Optimal transformations leading to normal distributions of positron emission tomography standardized uptake values

The statistical analysis of positron emission tomography (PET) standardized uptake value (SUV) measurements is challenging due to the skewed nature of SUV distributions. This limits utilization of powerful parametric statistical models for analyzing SUV measurements. An ad-hoc approach, which is frequently used in practice, is to blindly use a log transformation, which may or may not result in normal SUV distributions. This study sought to identify optimal transformations leading to normally distributed PET SUVs extracted from tumors and assess the effects of therapy on the optimal transformations.

The optimal transformation for producing normal distributions of tumor SUVs was identified by iterating the Box-Cox transformation parameter (λ) and selecting the parameter that maximized the Shapiro-Wilk P-value. Optimal transformations were identified for tumor SUV_max distributions at both pre and post treatment. This study included 57 patients that underwent ¹⁸F-fluorodeoxyglucose (¹⁸F-FDG) PET scans (publically available dataset). In addition, to test the generality of our transformation methodology, we included analysis of 27 patients that underwent ¹⁸F-Fluorothymidine (¹⁸F-FLT) PET scans at our institution.

After applying the optimal Box-Cox transformations, neither the pre nor the post treatment ¹⁸F-FDG SUV distributions deviated significantly from normality (P  >  0.10). Similar results were found for ¹⁸F-FLT PET SUV distributions (P  >  0.10). For both ¹⁸F-FDG and ¹⁸F-FLT SUV distributions, the skewness and kurtosis increased from pre to post treatment, leading to a decrease in the optimal Box-Cox transformation parameter from pre to post treatment. There were types of distributions encountered for both ¹⁸F-FDG and ¹⁸F-FLT where a log transformation was not optimal for providing normal SUV distributions.

Optimization of the Box-Cox transformation, offers a solution for identifying normal SUV transformations for when the log transformation is insufficient. The log transformation is not always the appropriate transformation for producing normally distributed PET SUVs.