A comparison of several procedures to estimate the confidence interval for attributable risk in case-control studies

The estimation of a confidence interval for attributable risk from the logistic model based on data from case-control studies is a problem for which an accepted solution is lacking. Two methods, one based on the delta method and one bootstrap on the population base, have been described but their accuracy has not been compared. We present two other methods, one based on a jack-knife approach and the other using a bootstrap on two samples (cases and controls). The four methods are compared in a simulation study. The four methods are also applied to a case-control study on risk factors for preterm delivery; the confidence intervals are obtained assuming normality and by logarithmic transformation. When attributable risk is not smooth (for example, when exposure prevalence is low) both the jack-knife and the delta method tend to fail. If attributable risk is close to zero or one, normality cannot be assumed and log-transformed confidence intervals must be used. Finally, the extension to matched studies is analysed using a case-control study on risk factors of cutaneous malignant melanoma. In this situation, the population-based bootstrap is not available.