This study aimed to explore topological prediction models for relapses, i.e., locoregional relapse (LRR) and distant metastasis (DM), of stage I patients with non-small cell lung cancer (NSCLC) prior to stereotactic ablative radiotherapy (SABR). Pretreatment planning computed tomography (CT) images of 125 primary NSCLC patients with SABR were divided into training (n = 65) and test datasets (n = 60). The signatures on lung tumor heterogeneity in CT images were constructed with conventional wavelet features (WFs), invariant topological features (original: TFs, inverted: iTFs), and their combined features (TWFs, iTWFs). Invariant topological features are related to intrinsic holes or heterogeneity in the tumors. The predictability of the tumor volumes which may be associated with lung cancer prognosis was also delved into with the image signatures. The patients were stratified into high-risk and low-risk groups using a radiomics score calculated from the signature. The predictability was evaluated using a p-value (log-rank test) between Kaplan–Meier (KM) curves of high-risk and low-risk groups, a concordance index (c-index), and a multiplication of negative logarithm of p-value and c-index (nLPC), which was considered a comprehensive evaluation index. For the test dataset, the iTFs and WFs combined with the tumor volumes had statistically significant differences of p-values (< 0.05) of the KM curves and higher nLPCs for the relapses. The signatures derived from inverted topology-based features and wavelet features combined with tumor volumes showed the potential of improving the high-risk and low-risk stratification for the relapses.
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