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Entropy 2012, 14(8), 1306-1316; doi:10.3390/e14081306

Article

A New Entropy Optimization Model for Graduation of Data in Survival Analysis

Dayi He ^1,2 , Qi Huang ^1,*  and Jianwei Gao ³

¹ School of Humanities & Economics Management, Chinese University of Geosciences, Number 29, Xueyuan Rd., Haidian, Beijing 100083, China ² Lab of Resources & Environment Management, Chinese University of Geosciences, Number 29, Xueyuan Rd., Haidian, Beijing 100083, China ³ School of Business Administration, North China Electronic Power University, Number 2, Beinong Rd., Changpin, Beijing 102206, China

* Author to whom correspondence should be addressed.

Received: 7 March 2012; in revised form: 6 June 2012 / Accepted: 4 July 2012 / Published: 25 July 2012

(This article belongs to the Special Issue Concepts of Entropy and Their Applications)

Download PDF Full-Text [649 KB, uploaded 31 July 2012 07:54 CEST]

Abstract: Graduation of data is of great importance in survival analysis. Smoothness and goodness of fit are two fundamental requirements in graduation. Based on the instinctive defining expression for entropy in terms of a probability distribution, two optimization models based on the Maximum Entropy Principle (MaxEnt) and Minimum Cross Entropy Principle (MinCEnt) to estimate mortality probability distributions are presented. The results demonstrate that the two approaches achieve the two basic requirements of data graduating, smoothness and goodness of fit respectively. Then, in order to achieve a compromise between these requirements, a new entropy optimization model is proposed by defining a hybrid objective function combining both principles of MaxEnt and MinCEnt models linked by a given adjustment factor which reflects the preference of smoothness and goodness of fit in the data graduation. The proposed approach is feasible and more reasonable in data graduation when both smoothness and goodness of fit are concerned.

Keywords: entropy optimization; survival analysis; graduation of data

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