Additive-multiplicative regression for Poisson and binomial models with epidemiological applications

Abstract:

I will discuss work from a recently published paper (Marschner, Gillett and O'Connell, 2012) on regression models for counts and binary outcomes that have a combination of additive and multiplicative effects in the model. The approach is based on an additive Poisson model with multiplicative stratification. A reliable analysis method will be presented based on the ECM algorithm, which involves fitting the model by oscillating between the additive and multiplicative components. It will be shown that this conveniently accommodates the non-negative parameter constraints that can be problematic in Poisson models with additive effects. It also allows flexible high dimensional models, including unspecified isotonic regression functions. As well as applying directly to Poisson count data, the model can also be used as a working model for binomial data using robust standard errors. I will discuss application of the methodology to the development of risk factor models in clinical epidemiology. Using data on heart attack mortality in a large clinical trial, it is found that the combination of additive and multiplicative components allows a more parsimonious risk factor model by removing the need for interaction effects that are necessary in traditional models.

Marschner IC, Gillett AC & O'Connell RL. Stratified additive Poisson models: Computational methods and application in clinical epidemiology. Computational Statistics and Data Analysis, 2012; 56:1115-1130.