[Home ] [Archive]   [ فارسی ]  
:: Main :: About :: Current Issue :: Archive :: Search :: Submit :: Contact ::
:: Volume 25, Issue 1 (1-2021) ::
Andishe 2021, 25(1): 25-31 Back to browse issues page
Use of Frailty Propertional Risk Rate Model in Real Data Analysis
Habib Naderi *, Mohammad Mollanoori, Hamed Ahmadzadeh, Salman Izadkhah
University of Sistan and Baluchestan
Abstract:   (697 Views)
Many populations encountered in survival analysis are often not homogeneous. Individuals are flexible in their susceptibility to causes of death, response to treatment, and influence of various risk factors. Ignoring this heterogeneity can result in misleading conclusions. To deal with these problems, the proportional hazard frailty model was introduced. In this paper, the frailty model is explained as the product of the frailty random variable and baseline hazard rate. We examine the fit of the frailty model to the right-censored data from in the presence of explanatory variables (observable variables) and use it as a practical example to fit the frailty model to the data by considering the Weibull basis distribution and exponential in the likelihood functions. It is used to estimate the model parameters and compare the fit of the models with different criteria.
Keywords: Likelihood Maximum Estimator, Baseline Distribution, Unconditional Survival Functions, Frailty Model .
Full-Text [PDF 280 kb]   (223 Downloads)    
Type of Study: Research | Subject: Special
Received: 2020/04/1 | Accepted: 2021/01/20 | Published: 2021/01/29
References
1. Aalen, O.O. (1978). Nonparametric inference for a family of counting processes. Ann. Stat., 6, 701–726.
2. Aalen, O.O. (1998). Heterogeneity in survival analysis. Statist. Med., 7, 1121-1137.
3. Aalen, O.O. (1992). Modelling heterogeneity in survival analysis by the compound poisson distributhion. Ann. Appl. Probab., 2, 951-992.
4. Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723.
5. Fleming, T.R. and Harrington, D.P. (1991). Counting Processes and survival analysis. Wiley, New York.
6. Gupta, R.C., and Kirmani, S. (2005). Stochastic comparisons in frailty models. J Stat Plan Inference., 136, 3647–3658.
7. Hougaard, P. (1986). Survival models for heterogeneous populations derived from stable distributions. Biometrika, 73, 387–396.
8. Hougaard, P. (1995). Frailty models for survival analysis. Lifetime Data Anal., 1, 255-273.
9. Hougaard, P. (2000). Analysis of Multivariate Survival Data. Springer-Verlag, New York.
10. Hougaard, P. (1984). Life table methods for heterogeneous population: distribution describing the heterogeneity. Biometrika, 71, 75-83.
11. Hougaard, P. (1991). Modelling heterogeneity in survival analysis. J. Appl. Prpbab., 28, 695-701.
12. Kalbfleisch, D. and Prentice, R. L. (2011), The Statistical Analysis of Failure Time Data, John Wiley, New York.
13. Kayid, M., Izadkhah, S., & Zuo, M. J. (2017). Some results on the relative ordering of two frailty models. Statistical Papers, 58(2), 287-301.
14. Liang, K. Y., Self, S. G., Bandeen-Roche, K. J. and Zeger, S. L. (1995), Some Recent Developments for Regression Analysis of Multivariate Failure Time Data, Lifetime Data Analysis, 1, 403-415.
15. Muller, A. and Stoyan, D. (2002). Comparison Methods for Stochastic Models and Risks. Wiley, NewYork.
16. Nelsen, R. B. (2006). An Introduction to Copulas. Lectures Notes in Statistics, 139, Springer-Verlag, New York.
17. Vaupel, J.W., Manton, K.G., and Stallard, E., (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography., 16, 439–454.
18. Xu, M., and Li, X.,(2008). Negative dependence in frailty models. J Stat Plan Inference., 138, 1433–1441.
Send email to the article author

Add your comments about this article
Your username or Email:

CAPTCHA


XML   Persian Abstract   Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Naderi H, mollanoori M, Ahmadzadeh H, Izadkhah S. Use of Frailty Propertional Risk Rate Model in Real Data Analysis. Andishe. 2021; 25 (1) :25-31
URL: http://andisheyeamari.irstat.ir/article-1-790-en.html


Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Volume 25, Issue 1 (1-2021) Back to browse issues page
مجله اندیشه آماری Andishe _ye Amari
Persian site map - English site map - Created in 0.05 seconds with 30 queries by YEKTAWEB 4331