Inserting One Edge into a Simple Drawing is Hard.

A simple drawing D(G) of a graph G is one where each pair of edges share at most one point: either a common endpoint or a proper crossing. An edge e in the complement of G can be inserted into D(G) if there exists a simple drawing of G + e extending D(G). As a result of Levi's Enlargement Lemma, if a drawing is rectilinear (pseudolinear), that is, the edges can be extended into an arrangement of lines (pseudolines), then any edge in the complement of G can be inserted. In contrast, we show that it is NP-complete to decide whether one edge can be inserted into a simple drawing. This remains true even if we assume that the drawing is pseudocircular, that is, the edges can be extended to an arrangement of pseudocircles. On the positive side, we show that, given an arrangement of pseudocircles A and a pseudosegment  σ , it can be decided in polynomial time whether there exists a pseudocircle Φ σ extending σ for which A ∪ { Φ σ } is again an arrangement of pseudocircles.

Outcomes based on prior therapy in the phase 3 METEOR trial of cabozantinib versus everolimus in advanced renal cell carcinoma.

BACKGROUND: In the phase 3 METEOR trial, cabozantinib improved progression-free survival (PFS), objective response rate (ORR), and overall survival (OS) versus everolimus in patients with advanced renal cell carcinoma (RCC), after prior antiangiogenic therapy. METHODS: Outcomes were evaluated for subgroups defined by prior therapy with sunitinib or pazopanib as the only prior VEGFR inhibitor, or prior anti-PD-1/PD-L1 therapy. RESULTS: For the prior sunitinib subgroup (N = 267), median PFS for cabozantinib versus everolimus was 9.1 versus 3.7 months (HR 0.43, 95% CI 0.32-0.59), ORR was 16% versus 3%, and median OS was 21.4 versus 16.5 months (HR 0.66, 95% CI 0.47-0.93). For the prior pazopanib subgroup (N = 171), median PFS for cabozantinib versus everolimus was 7.4 versus 5.1 months (HR 0.67, 95% CI 0.45-0.99), ORR was 19% versus 4%, and median OS was 22.0 versus 17.5 months (HR 0.66, 95% CI 0.42-1.04). For prior anti-PD-1/PD-L1 therapy (N = 32), median PFS was not reached for cabozantinib versus 4.1 months for everolimus (HR 0.22, 95% CI 0.07-0.65), ORR was 22% versus 0%, and median OS was not reached versus 16.3 months (HR 0.56, 95% CI 0.21-1.52). CONCLUSIONS: Cabozantinib was associated with improved clinical outcomes versus everolimus in patients with advanced RCC, irrespective of prior therapy, including checkpoint inhibitor therapy.

Double-blinded randomized study of high-dose calcitriol plus docetaxel compared with placebo plus docetaxel in androgen-independent prostate cancer: a report from the ASCENT Investigators.

PURPOSE: To compare the safety and activity of DN-101, a new high-dose oral formulation of calcitriol designed for cancer therapy, and docetaxel with placebo and docetaxel. PATIENTS AND METHODS: Patients with progressive metastatic androgen-independent prostate cancer and adequate organ function received weekly docetaxel 36 mg/m2 intravenously for 3 weeks of a 4-week cycle combined with either 45 microg DN-101 or placebo taken orally 1 day before docetaxel. The primary end point was prostate-specific antigen (PSA) response within 6 months of enrollment, defined as a 50% reduction confirmed at least 4 weeks later. RESULTS: Two hundred fifty patients were randomly assigned. Baseline characteristics were similar in both arms. Within 6 months, PSA responses were seen in 58% in DN-101 patients and 49% in placebo patients (P = .16). Overall, PSA response rates were 63% (DN-101) and 52% (placebo), P = .07. Patients in the DN-101 group had a hazard ratio for death of 0.67 (P = .04) in a multivariate analysis that included baseline hemoglobin and performance status. Median survival has not been reached for the DN-101 arm and is estimated to be 24.5 months using the hazard ratio, compared with 16.4 months for placebo. Grade 3/4 adverse events occurred in 58% of DN-101 patients and in 70% of placebo-treated patients (P = .07). Most common grade 3/4 toxicities for DN-101 versus placebo were neutropenia (10% v 8%), fatigue (8% v 16%), infection (8% v 13%), and hyperglycemia (6% v 12%). CONCLUSION: This study suggests that DN-101 treatment was associated with improved survival, but this will require confirmation because survival was not a primary end point. The addition of weekly DN-101 did not increase the toxicity of weekly docetaxel.