Comparison of Robustness to Model Misspecification Between Log-Binomial Models and the Robust Poisson Models When Estimating Relative Risks for Common Binary Outcomes

• Activity Number: 136
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Wansu Chen* and Jiaxiao Shi and Lei Qian and Stan P. Azen
• Companies: Kaiser Permanente Southern California and Kaiser Permanente Southern California and Kaiser Permanente Southern California and University of Southern California Keck School of Medicine
• Keywords: relative risk ; common binary outcomes ; log-binomial regression ; robust Poisson regression ; quasi-likelihood ; model misspecification

Abstract

To estimate relative risks or risk ratios for common binary outcomes, the most popular model-based methods are the quasi-likelihood based robust (also known as modified) Poisson (RP) and the maximum likelihood based log-binomial (LB) regression. Our previous work showed that the RP models are more robust to outliers compared to the LB models in some scenarios. In this study, simulation was conducted to evaluate the performance of the two methods in various scenarios when the models were mis-specified. Our findings suggest that when the link functions were mis-specified or the distributions of the outcome variable were altered by the linear predictors, the RP models yielded less biased point estimators compared to the LB models, especially when the level of model misspecification is high. The PR models produced near optimal 95% coverage rates in all the scenarios we examined. The gains in mean square errors (MSE) were quite obvious when the sample size was large (n=1,000) yet compromised when the sample size reduced to 500, due to the efficiency loss of the RP models. Users should be aware of the limitations when choosing the most appropriate models to estimate relative risks.