Confidence intervals, hypothesis tests, and sample sizes for the prevented fraction in cross‐sectional studies

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Abstract
The prevented fraction (PF) is the proportion of disease occurrence in a population averted due to a protective risk factor or public health intervention. The PF is not equivalent to the population attributable risk (AR). The AR is appropriate for epidemiologic studies of disease etiology, and for estimating the potential impact of modifying risk factor prevalence. The PF more directly measures the impact of public health interventions, however, and thus is an important evaluation tool. We derived the variance of the estimated PF by using maximum likelihood theory for cross‐sectional studies. We used simulations to compare the performance of confidence intervals based on various transformations of the estimated PF. The logit transformation was the best choice when PF ≥ 0·3, whereas the untransformed estimate was best when PF < 0·3. We present formulae for hypothesis testing and sample size calculations, discuss the issues of interaction and confounding and give two estimators adjusted for confounding.