Data transformations for variance stabilization in the statistical assessment of quantitative imaging biomarkers

Variance stabilization is an important step in statistical assessment of quantitative imaging biomarkers (QIBs) to meet the equal variances requirements across different subgroups for many statistical tests. The objective of this study is to compare the commonly used Log transformation to the Box-Cox transformation for variance stabilization in the context of the assessment of a computed tomography (CT) lung nodule volume estimation QIB. Our investigation included the following: (1) We developed a model characterizing repeated measurements typically observed in CT lung nodule volume estimation. Given the model, we derived the parameter of the Box-Cox transformation that stabilizes the variance of the volume measurements across lung nodules. (2) We validated our approach using simulation data and examined factors that impact the performance of the transformations by comparing it to the standard Log transformation. The coefficient of variation for the standard deviation (CVstd) was used as the metric for quantifying the performance of transformations, with smaller CVstd indicating better variance stabilization. Results showed for both transformations, CVstd decreased with larger number of repeated measurements. For all simulated datasets, the Box-Cox transformation yielded smaller CVstd than the Log transformation. This suggests the Box-Cox transformation has better performance in variance stabilization for the estimation of lung nodule volume from CT data and can be a practical alternative for improved variance stabilization in the assessment of some types of QIBs. We are generating a guideline for determining when the Box-Cox might be a viable option to the Log transformation within a QIB assessment framework.