title: Comparison of robustness to outliers between robust poisson models and log-binomial models when estimating relative risks for common binary outcomes: a simulation study.
abstract: BACKGROUND
  To estimate relative risks or risk ratios for common binary outcomes, the most popular model-based methods are the robust (also known as modified) Poisson and the log-binomial regression. Of the two methods, it is believed that the log-binomial regression yields more efficient estimators because it is maximum likelihood based, while the robust Poisson model may be less affected by outliers. Evidence to support the robustness of robust Poisson models in comparison with log-binomial models is very limited.
  
  
  METHODS
  In this study a simulation was conducted to evaluate the performance of the two methods in several scenarios where outliers existed.
  
  
  RESULTS
  The findings indicate that for data coming from a population where the relationship between the outcome and the covariate was in a simple form (e.g. log-linear), the two models yielded comparable biases and mean square errors. However, if the true relationship contained a higher order term, the robust Poisson models consistently outperformed the log-binomial models even when the level of contamination is low.
  
  
  CONCLUSIONS
  The robust Poisson models are more robust (or less sensitive) to outliers compared to the log-binomial models when estimating relative risks or risk ratios for common binary outcomes. Users should be aware of the limitations when choosing appropriate models to estimate relative risks or risk ratios.
authors: Kaiser Permanente Southern California, Department of Research and Evaluation, Pasadena, CA, USA. Wansu.Chen@kp.org.
authors: Wansu
authors: W
authors: Chen
authors: Jiaxiao
authors: J
authors: Shi
authors: Lei
authors: L
authors: Qian
authors: Stanley P
authors: SP
authors: Azen
mesh_terms: D003198:Computer Simulation / Q000706:statistics & numerical data*; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D008962:Models, Theoretical; D016017:Odds Ratio; D016012:Poisson Distribution