APPROXIMATE CONFIDENCE-INTERVALS IN CALIBRATION USING THE BOOTSTRAP

The goal of calibration is to estimate a sample's concentration and the error associated with that estimate when only its signal response is known. Simulations were run to test the accuracy and precision of various parametric confidence intervals to confidence intervals generated by the bias-corrected, nonparametric bootstrap approach. None of the methods studied reached their asymptotic coverage probability, although the exact parametric confidence interval came the closest. The ranges of exact parametric confidence intervals were significantly larger than the other methods. Approximate parametric confidence intervals and bootstrap confidence intervals were both dependent on the number of replicates analyzed and on the coefficient of variation of the assay. When only a single replicate was available for analysis, the bootstrap method was dismal in containing the true sample concentration. As the number of replicates increases, the width of the bootstrap confidence interval converged to the exact parametric confidence interval, whereas the approximate parametric confidence interval width increased and began to diverge from the exact parametric confidence interval. Bootstrap confidence intervals produce maximal coverage with minimal range when 2-4 replicate samples are available for analysis.