Model-Based Estimation of the Attributable Risk: A Loglinear Approach

This paper considers model-based methods for estimation of the adjusted attributable risk (AR) in both case-control and cohort studies. An earlier review discussed approaches for both types of studies, using the standard logistic regression model for case-control studies, and for cohort studies proposing the equivalent Poisson model in order to account for the additional variability in estimating the distribution of exposures and covariates from the data. In this paper we revisit case-control studies, arguing for the equivalent Poisson model in this case as well. Using the delta method with the Poisson model, we provide general expressions for the asymptotic variance of the AR for both types of studies. This includes the generalized AR, which extends the original idea of attributable risk to the case where the exposure is not completely eliminated. These variance expressions can be easily programmed in any statistical package that includes Poisson regression and has capabilities for simple matrix algebra. In addition, we discuss computation of standard errors and confidence limits using bootstrap resampling. For cohort studies, use of the bootstrap allows binary regression models with link functions other than the logit.