• ISSN: 2148-2225 (online)

Ulaştırma ve Lojistik Kongreleri

alphanumeric journal

The Journal of Operations Research, Statistics, Econometrics and Management Information Systems

Unshared and Shared Frailty Models


Nihal Ata Tutkun, Ph.D.

Diren Yeğen


Abstract

The Cox regression model which is commonly used in survival analysis is established under the proportional hazards assumption. However cases in which the data shows heterogeneity come across in studies. In this case, heterogeneity should be explained in order to make the interpretations more effective which were obtained depending on the model. Frailty models are one of the survival analysis methods which were developed for explaining heterogeneity. In this study, frailty models are examined theoretically and were applied to the lung cancer data. The unshared frailty model has been used to explain the difference between general risk and momentary risk of individuals in the data set. As for comparing the momentary risk between individuals with various levels of explanatory variables with other individuals, shared frailty models have been used.

Keywords: Cox Regression, Frailty Models, Nonproportional Hazards, Parametric Regression Models, Survival Analysis

Jel Classification: C24, C80

Paylaşılmamış ve Paylaşılmış Zayıflık Modelleri


Öz

Yaşam çözümlemesinde sıklıkla kullanılan Cox regresyon modeli orantılı tehlikeler varsayımı altında kurulmaktadır. Ancak çalışmalarda verinin heterojen özellik gösterdiği durumlar ile karşılaşılmaktadır. Bu durumda modele bağlı olarak elde edilen yorumların daha etkin olabilmesi için heterojenliğin açıklanması gerekmektedir. Zayıflık modelleri heterojenliğin açıklanması için geliştirilmiş bir yaşam çözümlemesi yöntemidir. Bu çalışmada, zayıflık modelleri teorik açıdan incelenmiş ve akciğer kanseri verisi kullanılarak bir uygulama yapılmıştır. Veri kümesindeki bireylerin taşıdığı genel risk ile herhangi bir bireyin anlık riski arasındaki farklılığı açıklamada paylaşılmamış zayıflık modeli kullanılmıştır. Açıklayıcı değişkenlerin çeşitli düzeylerine sahip bireylerin veri kümesindeki diğer bireylere göre anlık riskinin karşılaştırılmasında ise paylaşılmış zayıflık modelleri kullanılmıştır.

Anahtar Kelimeler: Cox Regresyon, Orantısız Tehlikeler, Parametrik Regresyon Modelleri, Yaşam Çözümlemesi, Zayıflık Modelleri


Cite this article

Ata Tutkun, N., Yeğen, D. (2016). Paylaşılmamış ve Paylaşılmış Zayıflık Modelleri. Alphanumeric Journal, 4(1), 45-56. http://dx.doi.org/10.17093/aj.2016.4.1.5000163276

References

  • Ata, N. (2005). Yaşam Çözümlemesinde Orantısız Hazard Modeli, Yüksek Lisans Tezi, Hacettepe Üniversitesi Fen Bilimleri Enstitüsü, Ankara, 2005.
  • Babiker A., Cuzick J. (1994). A simple frailty model for family studies with covariates. Statistics in Medicine, 13, 1679-1692.
  • Clayton, D. (1978). A model for association in bivariate life tables and ıts applications in epidemiological studies of familial tendency in chronic disease ıncidence. Biometrika, 65, 141–151.
  • Clayton, D., Cuzick, J. (1995). Multivariate generalisations of the proportional hazards model (with discussion). Journal of the Royal Statistical Society, Series A, 148, 82–117.
  • Congdon, P. (1995). Modelling Frailty İn Area Mortality. Statistics in Medicine, 14, 1859-1874.
  • Cox, D.R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society,Series B, 34, 187-220.
  • Duchateau, L., Janssen, P. (2007). The Frailty Model, Springer, New York.
  • Economou, P., Caroni, C. (2005). Graphical tests for the assumption of gamma and inverse Gaussian frailty distributions. Lifetime Data Analysis 11, 565–582.
  • Guo, G., Rodriguez, G. (1992). Estiamting amultivariate proportional hazards model for clustered data using the EM algorithm with an application to child survival in
  • Guatemala. Journal of the American Statistical Association, 87, 969-976.
  • Gutierrez, R.G. (2002). Parametric frailty and shared frailty survival models. The Stata Journal, 2, 22–44.
  • Hougaard, P.(1984). Life table methods for heterogeneous populations. Biometrika, 71, 75–83.
  • Hougaard, P. (1986). Survival models for heterogeneous populations derived from stable distributions. Biometrika 73, 387–396.
  • Hougaard, P.(1995). Frailty models for survival data. Lifetime Data Analysis, 1, 255–273.
  • Hougaard, P. (2000). Analysis of Multivariate Survival Data, Springer, New York.
  • Ibrahim, J. G., Chen, M., Sinha, D. (2001), Bayesian Survival Analysis, Springer, New York.
  • Keiding, N., Andersen, P., Klein, J. (1997). The role of frailty models and accelerated failure time models in describing heterogeneity due to omitted covariates. Statistics in Medicine 16, 215–224.
  • Kheiri, S., Kimber, A., Meshkani, M.R. (2007). Bayesian analysis of an inverse Gaussian correlated frailty model, Computational Statistics and Data Analysis 51, 5317–5326.
  • Klein, J.P. (1992). Semiparametric estimation of random effects using the Cox model based on the EM algorithm. Biometrics 48, 795–806.
  • Klein, J. P. and Moeschberger, M. L. (2003). Survival Analysis: Techniques for Censored and Truncated Data, 2nd edition, Springer, New York.
  • Lanchester, T. (1979). Econometric methods for the duration of unemployment. Econometrica, 47, 939–956.
  • McGilchrist, C.A., Aisbett, C.W. (1991). Regression with frailty in survival analysis. Biometrics 47, 461–466.
  • Oakes, D. (1982). A concordance test for independence in the presence of censoring. Biometrics 38, 451–455.
  • O’Quigley J,, Stare, J. (2002). Proportional hazards models with frailties and random effects. Statistics in Medicine, 21, 3219-3233.
  • O’Quigley J,, Stare, J. (2004). Fit and frailties in proportional hazards regression. Statistics in Medicine, 21, 3219-3233.
  • Pankratz, V. S., de Andrade, M. and Thernau, T. M. (2005). Random effects Cox proportional hazard model: general variance components methods for time-to-event data. Genetic Epidemology, 28, 97-109.
  • Price, D.L., Manatunga, A.K. (2001). Modelling survival data with a cured fraction using frailty models. Statistics in Medicine 20, 1515–1527.
  • Sahu, S.K., Dey, D.K., Aslanidou, H., Sinha, D. (1997). A weibull regression model with gamma frailties for multivariate survival data. Lifetime Data Analysis, 3, 123–137.
  • Vaupel, J.W., Manton, K., Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16, 439–454, 1979.
  • Whitmore, G.A, Lee, M.L.T. (1991). A multivariate survival distribution generated by an ınverse gaussian mixture of exponentials, Technometrics, 33, 39–50.
  • Wienke A. (2011). Frailty Models in Survival Analysis, Chapman&Hall, Florida.
  • Wienke, A., Christensen, K., Holm, N., Yashin, A. (2000). Heritability of death from respiratory diseases: an analysis of Danish twin survival data using a correlated frailty model. In: Medical Infobahn for Europe. A. Hasman et al. (eds.), IOS Press, Amsterdam, 407–411.
  • Wienke, A., Yashin, I.A., Zdravkovic, S., Pedersen, N.L., Marenberg, M.E., De Faire, U. (2004). Genetic influences on CHD-Death and the impact of known risk factors: Comparison of two frailty models. Behavior Genetics, 34, 585-592.
  • Xue, X., Brookmeyer, R. (1996). Bivariate frailty model for the analysis of multivariate survival time. Lifetime Data Analysis 2, 277-289.
  • Yashin, A.I., Iachine, I.A. (1995). Genetic analysis of durations: correlated frailty model applied to survival of danish twins. Genetic Epidemiology, 12, 529 – 538.
  • Yashin, A.I., Vaupel, J.W., Iachine, I.A. (1995). Correlated individual frailty: An advantageous approach to survival analysis of bivariate data. Mathematical Population Studies, 5, 145 – 159.

Volume 4, Issue 1, 2016

2016.04.01.STAT.02

alphanumeric journal

Volume 4, Issue 1, 2016

Pages 45-56

Received: Dec. 28, 2015

Accepted: April 27, 2016

Published: June 30, 2016

Full Text [1.1 MB]

  • Share

2016 Ata Tutkun, N., Yeğen, D.

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence, which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Creative Commons Attribution licence

scan QR code to access this article from your mobile device


Contact Us

School of Transportation and Logistics, Istanbul University
Avcilar Campus 34320 Avcilar/Istanbul/TURKEY

Bahadır Fatih Yıldırım, Ph.D.
editor@alphanumericjournal.com
+ 90 (212) 473 70 00 - 19263

alphanumeric journal

alphanumeric journal has been publishing as "International Peer-Reviewed Journal" every six months since 2013. alphanumeric serves as a vehicle for researchers and practitioners in the field of quantitative methods, and is enabling a process of sharing in all fields related to the operations research, statistics, econometrics and management informations systems in order to enhance the quality on a globe scale.