Estimating standardized parameters from generalized linear models

Abstract

Although the traditional unrestricted ('non-parametric') estimators of directly standardized rates and rate differences remain unbiased in sparse data, they tend to suffer from instability (low precision). As a result, many authors have proposed more precise estimators based on parametric models for the rates. This paper provides a general approach for constructing estimators of standardized parameters using generalized linear models, and shows that, in some common special cases, these model-based ('smoothed') estimators can have an exceptionally simple form.