This study demonstrated the usefulness of radiomic features based on the Hessian index of differential topology for the prediction of prognosis prior to treatment in head-and-neck (HN) cancer patients. The Hessian index, which can indicate tumor heterogeneity with convex, concave, and other points (saddle points), was calculated as the number of negative eigenvalues of the Hessian matrix at each voxel on computed tomography (CT) images. Three types of signatures were constructed in a training cohort (n = 126), one type each from CT conventional features, Hessian index features, and combined features from the conventional and index feature sets. The prognostic value of the signatures were evaluated using statistically significant difference (p value, log-rank test) to compare the survival curves of low- and high-risk groups. In a test cohort (n = 68), the p values of the models built with conventional, index, combined features, and clinical variables were 2.95 × 10–2, 1.85 × 10–2, 3.17 × 10–2, and 1.87 × 10–3, respectively. When the features were integrated with clinical variables, the p values of conventional, index, and combined features were 3.53 × 10–3, 1.28 × 10–3, and 1.45 × 10–3, respectively. This result indicates that index features could provide more prognostic information than conventional features and further increase the prognostic value of clinical variables in HN cancer patients.
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