General Comments on Model Specification

A wide variety of risk regression models arise in the analysis of epidemiologic data. The class of generalized risk models available in EPICURE can be used to fit most of these models. Before describing the models in detail, it will be useful to present some examples of models which might arise in standard situations. The EPICURE User's Guide provides additional, more detailed examples.

First, consider a matched case-control study of ovarian cancer and estrogen usage. Using PECAN one might want to consider a simple multiplicative model for the odds-ratio as a function of estrogen usage (est), history of gall bladder disease ( gall), and a possible interaction between these factors. A commonly used model for this would be

         

Now consider a large cohort study of radiation effects on cancer mortality data. One might use AMFIT to fit a linear dose response model for the excess relative risk. In this model the risk depends on sex (sex) and age-at-exposure (agex), and background rates are modeled as a loglinear function of sex and the log of attained age (lage). One such model is written:

It is often the case in cohort studies that one uses rates from an external population as a basis for comparison. Modifying the previous example, let brate denote a variable containing the age-, time- and sex-specific background rate and consider the following nonlinear dose response model for the time- and sex-dependent absolute excess risk:

         

where ltime is the logarithm of time-since-exposure. In this model the parameter  is the standardized mortality ratio (SMR) at the 0 dose level. As a final example, consider a clinical trial in which one wishes to use PEANUTS to estimate the excess relative risk of survival associated with the treatment of interest (trmnt) with an explicit adjustment for differences in the risk associated with age-at-entry (agein) and stratification of the background rates by initial stage of disease (stage). If we denote the stratified background hazard as , a model for the excess relative risk is: