Radioanalytical data interpretation when the ratio reading/median is lognormally distributed

Area of Science:

• Radiochemistry
• Analytical Chemistry
• Statistics

Background:

• Fission track analysis data for plutonium in urine often exhibit non-normal and non-homoscedastic error distributions.
• Traditional calibration methods may not accurately represent these complex data variations.
• Accurate statistical interpretation is crucial for bioassay data and radiochemical procedures.

Purpose of the Study:

• To develop mathematical algorithms for a "best fit" calibration line with non-normal data.
• To provide methods for obtaining uncertainty ranges in the interpretation of unknowns from calibration.
• To demonstrate these methods using Brookhaven National Laboratory fission track analysis data for plutonium in urine.

Main Methods:

• Data analysis revealed lognormal distribution of track ratios and normal distribution of differences between logarithms of observed tracks and the median.
• A new "best fit" calibration line was obtained by minimizing a reduced chi-square statistic.
• Algorithms were developed to obtain the calibration line and uncertainty distributions for various analyte levels.

Main Results:

• The study demonstrates improved detection limits for plutonium in urine samples.
• The new calibration method requires a higher average sample activity to detect a worker's sample above the 95th percentile control population.
• This enhances the statistical robustness of bioassay data interpretation.

Conclusions:

• The developed mathematical algorithms effectively handle non-normal and non-homoscedastic error distributions in bioassay data.
• Accurate statistical interpretation and process control are vital for achieving low detection levels in radiochemical analyses.
• The findings contribute to more reliable monitoring of plutonium exposure in workers.