Abstract
The purpose of this study is to develop a method of estimating transition probabilities between the disease “states” indicating its severity for the chronic diseases, in which repeated observations to estimate the probabilities are difficult. This method has been applied to the analysis of the natural history of patients with coronary heart diseases. The transition process among “states” is assumed to be expressed by a time discrete simple Markov process. Nine years' follow-up data on coronary heart diseases by Bruschke et al. have been used for the present analysis. The severity of the disease is classified into 3 “states”, i. e., S1: single vessel disease, S2: double vessel disease, and S3: triple vessel disease. Estimation of the parameters (transition probabilities) was made by the maximum likelihood method, using the follow-up data on the numbers of the survival. The accuracies of the estimated values are evaluated by the asymptotic variances. An information criterion AIC is used to compare the aptness of applicability among several supposed Markov models. From the present study the following have been obtained: (1) the accuracy of the curve fitting for the follow-up data was satisfactory, (2) the catenary model was most prominent in the sense that the AIC is minimum, and (3) there may exist reversible transitions among some disease states.
