A Novel Prognostication System for Spinal Metastasis Patients Based on Network Science and Correlation Analysis.

AIMS: During the progress of oncological diseases, there is an increased probability that spinal metastases may develop, requiring personalised treatment options. Risk calculator systems aim to provide assistance in the therapeutic decision-making process by estimating survival chances. The predictive ability of such calculators can be improved, thereby optimising the choice of personalised therapy. The aim of this research was to create a new risk assessment system and show a method with which other centres can develop their own local score. MATERIALS AND METHODS: We created a database by retrospectively processing 454 patients. The prognostic factors were selected via a network science-based correlation analysis that maximises Uno's C-index, keeping only a small number of predictors. To validate the new system, we calculated the D-statistic, the Integrated Discrimination Index, made a five-fold cross-validation and also calculated the integrated time-dependent Brier score. RESULTS: As a result of multivariate Cox analysis, we found five independent prognostic factors suitable for the design of the risk calculator. This new system has a better predictive ability compared with six other well-known systems with an average C-index of 0.706 at 10 years (95% confidence interval 0.679-0.733). CONCLUSIONS: An accurate estimation of the life expectancy of cancer patients is essential for the implementation of personalised medicine. The training performance of our system is encouraging, indicating the benefit of a network science-based visualisation step. We believe that in order to further improve the prediction ability, it is necessary to systematise previously 'unknown' factors (e.g. radiological morphology).

Spectral correlations in systems undergoing a transition from periodicity to disorder.

We study the spectral statistics for extended yet finite quasi-one-dimensional systems, which undergo a transition from periodicity to disorder. In particular, we compute the spectral two-point form factor, and the resulting expression depends on the degree of disorder. It interpolates smoothly between the two extreme limits-the approach to Poissonian statistics in the (weakly) disordered case, and the universal expressions derived in T. Dittrich, B. Mehlig, H. Schanz, and U. Smilansky, Chaos Solitons Fractals 8, 1205 (1997); Phys. Rev. E 57, 359 (1998); B. D. Simons and B. L. Altshuler, Phys. Rev. Lett. 70, 4063 (1993); and N. Taniguchi and B. L. Altshuler, ibid. 71, 4031 (1993) for the periodic case. The theoretical results agree very well with the spectral statistics obtained numerically for chains of chaotic billiards and graphs.