Constraint Approaches to the Estimation of Relative Risk

• Activity Number: 74 - Developments in Epidemiologic Models
• Type: Contributed
• Date/Time: Sunday, July 30, 2017 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Yuanyuan Tang* and Philip Jones and Liangrui Sun and Suzanne Arnold and John Spertus
• Companies: Saint Luke's Health System and Saint Luke's Health System and University of Nebraska-Lincoln and Saint Luke's Health System and Saint Luke's Health System
• Keywords: Adjusted relative risk ; bootstrapping ; constraint optimization ; sandwich estimator

Abstract

Calculating relative risk using log-Binomial regression often encounters non-convergence. A modified Poisson regression, which uses robust variance, was proposed by Zou in 2006. Even the modified Poisson regression with sandwich variance estimator is valid for estimation of relative risk; the predicted probability of the outcome may be greater than the natural boundary 1.0 for the unobserved but plausible covariate combinations. Moreover, the lower and upper bound of confidence intervals for predicted probabilities could fall out of (0, 1). In 2010, Chu and Cole proposed a Bayesian approach to overcome this issue. Posterior median was used to get the parameter estimation. However, the Bayesian approach provides biased estimation, especially when the probability of outcome is high. In this paper, we propose an alternative constraint optimization approach for estimating relative risk. Our approach can reach similar or better performance than Bayesian approach. Simulation studies are conducted to demonstrate the usefulness of this approach. Our method is also illustrated by PREMIER Data.