Confidence interval for quantiles and percentiles

Abstract

Quantiles and percentiles represent useful statistical tools for describing the distribution of results and deriving reference intervals and performance specification in laboratory medicine. They are commonly intended as the sample estimate of a population parameter and therefore they need to be presented with a confidence interval (CI). In this work we discuss three methods to estimate CI on quantiles and percentiles using parametric, nonparametric and resampling (bootstrap) approaches. The result of our numerical simulations is that parametric methods are always more accurate regardless of sample size when the procedure is appropriate for the distribution of results for both extreme (2.5^th and 97.5^th) and central (25^th, 50^th and 75^th) percentiles and corresponding quantiles. We also show that both nonparametric and bootstrap methods suit well the CI of central percentiles that are used to derive performance specifications through quality indicators of laboratory processes whose underlying distribution is unknown.