• ISSN: 2148-2225 (online)

Ulaştırma ve Lojistik Kongreleri

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

Unshared and Shared Frailty Models

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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

Suggested citation

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

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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]

2016 Ata Tutkun, N., Yeğen, D.

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