. Methods Med., pp. 1–7.

Document Type

Publication order reference

Identifiers

Biblioteka Nauki
2156991

YADDA identifier

bwmeta1.element.ojs-doi-10_2478_stattrans-2022-0048
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.