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

摘要

Variance stabilization is an important step in statistical assessment of quantitative imaging biomarkers (QIBs) to meetthe equal variances requirements across different subgroups for many statistical tests. The objective of this study is tocompare the commonly used Log transformation to the Box-Cox transformation for variance stabilization in the contextof the assessment of a computed tomography (CT) lung nodule volume estimation QIB. Our investigation included thefollowing: (1) We developed a model characterizing repeated measurements typically observed in CT lung nodulevolume estimation. Given the model, we derived the parameter of the Box-Cox transformation that stabilizes thevariance of the volume measurements across lung nodules. (2) We validated our approach using simulation data andexamined 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 oftransformations, 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 transformationyielded smaller CVstd than the Log transformation. This suggests the Box-Cox transformation has better performance invariance stabilization for the estimation of lung nodule volume from CT data and can be a practical alternative forimproved variance stabilization in the assessment of some types of QIBs. We are generating a guideline for determiningwhen the Box-Cox might be a viable option to the Log transformation within a QIB assessment framework.