Interval estimation of the attributable risk in case-control studies with matched pairs

Objective-The attributable risk (AR), which represents the proportion of ca ses who can be preventable when we completely eliminate a risk factor in a population, is the most commonly used epidemiological index to assess the i mpact of controlling a selected risk factor on community health. The goal o f this paper is to develop and search for good interval estimators of the A R for case-control studies with matched pairs. Methods-This paper considers five asymptotic interval estimators of the AR, including the interval estimator using Wald's statistic suggested elsewher e, the two interval estimators using the logarithmic transformations: log(x ) and log(1-x), the interval estimator using the logit transformation log(x /(1-x)), and the interval estimator derived from a simple quadratic equatio n developed in this paper. This paper compares the finite sample performanc e of these five interval estimators by calculation of their coverage probab ility and average length in a variety of situations. Results-This paper demonstrates that the interval estimator derived from th e quadratic equation proposed here can not only consistently perform well w ith respect to the coverage probability, but also be more efficient than th e interval estimator using Wald's statistic in almost all the situations co nsidered here. This paper notes that although the interval estimator using the logarithmic transformation log(1-x) may also perform well with respect to the coverage probability, using this estimator is likely to be less effi cient than the interval estimator using Wald's statistic. Finally, this pap er notes that when both the underlying odds ratio (OR) and the prevalence o f exposure (PE) in the case group are not large (OR less than or equal to2 and PE less than or equal to0.10), the application of the two interval esti mators using the transformations log(x) and log(x/(1-x)) can be misleading. However, when both the underlying OR and PE in the case group are large (O R greater than or equal to4 and PE greater than or equal to0.50), the inter val estimator using the logit transformation can actually outperform all th e other estimators considered here in terms of efficiency. Conclusions-When there is no prior knowledge of the possible range for the underlying OR and PE, the interval estimator derived from the quadratic equ ation developed here for general use is recommended. When it is known that both the OR and PE in the case group are large (OR greater than or equal to 4 and PE greater than or equal to0.50), it is recommended that the interval estimator using the logit transformation is used.