Simulations of censoring effect in XRF analysis

Abstract

AbstractThe quantitative aspects of a use of random left‐censoring as a statistical approach accounting for the detection limit effects in x‐ray fluorescence (XRF) analysis were investigated using the Monte Carlo simulations. More precisely, the performance of the Kaplan–Meier method applied to the estimation of the original concentration distributions from detection limit censored concentration measurements are discussed. The simulations were performed for assumed log‐normal and log‐stable concentration distributions, which are known to model fairly well both concentrations and detection limits for biomedical and environmental samples. In particular, the question of the accuracy of the estimation of the mean value and median for the discussed concentration distributions using the Kaplan–Meier estimator was addressed. It is demonstrated that both the mean value and median of the concentration distribution can be estimated from censored data fairly precisely, typically within 4% for the log‐normal and within 15% for log‐stable models, even for substantial censoring levels (up to 80%). Moreover, the estimation of the median is much more precise than that of the mean value, in particular for stable distributions. Finally, the simulations show that random left‐censoring can be recommended as a standard tool for analysing the detection limit censored concentration measurements of trace elements in XRF analysis. Copyright © 2004 John Wiley & Sons, Ltd.