In this paper we present a new approach (Kalman Filter Smoothing) to estimate and forecast, Age Groups wise, survival of 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 [23]. The survival proportions of the CP obtained from Kaplan Meier method are used as observed values at 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 [8] and Cubic Interpolation method is used in estimation of the survivor’s proportions. The estimated and forecasted, Age Groups wise survival proportions of CP of the CABG patients from the Kalman Filter Smoothing approach are presented in terms of statistics, survival curves, discussion and conclusion.
Keywords: CABG Patients, Complete and Incomplete populations, DFP method, Estimation and Forecasting of Survivor’s Proportions., Kalman Filter, Maximum Likelihood method, Weibull Distribution
