Tumor Volume Distributions Based on Weibull Distributions of Maximum Tumor Diameters

Abstract

(1) Background: The distribution of tumor volumes is important for various aspects of cancer research. Unfortunately, tumor volume is rarely documented in tumor registries; usually only maximum tumor diameter is. This paper presents a method to derive tumor volume distributions from tumor diameter distributions. (2) Methods: The hypothesis is made that tumor maximum diameters d are Weibull distributed, and tumor volume is proportional to dk, where k is a parameter from the Weibull distribution of d. The assumption is tested by using a test dataset of 176 segmented tumor volumes and comparing the k obtained by fitting the Weibull distribution of d and from a direct fit of the volumes. Finally, tumor volume distributions are calculated from the maximum diameters of the SEER database for breast, NSCLC and liver. (3) Results: For the test dataset, the k values obtained from the two separate methods were found to be k = 2.14 ± 0.36 (from Weibull distribution of d) and 2.21 ± 0.25 (from tumor volume). The tumor diameter data from the SEER database were fitted to a Weibull distribution, and the resulting parameters were used to calculate the corresponding exponential tumor volume distributions with an average volume obtained from the diameter fit. (4) Conclusions: The agreement of the fitted k using independent data supports the presented methodology to obtain tumor volume distributions. The method can be used to obtain tumor volume distributions when only maximum tumor diameters are available.