Risk ratio regression-simple concept yet simple computation.

Abstract

A new IJE paper includes in its title ‘Risk ratio regression—simple concept yet complex computation’.1 This is only true if one wants to read the risk ratio directly from the coefficients of one’s model. Given a binary outcome and binary exposure as in the aforementioned paper, a logistic regression is the ‘natural’ choice. Its coefficients will be (log) odds ratios, and it is simple to derive a number of other effect measures including the risk ratio. This can be done easily using modern software such as R (see the Supplementary File, available as Supplementary data at IJE online for accompanying code). In the paper under discussion, the risk of weight gain relative to quitting smoking or not was studied. Using standardization (g formula),2 I easily estimate a risk ratio. The three-stage method is simple. Stage 1: fit the model of outcome by exposure and confounders, using a logistic regression model; Stage 2: from this model predict for each person the probability of the outcome, treating everyone as exposed (E) and then everyone as not exposed (NE) (everyone quit or no one quit in our example; Stage 3: average these probabilities for each of the two scenarios. We can then compare these two average predictions to obtain an absolute difference (E-NE), the risk ratio (E/NE) or the odds ratio [E/(1-E)) / (NE/(1-NE)], see Table 1.