International Journal of Nonlinear Analysis and Applications

Parametric proportional hazard models using the Bayesian approach with applications to healthcare data

Document Type : Research Paper

Authors

Department of Mathematics, College of Science, University of Baghdad, Iraq

Abstract

The aim of this study is on using Bayesian inference to analyze right-censored healthcare data using Frechet and exponential baseline proportional hazard (PH) models. For the baseline hazard parameters, a gamma prior was used, and for the regression coefficients, normal priors were used. The exact form of the joint posterior distribution was obtained. Bayes estimators of the parameters are obtained using the Markov chain Monte Carlo (MCMC) simulation technique. Two real-survival data applications were analyzed by the Frechet PH model and the exponential PH model. The convergence diagnostic tests are presented. We found that the Frechet PH model was better than the exponential PH model because it is flexible and could be beneficial in analyzing survival data.

Keywords

[1] K. Abbas and T. Yincai, Comparison of estimation methods for Frechet distribution with known shape, Caspian J. Appl. Sci. Res. 1 (2012), no. 10.
[2] W.M. Bolstad, Understanding computational Bayesian statistics, Vol. 644, John Wiley & Sons, 2009.
[3] S.L. Brilleman, E.M. Elci, J.B. Novik, and R. Wolf, Baysian survival analysis using the rstanarm R package, arXiv preprint arxiv: 2002.09633 (2020)
[4] J. Caplehorn, Methadone Dosage and Retention of Patients in Maintenance Treatment, Med. J. Aust. 154 (1991), 195–199.
[5] D. Collett, Modelling Survival Data in Medical Research, CRC Press, Florida, USA, 2015.
[6] D.R. Cox, Regression models and life-tables, J. Royal Statist. Soc.: Ser. B 34 (1972), no. 2, 187–202.
[7] A. Gelman, J.B. Carlin, H.S. Stern, D.B. Rubin. Bayesian Data Analysis, 2nd edition, Chapman & Hall/CRC, Boca Raton, 2003.
[8] A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, A. Vehtari, and B.D. Rubin, Bayesian Data Analysis, 3rd editio edition, Chapman and Hall/ CRC, London, UK, 2013.
[9] R.D. Gupta and D. Kundu, Generalized exponential distribution: different method of estimations, J. Statist. Comput. Simul. 69 (2001), no. 4, 315–337.
[10] J.G. Ibrahim, M.H. Chen, D. Sinha, J.G. Ibrahim, and M.H. Chen, Baysisn Survaival Analysis, Springer, New Yourk, 2001.
[11] N.M. Ismail, Z.M. Khalid, and N. Ahmad, Estimating proportional hazards model using frequentist and bayesian approaches, Malay. J. Funda. Appl. Sci. 8 (2012)., no. 2.
[12] Y. Kim, and J. Lee, Bayesian analysis of proportional hazard models, Ann. Statist. 31 (2003), no. 2, 493–511.
[13] D. Lunn, C. Jackson, N. Best, A. Thomas, and D. Spiegelhalter, The BUGS book, A Practical Introduction to Bayesian Analysis, Chapman Hall, London, 2013.
[14] D. Machin, Y.B. Cheung, and M. Parmar, Survival Analysis: A Practical Approach, John Wiley & Sons, 2006.
[15] A.D. Martin, K.M. Quinn, and J.H. Park. MCMCpack: Markov chain Monte Carlo in R, J. Statist. Software 42 (2011), no. 9, 1–21.
[16] A.H. Muse, O. Ngesa, S. Mwalili, H.M. Alshanbari, and A.A.H. El-Bagoury, A flexible Bayesian parametric proportional hazard model: simulation and applications to right-censored healthcare data, J. Healthcare Engin. 2022 (2022), Article ID 2051642.
[17] S. Nilima, Under-five child mortality in Bangladesh: classical and Bayesian approaches to Cox proportional hazard model, Bangladesh J. Sci. Res. 30 (2017), no. 1-2, 45–54.
[18] C. Robert and G. Casella, Monte Carlo Statistical Methods, 2nd edition. Springer-Verlag, New York, 2004.
[19] S. Sinharay, Assessing convergence of the Markov chain Monte Carlo algorithms: a review, ETS Res. Rep. Ser. 2003 (2003), no. 1, 1–52.
[20] D.J. Spiegelhalter, N.G. Best, B.P. Carlin and A.V.D. Linde, Bayesian measures of model complexity and fit, J. Royal Statist. Soc.: Ser. B 64 (2002), no. 4, 583–639.
[21] G. Thiruvengadam, M. Lakshmi and R. Ramanujam, A study of factors affecting the length of hospital stay of COVID-19 patients by cox-proportional hazard model in a South Indian tertiary care hospital, J. Primary Care Commun. Health 12 (2021).
International Journal of Nonlinear Analysis and Applications
Volume 14, Issue 4
April 2023
Pages 15-36
  • Receive Date: 20 November 2022
  • Revise Date: 16 January 2023
  • Accept Date: 26 February 2023