Are Robust Poisson Models Less Affected by Outliers Comparing to Log-Binomial Models When Estimating Relative Risks for Common Binary Outcomes?

• Activity Number: 137
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Wansu Chen*+ and Bonnie H. Li and Jiaxiao Shi and Lei Qian and Robert S Zeiger and Michael Schatz
• Companies: Kaiser Permanente and Kaiser Permanente Southern California and Kaiser Permanente and Kaise Permanente Southern California and Kaiser Permanente Southern California and Kaiser Permanente Medical Center
• Keywords: relative risk ; log-binomial regression ; robust Poisson regression ; outliers ; common binary outcomes ; risk ratio

Abstract

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 (RP) and the log-binomial (LB) regression. Of the two methods, it is believed that the LB method yields more efficient estimators because they are maximum likelihood based while the RP model may be less affected by outliers and misspecification. Evidence to support the robustness of the RP model is very limited. In this study, simulation was conducted to evaluate the performance of the two methods in several scenarios when outliers existed. Our findings suggest that for data coming from a population in which the relationship between the outcome and the covariate was in a simple form (e.g. log-linear), the two models yielded comparable bias and MSE. However, if the true relationship between the outcome and the covariate contained a higher order term, the RP model outperformed the LB model at various levels of contamination. The magnitude of difference between the two models increased with the level of contamination. Users should be aware of the limitations when choosing appropriate models to estimate relative risks.