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Background The aim of this nationwide observational study was to evaluate factors associated with multivisceral resection (MVR), margin status and overall survival in locally advanced colorectal cancer (CRC). Material and methods Patients with (y)pT4, cM0 CRC between 2006 and 2017 were selected from the Netherlands Cancer Registry. Cox-proportional hazards modelling was used for survival analysis, stratified for T4a and T4b. Annual hospital volume cut-off was 75 for colon and 40 for rectal resections. Results A total of 11.930 patients were included and 2410 patients (20.2%) underwent MVR. Factors associated with MVR for colon and rectal cancer besides cT4 category were more recent diagnosis (OR 3.61, CI 95% 3.06–4.25 (colon) and OR 2.72, CI 95% 1.82–4.08 (rectum)) and high hospital volume (OR 1.20, CI 95% 1.05–1.38 (colon) and OR 2.17, CI 95% 1.55–3.04 (rectum)). Patients ≥70 year were less likely to undergo MVR for colon cancer (OR 0.80, 95% CI 0.70–0.90). Risk factors for incomplete resection were cT4 (OR 3.08, CI 95% 2.35–4.04 (colon) and OR 1.82, CI 95% 1.13–2.94 (rectum)) and poor/undifferentiated tumors (OR 1.41, CI 95% 1.14–1.72 (colon) and OR 1.69, CI 95% 1.05–2.74 (rectum)). More recent diagnosis was independently associated with less incomplete resections in colon cancer (OR 0.58, CI 95% 0.40–0.76). Independent predictors of survival were age, resection margin, nodal status and adjuvant chemotherapy, but not MVR. Conclusion Treatment of locally advanced CRC with MVR at population level was influenced by year of diagnosis and hospital volume. Margin status in colon cancer improved substantially over time.

We study the observability of a permutation on a finite set by a complex-valued function. The analysis is done in terms of the spectral theory of the unitary operator on functions defined by the permutation. Any function f can be written uniquely as a sum of eigenfunctions of this operator; we call these eigenfunctions the eigencomponents of f. It is shown that a function observes the permutation if and only if its eigencomponents separate points and if and only if the function has no nontrivial symmetry that preserves the dynamics. Some more technical conditions are discussed. An application to the security of stream ciphers is discussed.