Education 231C

Applied Categorical & Nonnormal Data Analysis

Relative Risk for Non-rare Events

To a certain extent relative risk is a more intuitive concept then is odds ratio. In the case of rare events (probability less than .1) odds ratios and relative risk are nearly equal. But what about the situations in which events are not rare. We will present two methods of obtaining relative risk using several of Stata's estimation commands along with their equivalent glm commands.

Acknowledgements: Numerous contributors to the Statalist and to Karla Lindquist of UCSF.

First we will compute the odds ratio using logistic regression followed by the equivalent glm command. With glm the eform option displays the exponentiated coefficient.

Next, we will compute the risk ratio using binary regression. Binary regression is notorious for poor convergence. The equivalent glm command keeps the binomial family but switches to the log link.

Next, we will use poisson regression to accomplish the same thing. In order to obtain reasonable standard errors we need to include the robust option with poisson. And for glm we need to change the family from binomial to poisson while leaving the link at log.

This use of poisson regression to obtain relative risk is from an article by Guangyong Zou (A Modified Poisson Regression Approach to Prospective Studies with Binary Data. Am J Epidemiol 2004; 159(7):702-6.). This "modified poisson" approach is interesting in that each observation is only a 0/1 event, not the traditional count type variable typically found in poisson models.

We will conclude by running an example which includes several continuous predictors. This is the type of model that often fails to converge using binary regression.

Categorical Data Analysis Course

Phil Ender