Confidence Statements about the Prediction Process

Abstract

So far our approach has been purely probabilistic. The hypothetical hazards in the example in Chapter 2 were chosen appropriately for illustration purposes. However, in order to apply the method in statistical analysis with real data sets, we must specify how the hazards are estimated from the data. This amounts to specifying a statistical model for the hazards. Hazard regression models are standard tools in modelling dependence between hazard related to a response variable and a set of explanatory variables. As an example, we consider in this work the discrete time logistic regression model. In general, the way the hazards are estimated is a secondary question in a further analysis of the prediction probabilities, but it is of course a crucial part of relevant data analysis. We return to that in Chapter 4.