Comparison of adjusted attributable risk estimators

The estimation of attributable risk in the presence of confounding and effect modification is studied in this paper. Different adjustment methods for the attributable risk are reviewed. The results of a stimulation study comparing these methods under the unrestricted multinomial sampling model are reported. From the study it is concluded that the maximum likelihood estimator resulting from the 'case load weighting' of the stratum-specific attributable risk estimates will be the best overall choice in all practical situations with relatively large sample sizes. Other adjusted attributable risk estimators depend heavily on the underlying structure of the multinomial model.