Censoring approach to the detection limits in X-ray fluorescence analysis

Abstract

We demonstrate that the effect of detection limits in the X-ray fluorescence analysis (XRF), which limits the determination of very low concentrations of trace elements and results in appearance of the so-called “nondetects”, can be accounted for using the statistical concept of censoring. More precisely, the results of such measurements can be viewed as the left random censored data, which can further be analyzed using the Kaplan–Meier method correcting the data for the presence of nondetects. Using this approach, the results of measured, detection limit censored concentrations can be interpreted in a nonparametric manner including the correction for the nondetects, i.e. the measurements in which the concentrations were found to be below the actual detection limits. Moreover, using the Monte Carlo simulation technique we show that by using the Kaplan–Meier approach the corrected mean concentrations for a population of the samples can be estimated within a few percent uncertainties with respect of the simulated, uncensored data. This practically means that the final uncertainties of estimated mean values are limited in fact by the number of studied samples and not by the correction procedure itself. The discussed random-left censoring approach was applied to analyze the XRF detection-limit-censored concentration measurements of trace elements in biomedical samples.