Estimation and Forecasting Age Groups wise Survival of CABG Patients (Kalman Filter Smoothing Approach) (Published)
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
Bayesian Inferences for Two Parameter Weibull Distribution (Published)
In this paper, Bayesian estimation using diffuse (vague) priors is carried out for the parameters of a two parameter Weibull distribution. Expressions for the marginal posterior densities in this case are not available in closed form. Approximate Bayesian methods based on Lindley (1980) formula and Tierney and Kadane (1986) Laplace approach are used to obtain expressions for posterior densities. A comparison based on posterior and asymptotic variances is done using simulated data. The results obtained indicate that, the posterior variances for scale parameter obtained by Laplace method are smaller than both the Lindley approximation and asymptotic variances of their MLE counterparts.
Keywords: Laplace Approximation, Lindley Approximation, Maximum Likelihood Estimates, Weibull Distribution