Random left‐censoring: a statistical approach accounting for detection limits in x‐ray fluorescence analysis

Abstract

AbstractThe use of x‐ray fluorescence techniques (XRF, TXRF, µXRF) in studies of trace element concentrations is limited by the detection limits (DL) of these methods. In this work we demonstrate that concentration measurements below the DL level, the so‐called ‘non‐detects’, can be included in data analysis by using the statistical concept of ‘censoring’, which is widely used, for instance, in survival analysis. This paper describes the non‐parametric methods of analysis of censored data using the random left‐censoring formalism, which can be used to account for the detection limits in XRF analysis. In particular, the application of the Kaplan–Meier and Nelson–Aalen estimators for the estimation of concentration distributions under censoring is discussed. These approaches are compared with the ‘reconstruction method’ developed earlier in our group to correct XRF data for the effect of detection limits. By using Monte Carlo simulations, the accuracy of the Kaplan–Meier and Nelson–Aalen estimators for censored data is discussed, in particular in the context of the estimation of the mean value and median of a concentration distribution. We demonstrate that for the ‘two‐group’ comparison of left‐censored concentrations, which is a problem of great practical importance, the log‐rank test can be used. The idea of random left censoring is applied to analyse the TXRF detection limit‐censored measurements of the concentrations of trace elements in biomedical samples. Copyright © 2004 John Wiley & Sons, Ltd.