EPICURE Models and the Basics of Model Specification

The next three sections provide basic information about the modeling modules. As noted above, each of the models involves a quantity  that is modeled as a function of parameters and covariables using one of the general EPICURE model forms. The default model in each of the modules is the loglinear model . Loglinear models can be specified and fit using the command FIT varlist, where varlist is a list of covariates to be included in the model.

A complete description of the EPICURE models is given in Fitting Models with Epicure of this Guide and in Risk Models in EPICURE Programs of the EPICURE Command Summary. In the following sections we write the model as  to emphasize the general models, but it may be easiest to think in terms of a simple loglinear models as you read the next few sections.

As described in Categorical Variables in EPICURE Models, categorical variables specify levels of factors for use in modeling or the computation of summary statistics. Variables are designated as categorical with the LEVELS command. When a categorical variable is included in a model, an indicator variable is created for each level or factor. Model specifications can include ordinary (continuous) variables, categorical variables, and products of two continuous or categorical variables. When a model includes the product of a categorical and a continuous variable, a separate parameter is estimated for each level of the categorical variable. When the product of two categorical variables is included in a model, parameters are estimated for each level of the cross-classification defined by the levels of the two factors.

The basic EPICURE model can be extended to include multiplicative strata parameters. The extended models can be written as , where the  are the stratum parameters. The strata are defined by a set of categorical variables. Because the stratum parameters are estimated using a computationally efficient algorithm that does not require the inversion of large matrices, models can include large numbers of such parameters. Stratification is discussed further in Stratified Models.

Model specification in EPICURE requires specification of key variables, such as the response variable, number of trials, or time at risk. These key variables are described below and in more detail in Key Variables for the Regression Programs. As noted below, each module has its own set of key variables and automatically recognizes certain default names for these variables. In addition, as discussed in Key Variables for the Regression Programs of this guide and in Key Variable Commands of the EPICURE Command Summary, you can easily specify alternative names for these variables.