Coverage and precision of confidence intervals for area under the curve using parametric and non-parametric methods in a toxicokinetic experimental design

Purpose. The coverage and precision of parametric Bailer-type confidence intervals (CIs) for area under the curve (AUG) was compared to nonparametric bootstrap confidence intervals. Methods. Concentration-time data was simulated using Monte Carlo simulation under a toxicokinetic paradigm with sparse (SSC) and dense sampling (DSC) conditions. AUC was calculated using the trapezoidal rule and 95% CIs were computed using various parametric and nonparametric methods. Results. Under SSC, the various parametric CIs contained the true population AUC with coverage probabilities ranging from 0.77 to 0.95 with low inter-subject variation (coefficient of variation (CV) = 15%) and from 0.82 to 0.95 with high inter-subject variation (CV = 50%). The nominal value should be close to 0.95. DSC tended to increase coverage by about 0.05. Bailer's method always produced the lowest coverage of all parametric CIs examined. Under SSC, bootstrap CIs had coverage probabilities ranging from 0.62 (CV = 15%) to 0.68 (CV = 50%). DSC increased coverage to 0.77. Parametric CIs were wider than their nonparametric counterparts, often giving lower CI estimates less than zero. Bailer's method and Bailer's method using the jackknife estimate of the standard error were the worst in this respect. Bootstrap CIs never had lower CI estimates less than zero. However, SSC tends to produce bootstrap distributions that are not continuous which, if used, may produce biased CI estimates. Conclusions. Bootstrap CI estimates were judged to be the "best". However, the limitations of the bootstrap should be clearly recognized and it should not be used indiscriminately. Examination of the bootstrap distribution for its degree of discrete-ness must be part of the statistical process.