Estimation of the probability of an event as a function of several independent variables

Abstract

SUMMARY A method for estimating the probability of occurrence of an event from dichotomous or polychotomous data is developed, using a recursive approach. The method in the dichotomous case is applied to the data of a 10-year prospective study of coronary disease. Other areas of application are briefly indicated. The purpose of this paper is to develop a method for estimating from dichotomous (quantal) or polychotomous data, the probability of occurrence of an event as a function of a relatively large number of independent variables. A key feature of the method is a recursive approach based on Kalman's work (Kalman, 1960 and unpublished report) in linear dynamic filtering and prediction, derivable also from the work of Swerling (1959), which provides an example of many other possible uses of recursive techniques in nonlinear estimation and in related areas. The problem that motivated the investigation is a central one in the epidemiology of coronary heart disease, and it will be used to fix ideas and illustrate the method. Some indication of the range of applications will be given in the conclusion.