Comparison of confidence intervals for adjusted attributable risk estimates under multinomial sampling

The epidemiologic concept of the adjusted attributable risk is a useful approach to quantitatively describe the importance of risk factors on the population level. It measures the proportional reduction in disease probability when a risk factor is eliminated from the population, accounting for effects of confounding and effect-modification by nuisance variables. The computation of asymptotic variance estimates for estimates of the adjusted attributable risk is often done by applying the delta method. Investigations on the delta method have shown, however, that the delta method generally tends to underestimate the standard error, leading to biased confidence intervals. We compare confidence intervals for the adjusted attributable risk derived by applying computer intensive methods like the bootstrap or jackknife to confidence intervals based on asymptotic variance estimates using an extensive Monte Carlo simulation and within a real data example from a cohort study in cardiovascular disease epidemiology. Our results show that confidence intervals based on bootstrap and jackknife methods outperform intervals based on asymptotic theory. Best variants of computer intensive confidence intervals are indicated for different situations.