Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

Efficacy and Safety of Radium-223 Dichloride in Symptomatic Castration-resistant Prostate Cancer Patients With or Without Baseline Opioid Use From the Phase 3 ALSYMPCA Trial

Background: The phase 3 ALSYMPCA trial enrolled metastatic castration-resistant prostate cancer patients with or without baseline opioid use.

Objective: To assess the efficacy and safety of radium-223 dichloride (radium-223) versus placebo in ALSYMPCA patients by baseline opioid use.

Design, setting, and participants: Nine hundred and twenty one patients enrolled at 136 centers globally.

Intervention: Radium-223 (50 kBq/kg, intravenous injection) every 4 wk for six cycles or matching placebo, each plus best standard of care.

Outcome measurements and statistical analysis: Primary endpoint (overall survival [OS]), main secondary efficacy endpoints, and safety were evaluated by baseline opioid use. Additional analyses included time to first opioid use, time to first external beam radiation therapy for bone pain, and safety of concomitant external beam radiation therapy.

Results and limitations: At baseline, 408 (44%) patients had no pain and no analgesic use or mild pain with nonopioid therapy (World Health Organization ladder pain score 0–1 [nonopioid subgroup]), and 513 (56%) had moderate pain with occasional opioids or severe pain with regular daily opioids (World Health Organization ladder pain score 2–3 [opioid subgroup]). Radium-223 significantly prolonged OS versus placebo in nonopioid (hazard ratio [HR] = 0.70; 95% confidence interval [CI]: 0.52–0.93; p = 0.013) and opioid (HR = 0.68; 95% CI: 0.54–0.86; p = 0.001) subgroups, and significantly reduced risk of symptomatic skeletal events versus placebo, regardless of baseline opioid use (nonopioid subgroup: HR = 0.56, 95% CI: 0.39–0.82, p = 0.002; opioid subgroup: HR = 0.72, 95% CI: 0.53–0.98, p = 0.038). Time to first opioid use for bone pain was significantly delayed with radium-223 versus placebo (HR = 0.62, 95% CI: 0.46–0.85,p = 0.002). Adverse event incidences were similar between opioid subgroups.

Conclusions: Radium-223 versus placebo significantly prolonged OS and reduced symptomatic skeletal event risk with a favorable safety profile in castration-resistant prostate cancer patients with symptomatic bone metastases, regardless of baseline opioid use.

Patient summary: In this ALSYMPCA opioid subgroup analysis, baseline symptom levels did not appear to impact radium-223 dichloride efficacy or safety.