• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1859-1871
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• 2017

We compute the Jordan constant for the group of birational automorphisms of a projective plane ${\mathbb{P}}^2_{\mathbb{k}}$, where ${\mathbb{k}}$ is either an algebraically closed field of characteristic 0, or the field of real numbers, or the field of rational numbers.

• Journal of Gastric Cancer
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• v.17 no.2
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• pp.132-144
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• 2017

Purpose: To identify baseline prognostic factors for survival in patients with disease progression, during or after chemotherapy for the treatment of advanced gastric or gastroesophageal junction (GEJ) cancer. Materials and Methods: We pooled data from patients randomized between 2009 and 2012 in 2 phase III, global double-blind studies of ramucirumab for the treatment of advanced gastric or GEJ adenocarcinoma following disease progression on first-line platinum- and/or fluoropyrimidine-containing therapy (REGARD and RAINBOW). Forty-one key baseline clinical and laboratory factors common in both studies were examined. Model building started with covariate screening using univariate Cox models (significance level=0.05). A stepwise multivariable Cox model identified the final prognostic factors (entry+exit significance level=0.01). Cox models were stratified by treatment and geographic region. The process was repeated to identify baseline prognostic quality of life (QoL) parameters. Results: Of 1,020 randomized patients, 953 (93%) patients without any missing covariates were included in the analysis. We identified 12 independent prognostic factors of poor survival: 1) peritoneal metastases; 2) Eastern Cooperative Oncology Group (ECOG) performance score 1; 3) the presence of a primary tumor; 4) time to progression since prior therapy <6 months; 5) poor/unknown tumor differentiation; abnormally low blood levels of 6) albumin, 7) sodium, and/or 8) lymphocytes; and abnormally high blood levels of 9) neutrophils, 10) aspartate aminotransferase (AST), 11) alkaline phosphatase (ALP), and/or 12) lactate dehydrogenase (LDH). Factors were used to devise a 4-tier prognostic index (median overall survival [OS] by risk [months]: high=3.4, moderate=6.4, medium=9.9, and low=14.5; Harrell's C-index=0.66; 95% confidence interval [CI], 0.64-0.68). Addition of QoL to the model identified patient-reported appetite loss as an independent prognostic factor. Conclusions: The identified prognostic factors and the reported prognostic index may help clinical decision-making, patient stratification, and planning of future clinical studies.