A review of adjusted estimators of attributable risk

This paper reviews adjusted methods of estimation of attributable risk (AR), that is methods that allow one to obtain estimates of AR while controlling far other factors. Estimability and basic principles of AR estimation are first considered and the rationale for adjusted AR estimators is discussed. Then, adjusted AR estimators are reviewed focusing on cross-sectional, cohort and case-control studies. Two inconsistent adjusted estimators are briefly commented upon. Next, adjusted estimators based on stratification, namely the weighted-sum and Mantel-Haenszel (MH) approaches, are reviewed and contrasted. It appears that the weighted-sum approach, which allows for full interaction between exposure and adjustment factors, can be affected by small-sample bias. By contrast, the MH approach, which rests on the assumption of no interaction between exposure and adjustment factors may be misleading if interaction between exposure and adjustment factors is present. Model-based adjusted estimators represent a more general and flexible approach that includes both stratification approaches as special cases and offers intermediate options. Bruzzi et al.'s and Greenland and Drescher's estimators are reviewed and contrasted. Finally, special problems of adjusted estimation are considered, namely estimation from case-cohort data, estimation for risk factors with multiple levels, for multiple risk factors, for recurrent events, estimation of the prevented and preventable fractions, and estimation of the generalized impact fraction. Comments on future directions are presented.