Bayes prediction of binary outcomes based on correlated discrete predictors.

Abstract

An approach based on Bayes theorem is proposed for predicting the binary outcomes X = 0, 1, given that a vector of predictors Z has taken the value z. It is assumed that Z can be decomposed into 9 independent vectors given X = 1 and h independent vectors given X = 0. First, point and interval estimators are derived for the target probability P (X = 1|z). In a second step these estimators are used to predict the outcomes for new subjects chosen from the same population. Sample sizes needed to achieve reliable estimates of the target probability in the first step are suggested, as well as sample sizes needed to get stable estimates of the predictive values in the second step_ It is also shown that the effects of ignoring correlations between the predictors can be serious. The results are illustrated on Swedish data of work resumption among long-term sick-listed individuals.