Bias in methods for deriving standardized morbidity ratio and attributable fraction estimates

This paper examines several methods for deriving standardized morbidity ratios (SMR) and attributable fraction (attributable risk percentage) estimates. We show that some of the proposed methods will, in general, produce biased estimators, although the low variance of certain estimators sometimes compensates for their bias. A few methods are based on statistical fallacies and should be avoided, especially the method of deriving the expected number of cases from a regression equation that does not include the exposure under study.