Unpublished manuscript:
"Choosing an estimate of initial activity level for multiple radioactive sources"
by Christopher Tong, Alex Cardenas, and Richard F. Raubertas
March 18, 2023
Abstract
For brachytherapy procedures, a small number, n, of radioactive Cs-137 sources are stored together in a lead safe. Their initial activity levels are measured upon delivery from the supplier, and are all found to be within 5% of each other. The physicist "randomly" chooses m sources for an individual therapeutic procedure. To determine dosage, the activity at the time of use can be calculated from knowledge of the initial activity and the decay factor of Cs-137. However, the sources are visually indistinguishable, so the initial activity values for a specific selected subset of sources are unknown, and an estimate must be used. Since the sources have similar activity levels, there is no practical difference among any estimates from within the range of values of the n sources. Nonetheless, some estimate must be chosen for the calculation; the physicist is free to make the choice based on principle. The problem is solved using an optimization approach, either of the mean squared error or the mean absolute error. The former results in the arithmetic mean of the whole set, but the latter results in a new, m-dependent estimator we call the combinatorial median. Artificial data sets are used to illustrate the findings.
Keywords: brachytherapy, statistical analysis, Cs-137