An Alternative Perspective on the Robust Poisson Model for Estimating Risk or Prevalence Ratios

The robust Poisson model is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson model yields results that can be interpreted as risk or prevalence ratios. In addition, it does not suffer from frequent non-convergence problems like the log-binomial model. However, using a Poisson distribution to model a binary outcome may seem counterintuitive. Methodological papers have often presented this as a good approximation to the more natural binomial distribution. In this paper, we provide an alternative perspective to the robust Poisson model based on the semiparametric theory. This perspective highlights that the robust Poisson model does not require assuming a Poisson distribution for the outcome. In fact, the model can be seen as making no assumption on the distribution of the outcome; only a log-linear relationship assumption between the risk/prevalence of the outcome and the explanatory variables is required. This assumption and consequences of its violation are discussed. Suggestions to reduce the risk of violating the modeling assumption are also provided.