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

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 (<i>CP</i>) from its incomplete population (<i>IP</i>) of the patients with 12 years observations/follow-up is used for their survival analysis [1]. The survival proportions of the <i>CP</i> obtained from Kaplan Meier method are used as observed values <i>y_t</i> at time <i>t</i> (input) for Kalman Filter Smoothing process to update time varying parameters. In case of <i>CP</i>, 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 <i>CP</i> 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.