This study proposes a new method for a prognostic analysis on the course of diseases. This method aims to separate, among same disease population, several prognostic groups showing different temporal patterns in the course of the disease and evaluate the influence of prognostic factors separately for each group. To do this, we develop a new temporal distribution that we call multiple component Weibull distribution, which is given by a linear combination of Weibull distributions with different shape and scale parameters. This method is applied to the prognostic analysis of cardiac death of acute myocardial infarction (AMI) during hospitalization. The subjects are the first year study population enrolled in the 5-year prospective survey conducted by the Heart Institute, Tokyo Women's University. We separated the prognosis of AMI into two prognostic groups, one with early death of initial failure type and the other with late death of weak abrasion failure type. It was found that a prognostic factor of early death, mostly caused by cardiogenic shock or cardiac failure, was Killip classification, whereas, in the late death, mostly caused by cardiac rupture or perforation, Q type MI and age other than Killip classification were found to be influential prognostic factors.