Harmonic Measure and Winding of Conformally Invariant Curves

The exact joint multifractal distribution for the scaling and winding of the electrostatic potential lines near any conformally invariant scaling curve is derived in two dimensions. Its spectrum f(alpha,lambda) gives the Hausdorff dimension of the points where the potential scales with distance $r$ as $H \sim r^{\alpha}$ while the curve logarithmically spirals with a rotation angle phi=lambda ln r. It obeys the scaling law f(\alpha,\lambda)=(1+\lambda^2) f(\bar \alpha)-b\lambda^2 with \bar \alpha=\alpha/(1+\lambda^2) and b=(25-c)/{12}$, and where f(\alpha)\equiv f(\alpha,0) is the pure harmonic measure spectrum, and c the conformal central charge. The results apply to O(N) and Potts models, as well as to {\rm SLE}_{\kappa}.Comment: 3 figure

A Randomized Study of Lenvatinib 18 mg vs 24 mg in Patients With Radioiodine-Refractory Differentiated Thyroid Cancer

Background: Lenvatinib is a multikinase inhibitor approved to treat radioiodine-refractory differentiated thyroid cancer (RR-DTC) at a starting dose of 24 mg/day. This study explored, in a double-blinded fashion, whether a starting dose of 18 mg/day would provide comparable efficacy with reduced toxicity. Methods: Patients with RR-DTC were randomized to lenvatinib 24 mg/day or 18 mg/day. The primary efficacy endpoint was objective response rate as of week 24 (ORRwk24); the odds ratio noninferiority margin was 0.4. The primary safety endpoint was frequency of grade ≥3 treatment-emergent adverse events (TEAEs) as of week 24. Tumors were assessed using RECIST v1.1. TEAEs were monitored and recorded. Results: The ORRwk24 was 57.3% (95% CI 46.1, 68.5) in the lenvatinib 24-mg arm and 40.3% (95% CI 29.3, 51.2) in the lenvatinib 18-mg arm, with an odds ratio (18/24 mg) of 0.50 (95% CI 0.26, 0.96). As of week 24, the rates of TEAEs grade ≥3 were 61.3% in the lenvatinib 24-mg arm and 57.1% in the lenvatinib 18-mg arm, a difference of -4.2% (95% CI -19.8, 11.4). Conclusion: A starting dose of lenvatinib 18 mg/day did not demonstrate noninferiority compared to a starting dose of 24 mg/day as assessed by ORRwk24 in patients with RR-DTC. The results represent a clinically meaningful difference in ORRwk24. The safety profile was comparable, with no clinically relevant difference between arms. These results support the continued use of the approved starting dose of lenvatinib 24 mg/day in patients with RR-DTC and adjusting the dose as necessary. Trial registration: ClinicalTrials.gov NCT02702388

Health-related quality-of-life analyses from a multicenter, randomized, double-blind phase 2 study of patients with differentiated thyroid cancer treated with lenvatinib 18 or 24 mg/day.

BACKGROUND: In the phase 2 double-blind Study 211, a starting dose of lenvatinib 18 mg/day was compared with the approved starting dose of 24 mg/day in patients with radioiodine-refractory differentiated thyroid cancer (RR-DTC). Predefined criteria for noninferiority for efficacy in the 18 mg arm were not met; safety was similar in both arms. Impact of lenvatinib treatment on health-related quality-of-life (HRQoL) was a secondary endpoint of Study 211. METHODS: Patients with RR-DTC were randomly assigned to a blinded starting dose of lenvatinib 18 mg/day or 24 mg/day. HRQoL was assessed at baseline, every 8 weeks until Week 24, then every 16 weeks, and at the off-treatment visit, using the EQ-5D-3L and FACT-G instruments. Completion and compliance rates, mean change from baseline, and times to first and definitive deterioration were evaluated. RESULTS: Baseline EQ-5D and FACT-G scores, and overall changes from baseline, were comparable between patients in the lenvatinib 18 mg/day (n = 77) and 24 mg/day arms (n = 75). For the 18 mg versus 24 mg arms, least squares mean differences were -0.42 (95% CI -4.88, 4.03) for EQ-5D-VAS and 0.47 (95% CI -3.45, 4.39) for FACT-G total. Time to first deterioration did not significantly favor either arm; EQ-5D-VAS HR [18 mg/24 mg] 0.93 (95% CI 0.61-1.40), EQ-5D-HUI HR [18 mg/24 mg] 0.68 (95% CI 0.44-1.05), FACT-G total HR [18 mg/24 mg] 0.73 (95% CI 0.48-1.12). Time to definitive deterioration did not significantly favor either arm, though EQ-5D-VAS showed a trend in favor of the 24 mg arm (HR [18 mg/24 mg] 1.72; 95% CI 0.99-3.01); EQ-5D-HUI HR [18 mg/24 mg] was 0.96 (95% CI 0.57-1.63), FACT-G total HR [18 mg/24 mg] was 0.72 (95% CI 0.43-1.21). CONCLUSIONS: In Study 211, HRQoL for patients in the lenvatinib 18 mg/day arm was not statistically different from that of patients in the 24 mg/day arm. These data further support the use of the approved lenvatinib starting dose of 24 mg/day in patients with RR-DTC. GOV NUMBER: NCT02702388