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Identifying the Effects of Observed and Unobserved Risk Factors Using Weighted Lindley Shared Regression Model

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Abstract

Traditional survival testing approaches have generally placed a premium on the frequency of failures over time. During the investigation of such cases, a lack of awareness of related observed and unobserved covariates may be detrimental. In this scenario, frailty models are a decent choice for examining the effect of unobserved covariates. We can easily find baseline distributions for such models. However, due to certain constraints such as the identifiability condition and the requirement that their Laplace transform exists, finding a frailty distribution can be difficult. As a result, in this paper, we introduce a new frailty weighted Lindley distribution for reversed hazard rate setup that outperforms the gamma frailty distribution. So, our main motive is to establish a new frailty distribution under reversed hazard rate setup. Generalized inverse Rayleigh and modified inverse Weibull baseline distributions are proposed as a useful tool for ensuring the effect of unobserved heterogeneity. The model parameters are estimated using the Bayesian framework of Markov Chain Monte Carlo methodology. Following that, Bayesian comparison methods are used to compare models. To explain the findings and show that better models are recommended, the famous Australian twin data set is used.

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References

  1. Bakoban RA, Abubaker MI (2015) On the estimation of the generalized inverted Rayleigh distribution with real data applications. Matrix 2(2):2

    MATH  Google Scholar 

  2. Block HW, Savits TH, Singh H (1998) On the reversed hazard rate function. Probab Eng Inf Sci 12:69–90

    Article  MathSciNet  Google Scholar 

  3. Calabria R, Pulcini G (1996) Point estimation under asymmetric loss functions for left-truncated exponential samples. Commun Stat Theory Methods 25(3):585–600

    Article  MathSciNet  Google Scholar 

  4. Chacko M, Mohan R (2018) Bayesian analysis of Weibull distribution based on progressive type-II censored competing risks data with binomial removals. Comput Stat 34(4):233–252

    MathSciNet  MATH  Google Scholar 

  5. Chen MH, Shao QM (1999) Monte Carlo estimation of Bayesian credible intervals and HPD intervals. J Comput Gr Stat 8(1):69–92

    MathSciNet  Google Scholar 

  6. Clayton’s DG (1978) A model for association in bivariate life tables and its applications to epidemiological studies of familial tendency in chronic disease incidence. Biometrica 65:141–151

  7. Cox DR (1972) Regression models and life tables (with discussion). J R Stat Soc Ser B 34:187–220

    MATH  Google Scholar 

  8. Duffy DL, Martin NG, Mathews JD (1990) Appendectomy in Australian Twins. Aust J Hum Genet 47(3):590–92

    Google Scholar 

  9. Flinn CJ, Heckman JJ (1982) New methods for analyzing individual event histories. Sociol Methodol 13:99–140

    Article  Google Scholar 

  10. Ghitany ME, Alqallaf F, Al-Mutairi DK, Husain HA (2011) A two-parameter weighted Lindley distribution and its applications to survival data. Math Comput Simul 81(6):1190–1201

    Article  MathSciNet  Google Scholar 

  11. Hanagal DD (2019) Modeling survival data using frailty models, 2nd edn. Springer, Singapore

    Book  Google Scholar 

  12. Hanagal DD, Bhambure SM (2017) Shared gamma frailty models based on reversed hazard rate for modeling Australian twin data. Commun Stat Theory Methods 46(12):5812–5826

    Article  MathSciNet  Google Scholar 

  13. Hanagal DD, Pandey A (2014) Gamma shared frailty model based on reversed hazard rate for bivariate survival data. Stat Probab Lett 88:190–196

    Article  MathSciNet  Google Scholar 

  14. Hanagal DD, Pandey A (2015) Gamma frailty models for bivariate survival data. J Stat Comput Simul 85(15):3172–3189

    Article  MathSciNet  Google Scholar 

  15. Hanagal DD, Pandey A (2017) Shared frailty models based on reversed hazard rate for modified inverse Weibull distribution as baseline distribution. Commun Stat Theory Methods 46(1):234–246

    Article  MathSciNet  Google Scholar 

  16. Hougaard P (1985) Discussion of the paper by D.G. Clayton and J. Cuzick. J R Stat Soc A 148:113–114

    Google Scholar 

  17. Hougaard P (1986) A class of multivariate failure time distributions. Biometrika 73:671–678

    MathSciNet  MATH  Google Scholar 

  18. Hougaard P (1991) Modeling heterogeneity in survival data. J Appl Probab 28:695–701

    Article  MathSciNet  Google Scholar 

  19. Hougaard P (2000) Analysis of multivariate survival data. Springer, New York

    Book  Google Scholar 

  20. Ibrahim JG, Ming-Hui C, Sinha D (2001) Bayesian survival analysis. Springer, Verlag

    Book  Google Scholar 

  21. Kumar D, Singh A (2011) Recurrence relations for single and product moments of lower record values from modified-inverse Weibull distribution. Gen 3(1):26–31

    Google Scholar 

  22. Lindley DV (1958) Fiducial distributions and Bayes’ theorem. J R Stat Soc B 20:102–107

  23. Mazucheli J, Coelho-Barros EA, Achcar JA (2016) An alternative reparametrization for the weighted Lindley distribution. Pesqui Oper 36(2):345–353

    Article  Google Scholar 

  24. Oakes D (1989) Bivariate survival models induced by frailties. J Am Stat Assoc 84(406):487–493

    Article  MathSciNet  Google Scholar 

  25. Pandey A, Bhushan S, Pawimawha L, Tyagi S (2020) Analysis of bivariate survival data using shared inverse Gaussian frailty models: a Bayesian approach. In: Predictive analytics using statistics and big data: concepts and modeling. Bentham Books, vol. 14, pp. 75–88

  26. Pandey A, Hanagal DD, Gupta P, Tyagi S (2020) Analysis of Australian twin data using generalized inverse Gaussian shared frailty models based on reversed hazard rate. Int J Stat Reliabil Eng 7(2):219–235

    Google Scholar 

  27. Pandey A, Hanagal DD, Tyagi S, Gupta P (2021) Generalized Lindley shared frailty based on reversed hazard rate. Int J Reliabil Qual Saf Eng. https://doi.org/10.1142/S0218539321500406

    Article  Google Scholar 

  28. Pandey A, Hanagal DD, Tyagi S (2021) Generalized Lindley shared frailty models. Stat Appl 19(2):41–62

    Google Scholar 

  29. Sankaran PG, Gleeja VL (2011) On proportional reversed hazards frailty models. Metron 69(2):151–173

    Article  MathSciNet  Google Scholar 

  30. Santos CA, Achcar JA (2010) A Bayesian analysis for multivariate survival data in the presence of covariates. J Stat Theory Appl 9:233–253

    MathSciNet  Google Scholar 

  31. Shaked M, Shantikumar JG (1994) Stochastic orders and their applications. Academic Press, New York

    MATH  Google Scholar 

  32. Tyagi S, Pandey A, Hanagal DD, Gupta P (2021) Bayesian inferences in generalized Lindley shared frailty model with left censored bivariate data. Adv Res Trends Stat Data Sci 1:137–157

    Google Scholar 

  33. Tyagi S, Pandey A, Agiwal V, Chesneau C (2021) Weighted Lindley multiplicative regression frailty models under random censored data. Comput Appl Math 40(8):1–24

    Article  MathSciNet  Google Scholar 

  34. Vaupel JW, Manton KG, Stallaed E (1979) The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography 16:439–454

    Article  Google Scholar 

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Acknowledgements

We owe a debt of gratitude to the anonymous referees who made numerous suggestions for improvement.

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Authors and Affiliations

  1. Department of Statistics, Central University of Rajasthan, Ajmer, Rajasthan, India

    Shikhar Tyagi & Arvind Pandey

  2. LMNO, Université de Caen Normandie, Campus II, Science 3, 14032, Caen, France

    Christophe Chesneau

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  1. Shikhar Tyagi
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  2. Arvind Pandey
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  3. Christophe Chesneau
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Part of special issue guest edited by Dieter Rasch, Jürgen Pilz, and Subir Ghosh—Advances in Statistical and Simulation Methods.

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Tyagi, S., Pandey, A. & Chesneau, C. Identifying the Effects of Observed and Unobserved Risk Factors Using Weighted Lindley Shared Regression Model. J Stat Theory Pract 16, 16 (2022). https://doi.org/10.1007/s42519-021-00241-9

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