Purpose: To enhance prognostic information of protein biomarkers for clear cell renal cell carcinomas (ccRCCs), we analyzed them within prognostic groups of ccRCC harboring different tumor characteristics of this clinically and molecularly heterogeneous tumor entity. Methods: Tissue microarrays from 145 patients with primary ccRCC were immunohistochemically analyzed for VHL (von Hippel-Lindau tumor suppressor), Ki67 (marker of proliferation 1), p53 (tumor protein p53), p21 (cyclin-dependent kinase inhibitor 1A), survivin (baculoviral IAP repeat containing 5), and UEA-1 (ulex europaeus agglutinin I) to assess microvessel-density. Results: When analyzing all patients, nuclear staining of Ki67 (hazard ratio [HR] 1.08, 95% confidence interval [CI] 1.04–1.12) and nuclear survivin (nS; HR 1.04, 95% CI 1.01–1.08) were significantly associated with disease-specific survival (DSS). In the cohort of patients with advanced localized or metastasized ccRCC, high staining of Ki67, p53 and nS predicted shorter DSS (Ki67: HR 1.07, 95% CI 1.02–1.11; p53: HR 1.05, 95% CI 1.01–1.09; nS: HR 1.08, 95% CI 1.02–1.14). In organ-confined ccRCC, patients with high p21-staining had a longer DSS (HR 0.96, 95% CI 0.92–0.99). In a multivariate model with stepwise backward elimination, tumor size and p21-staining showed a significant association with DSS in patients with "organ-confined" ccRCCs. The p21-staining increased the concordance index of tumor size from 0.75 to 0.78. In patients with "organ-confined" ccRCC, no disease-related deaths occurred in the group with p21-expression below the threshold of 32.5% p21-positive cells (log rank test: P=0.002). Conclusion: The prognostic information of the studied protein biomarkers depended on anatomic tumor stages, which displayed different acquired biological tumor characteristics. Analysis of prognostic factors within different clinical ccRCC groups could help to enhance their prognostic power. The p21-staining was an independent prognostic factor and increased prognostic accuracy in a predictive model in "organ-confined" ccRCC.

Purpose: To enhance prognostic information of protein biomarkers for clear cell renal cell carcinomas (ccRCCs), we analyzed them within prognostic groups of ccRCC harboring different tumor characteristics of this clinically and molecularly heterogeneous tumor entity. Methods: Tissue microarrays from 145 patients with primary ccRCC were immunohistochemically analyzed for VHL (von Hippel-Lindau tumor suppressor), Ki67 (marker of proliferation 1), p53 (tumor protein p53), p21 (cyclin-dependent kinase inhibitor 1A), survivin (baculoviral IAP repeat containing 5), and UEA-1 (ulex europaeus agglutinin I) to assess microvessel-density. Results: When analyzing all patients, nuclear staining of Ki67 (hazard ratio [HR] 1.08, 95% confidence interval [CI] 1.04–1.12) and nuclear survivin (nS; HR 1.04, 95% CI 1.01–1.08) were significantly associated with disease-specific survival (DSS). In the cohort of patients with advanced localized or metastasized ccRCC, high staining of Ki67, p53 and nS predicted shorter DSS (Ki67: HR 1.07, 95% CI 1.02–1.11; p53: HR 1.05, 95% CI 1.01–1.09; nS: HR 1.08, 95% CI 1.02–1.14). In organ-confined ccRCC, patients with high p21-staining had a longer DSS (HR 0.96, 95% CI 0.92–0.99). In a multivariate model with stepwise backward elimination, tumor size and p21-staining showed a significant association with DSS in patients with 'organ-confined' ccRCCs. The p21-staining increased the concordance index of tumor size from 0.75 to 0.78. In patients with 'organ-confined' ccRCC, no disease-related deaths occurred in the group with p21-expression below the threshold of 32.5% p21-positive cells (log rank test: P=0.002). Conclusion: The prognostic information of the studied protein biomarkers depended on anatomic tumor stages, which displayed different acquired biological tumor characteristics. Analysis of prognostic factors within different clinical ccRCC groups could help to enhance their prognostic power. The p21-staining was an independent prognostic factor and increased prognostic accuracy in a predictive model in 'organ-confined' ccRCC.

Das „Strongly Constrained and Appropriately Normed“ (SCAN) Austausch-Korrelations-Funktional gehört zur Familie der meta-GGA (generalized gradient approximation) Funktionale. Es gibt aber auch Nachteile Zum einen leiden SCAN Rechnungen oft unter numerischen Instabilitäten, wodurch sehr viele Iteration zum Erreichen von Selbst-Konsistenz benötigt werden. Zum anderen leidet SCAN unter dem von GGA Methoden bekannten Selbstwechselwirkung-Fehler. Im ersten Teil der Arbeit habe ich die numerischen Stabilitätsprobleme in SCAN Rechnungen im Rahmen der numerischen Realraum-Integrationsroutinen im Code FHI-aims untersucht. Diese Analyse zeigt, dass die genannte Probleme durch Anwendung von standardisierten Dichte-Mischalgorithmen für die kinetische Energiedichte abgemildert werden können. Dadurch wird auch in SCAN-Rechnungen eine schnelle und stabile Konvergenz zur selbstkonsistenten Lösung ermöglicht. Im zweiten Teil der Arbeit habe ich untersucht, in welchem Rahmen sich der Selbstwechselwirkung-Fehler in SCAN mittels des von Perdew und Zunger vorgeschlagenen Selbstinteraktionskorrekturalgorithmus (PZ-SIC) verringern lässt. Es wurden aber auch Optimierungen für die PZ-SIC Methode entwickelt. Inspiriert von den ursprünglichen Argumenten in der PZ-SIC-Methode und anderen lokalisierten Methoden, wird in dieser Arbeit eine neuartige Randbedingung (orbital density constraint) vorgeschlagen, die sicherstellt, dass die PZ-SIC Orbitale während des Selbstkonsistenzzyklus lokalisiert bleiben. Dies mildert die Anfangswertabhängigkeit deutlich ab und hilft dabei, in die korrekte selbst-konsistente Lösung mit minimaler Energie zu konvergieren, unabhängig davon ob reelle oder komplexe SIC Orbitale verwendet werden. Die in dieser Arbeit getägtigen Entwicklungen und Untersuchungen sind Wegbereiter dafür, in Zukunft mit SIC-SCAN Rechnungen deutlich genauere ab initio Rechnungen mit nur gering höherem Rechenaufwand durchführen zu können. / The state-of-the-art “Strongly Constrained and Appropriately Normed” (SCAN) functional pertains to the family of meta-generalized-gradient approximation (meta-GGA) exchange-correlation functionals. Nonetheless, SCAN suffers from some well-documented deficiencies. In the first part of this thesis, I revisited the known numerical instability problems of the SCAN functional in the context of the numerical, real-space integration framework used in the FHI-aims code. This analysis revealed that applying standard density-mixing algorithms to the kinetic energy density attenuates and largely cures these numerical issues. By this means, SCAN calculations converge towards the self-consistent solution as fast and as efficiently as lower-order GGA calculations. In the second part of the thesis, I investigated strategies to alleviate the self-interaction error in SCAN calculations by using the self-interaction correction algorithm proposed by Perdew and Zunger (PZ-SIC). Inspired by the original arguments in PZ-SIC and other localized methods, I introduced a mathematical constraint, i.e., the orbital density constraint, that forces the orbitals to retain their localization throughout the self-consistency cycle. In turn, this alleviates the multiple-solutions problem and facilitates the convergence towards the correct, lowest-energy solution both for complex and real SIC orbitals. The developments and investigations performed in this thesis pave the road towards a more wide-spread use of SIC-SCAN calculations in the future, allowing more accurate predictions within only moderate increases of computational cost.