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Anatoli, I., Kenneth, G.M. and James, W.V. (1983) Mortality and Aging in a Heterogeneous Population: A Stochastic Process Model with Observed and Unobserved Variables. Theoretical Population Biology, 27, 154-175.

has been cited by the following article:

• TITLE: Estimation and Forecasting Survival of Diabetic CABG Patients (Kalman Filter Smoothing Approach)

  AUTHORS: M. Saleem, K. H. Khan, Nusrat Yasmin

  KEYWORDS: CABG Patients, Complete and Incomplete Populations, Weibull & Distribution, Kalman Filter, Maximum Likelihood Method, DFP Method, Estimation and Forecasting of Survivor’s Proportions

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.5 No.4, November 26, 2015

  ABSTRACT: In this paper, we present a new approach (Kalman Filter Smoothing) to estimate and forecast survival of Diabetic and Non Diabetic Coronary Artery Bypass Graft Surgery (CABG) patients. Survival proportions of the patients are obtained from a lifetime representing parametric model (Weibull distribution with Kalman Filter approach). Moreover, an approach of complete population (CP) from its incomplete population (IP) of the patients with 12 years observations/follow-up is used for their survival analysis [1]. The survival proportions of the CP obtained from Kaplan Meier method are used as observed values ytat time t (input) for Kalman Filter Smoothing process to update time varying parameters. In case of CP, the term representing censored observations may be dropped from likelihood function of the distribution. Maximum likelihood method, in-conjunction with Davidon-Fletcher-Powell (DFP) optimization method [2] and Cubic Interpolation method is used in estimation of the survivor’s proportions. The estimated and forecasted survival proportions of CP of the Diabetic and Non Diabetic CABG patients from the Kalman Filter Smoothing approach are presented in terms of statistics, survival curves, discussion and conclusion.