A Population-Based Model Selection in Single Time Point Dosimetry Using Non-Linear Mixed Effects Modeling for Benign Thyroid Disease

Introduction: Dosimetry with single-time-point (STP) biokinetic data for calculating time-integrated activity (TIA) is desirable in molecular radiotherapy. One of the promising methods is the non-linear mixed effects (NLME) modeling []. This method has been shown to perform better than a frequently used STP method introduced by Hänscheid et al. for [¹⁷⁷Lu]Lu-DOTATATE [, ]. However, this method has not been implemented in a large population of benign thyroid disease patients. Therefore, the aim of this study was to determine the accuracy of TIAs calculated using STP data with NLME modeling and population-based model selection (PBMS) in a population of 73 benign thyroid disease patients. In addition, we compared the accuracy of the STP method using the PBMS-NLME method to the STP method using a mono-exponential [].

Methods: Biokinetic data of ¹³¹I in benign thyroid diseases (Graves' disease, toxic nodular goiter, non-toxic goiter) were obtained from 73 patients with uptake measurements at multiple time points 2, 6, 24, 48, and 96 (n=53) or 120 (n=20) hours after oral capsule administration of ¹³¹I []. PBMS with seventeen sum-of-exponentials (SOE) functions with different parameterizations, with two to nine parameters, were employed for the analysis. The most suitable SOE function describing the biokinetic data was selected based on a goodness-of-fit test and the Akaike weight. The Akaike weight indicates a function’s likelihood to describe the data best. The selected optimal SOE function was employed to conduct STP dosimetry at various time points (sTIAs). Additionally, STP dosimetry was performed using the approach proposed by Hänscheid et al. for late time points to calculate the TIAs (hTIAs) at 96 and 120 hours post-administration [4]. The accuracy of the computed sTIAs and hTIAs was evaluated by comparing them to the rTIAs obtained from fitting all time points using the best model. The comparison was done by calculating the relative deviations (RDs) and root-mean-square errors (RMSEs).

Results: The SOE function with five adjustable parameters was selected as fit function most supported by the data based on the goodness-of-fit test with an Akaike weight of essentially 100%. The mean±standard deviation of RD (RMSE) of STP dosimetry with the best SOE function for 2, 6, 24, 48, and 96, and 120 hours post administration were 0.17±0.44 (0.47), 0.14±0.34 (0.36), 0.09±0.27 (0.28), 0.08±0.20 (0.22), 0.04±0.08 (0.09), and 0.03±0.04 (0.05), respectively. The mean±standard deviation of RD (RMSE) of STP dosimetry with the Hänscheid method for 96 and 120 hours post administration were -0.07±0.09 (0.11) and 0.01±0.05 (0.06), respectively.

Conclusions: Applying the model selection method helps improve the accuracy and precision of the fit function selection and, thus, the reproducibility between different observers. STP dosimetry with a late time point measurement at 120 h using the NLME modeling method shows that the simplified TIA calculation is acceptable and produces accurate TIA values in ¹³¹I thyroid therapy.

Reference

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