Statistical analysis of analytical results near detection limits with illustrations using elemental determinations in medical and biological samples by total reflection X-ray fluorescence

The following paper presents statistical analysis of measurement results close to the detection limit of an analytical technique and being random-left censored data. For such observations the measured value is not known precisely but is restricted by the detection limit. In the paper, the idea of random-left censored observations and data analysis are presented generally and next it is shown how to include censored observations into the statistical analysis with the use of available statistical analysis software (survival analysis procedure). Statistical procedure is presented on the examples of the X-ray spectroscopic analysis of element concentrations in medical and biological samples. Censored observations are included in data analysis and quartiles are estimated. Additionally, two- and multigroup comparison is presented for the censored observations. The accuracy of the presented procedure is demonstrated and discussed on the basis of Monte-Carlo simulations.