The impact of using voxel-level segmentation metrics on evaluating multifocal prostate cancer localisation

Dice similarity coefficient (DSC) and Hausdorff distance (HD) are widely used for evaluating medical image segmentation. They have also been criticised, when reported alone, for their unclear or even misleading clinical interpretation. DSCs may also differ substantially from HDs, due to boundary smoothness or multiple regions of interest (ROIs) within a subject. More importantly, either metric can also have a nonlinear, non-monotonic relationship with outcomes based on Type 1 and 2 errors, designed for specific clinical decisions that use the resulting segmentation. Whilst cases causing disagreement between these metrics are not difficult to postulate. This work first proposes a new asymmetric detection metric, adapting those used in object detection, for planning prostate cancer procedures. The lesion-level metrics is then compared with the voxel-level DSC and HD, whereas a 3D UNet is used for segmenting lesions from multiparametric MR (mpMR) images. Based on experimental results we report pairwise agreement and correlation 1) between DSC and HD, and 2) between voxel-level DSC and recall-controlled precision at lesion-level, with Cohen's [0.49, 0.61] and Pearson's [0.66, 0.76] (p-values}<0.001) at varying cut-offs. However, the differences in false-positives and false-negatives, between the actual errors and the perceived counterparts if DSC is used, can be as high as 152 and 154, respectively, out of the 357 test set lesions. We therefore carefully conclude that, despite of the significant correlations, voxel-level metrics such as DSC can misrepresent lesion-level detection accuracy for evaluating localisation of multifocal prostate cancer and should be interpreted with caution.