Unobserved heterogeneity is called frailty, measuring frailty and multiplying it with the baseline distribution is critical for clustered survival data analysis. Lindley distribution is the one among classical distribution, yet it has limited applications in lifetime data analysis. Therefore, the objective of the study is to fit the frailty models for Lindley distribution and to compare the results with other existing distributions such as Exponential, Weibull, Lognormal and Log-logistic to test the effectiveness. Two real-life data sets and simulated data were used to fit the baseline distributions with frailty models. The study results revealed that Lindley with Gamma frailty model is a good choice for kidney infection data and Lindley with Inverse Gaussian frailty model is the best fit for CGD (Chronic Granulomatous Disease) and the simulated data set. Further, Lindley with frailty models points out the lowest Akaike’s Information Criteria (AIC) and Bayesian Information Criteria (BIC) values than other baseline distributions. So we suggest that Lindley baseline distribution with the frailty models is a potential alternative approach for clustered survival data analysis.

Lindley distribution, frailty models, Lindley with frailty models, survival analysis.

Received: November 8, 2021; Revised: January 20, 2022; Accepted: March 7, 2022; Published: March 29, 2022

How to cite this article: J. Nagaraj, S. Parthasarathy and C. Ponnuraja, Lindley distribution as frailty models with application to lifetime data, Advances and Applications in Statistics 75 (2022), 119-134. http://dx.doi.org/10.17654/0972361722031

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:
[1] T. G. Clark, M. J. Bradburn, S. B. Love and D. G. Altman, Survival analysis part I: basic concepts and first analyses, British Journal of Cancer 89(2) (2003), 232-38. https://doi.org/10.1038/sj.bjc.6601118.
[2] Theodor A. Balan and Hein Putter, A tutorial on frailty models, Statistical Methods in Medical Research 29(11) (2020), 3424-3454.
https://doi.org/10.1177/0962280220921889.
[3] J. W. Vaupel, K. G. Manton and E. Stallard, The impact of heterogeneity in individual frailty on the dynamics of mortality, Demography 16 (1979), 439-454.
[4] D. Clayton and J. Cuzick, Multivariate generalisations of the proportional hazards model, Journal of the Royal Statistical Society 148 (1985), 82-117.
[5] David D. Hanagal and Alok D. Dabade, Comparisons of frailty models for kidney infection data under Weibull baseline distribution, International Journal of Mathematical Modelling and Numerical Optimisation 5(4) (2014), 342-373.
[6] D. R. Cox and D. Oakes, Analysis of Survival Data, Chapman and Hall, 1984.
[7] D. V. Lindley, Fiducial distributions and Bayes theorem, Journal of the Royal Statistical Society A 20(1) (1958), 102-107.
[8] L. Tomy, A retrospective study on Lindley distribution, Biom. Biostat. Int. J. 7(3) (2018), 163-169. https://doi.org/10.15406/bbij.2018.07.00205.
[9] M. Okwuokenye and K. E. Peace, Size and power of tests of hypotheses on survival parameters from the Lindley distribution with covariates, Austin Biom and Biostat. 2(4) (2015), 1026.
[10] S. Banerjee, M. M. Wall and B. P. Carlin, Frailty modeling for spatially correlated survival data, with application to infant mortality in Minnesota, Biostatistics 4(1) (2003), 123-142. https://doi.org/10.1093/biostatistics/4.1.123.
[11] A. Wienke, Frailty Models in Survival Analysis, Chapman & Hall/CRC, Boca Raton, 2010.
[12] L. Duchateau and P. Janssen, The Frailty Model, Series of Statistics for Biology and Health, Springer-Verlag New York, 2008.
https://doi.org/10.1007/978-0-387-72835-3.
[13] David D. Hanagal, Modeling Survival Data Using Frailty Models, Industrial and Applied Mathematics, Springer Nature Singapore Pte. Ltd. 2011, p. 295. https://doi.org/10.1007/978-981-15-1181-3.
[14] Marco Munda, Federico Rotolo and Catherine Legrand, parfm: Parametric Frailty Models in R, Journal of Statistical Software, Foundation for Open Access Statistics 51(11) (2012), 1-20. http://hdl.handle.net/10.18637/jss.v051.i11.
[15] T. A. Balan, H. Putter and E. M. Frailty, An R package for estimating semi parametric shared frailty models, Journal of Statistical Software 90(7) (2019), 1-29. https://doi.org/10.18637/jss.v090.i07.
[16] Dilip C. Nath, Atanu Bhattacharjee and Ramesh K. Vishwakarma, Risk assessment in liver transplantation patients: A shared frailty parametric approach, Clinical Epidemiology and Global Health 4(1) (2016), 1-15.
[17] P. Hougaard, Frailty models for survival data, Lifetime Data Analysis 1 (1995), 255-274.
[18] G. Guo and G. Rodriguez, Estimating a multivariate proportional hazards model for clustered data using the EM algorithm, with an application to child survival in Guatemala, J. Am. Statist. Assoc. 87 (1992), 969-976.
[19] C. A. McGilchrist and C. W. Aisbett, Regression with frailty in survival analysis, Biometrics 47(2) (1991), 461-466.
[20] T. R. Fleming and D. P. Harrington, Counting Processes and Survival Analysis, New York, Wiley, 1991.
[21] T. M. Therneau, Survival: A Package for Survival Analysis in S. R package version 2.44-1.1, 2019. URL https://CRAN.R-project.org/package=survival.
[22] V. Rondeau, Y. Mazroui and J. R. Gonzalez, frailtypack: An R package for the analysis of correlated survival data with frailty models using penalised likelihood estimation or parametrical estimation, Journal of Statistical Software 47(4) (2012), 1-28. URL http: //www.jstatsoft.org/v47/i04/.
[23] P. Hougaard, Analysis of Multivariate Survival Data, Springer-Verlag, 2000.