Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

Timing of Radiotherapy (RT) after Radical Prostatectomy (RP): Long-term outcomes in the RADICALS-RT trial [NCT00541047]

Background The optimal timing of radiotherapy (RT) after radical prostatectomy for prostate cancer has been uncertain. RADICALS-RT compared efficacy and safety of adjuvant RT versus an observation policy with salvage RT for PSA failure. Methods RADICALS-RT was a randomised controlled trial enrolling patients with ≥1 risk factor (pT3/4, Gleason 7-10, positive margins, pre-op PSA≥10ng/ml) for recurrence after radical prostatectomy. Patients were randomised 1:1 to adjuvant RT (“Adjuvant-RT”) or an observation policy with salvage RT for PSA failure (“Salvage-RT”) defined as PSA≥0.1ng/ml or 3 consecutive rises. Stratification factors were Gleason score, margin status, planned RT schedule (52.5Gy/20 fractions or 66Gy/33 fractions) and treatment centre. The primary outcome measure was freedom-from-distant metastasis, designed with 80% power to detect an improvement from 90% with Salvage-RT (control) to 95% at 10yr with Adjuvant-RT. Secondary outcome measures were bPFS, freedom-from-non-protocol hormone therapy, safety and patient-reported outcomes. Standard survival analysis methods were used; HR<1 favours Adjuvant-RT. Findings Between Oct-2007 and Dec-2016, 1396 participants from UK, Denmark, Canada and Ireland were randomised: 699 Salvage-RT, 697 Adjuvant-RT. Allocated groups were balanced with median age 65yr. 93% (649/697) Adjuvant-RT reported RT within 6m after randomisation; 39% (270/699) Salvage-RT reported RT during follow-up. Median follow-up was 7.8 years. With 80 distant metastasis events, 10yr FFDM was 93% for Adjuvant-RT and 90% for Salvage-RT: HR=0.68 (95%CI 0·43–1·07, p=0·095). Of 109 deaths, 17 were due to prostate cancer. Overall survival was not improved (HR=0.980, 95%CI 0.667–1.440, p=0.917). Adjuvant-RT reported worse urinary and faecal incontinence one year after randomisation (p=0.001); faecal incontinence remained significant after ten years (p=0.017). Interpretation Long-term results from RADICALS-RT confirm adjuvant RT after radical prostatectomy increases the risk of urinary and bowel morbidity, but does not meaningfully improve disease control. An observation policy with salvage RT for PSA failure should be the current standard after radical prostatectomy

Progression from high-grade prostatic intraepithelial neoplasia to cancer: a randomized trial of combination vitamin-E, soy, and selenium

Item does not contain fulltextPURPOSE: High-grade prostatic intraepithelial neoplasia (HGPIN) is a putative precursor of invasive prostate cancer (PCa). Preclinical evidence suggests vitamin E, selenium, and soy protein may prevent progression of HGPIN to PCa. This hypothesis was tested in a randomized phase III double-blind study of daily soy (40 g), vitamin E (800 U), and selenium (200 mug) versus placebo. PATIENTS AND METHODS: Three hundred three men in 12 Canadian centers were analyzed. The main eligibility criterion was confirmed HGPIN in at least one of two biopsies within 18 months of random assignment. Treatment was administered daily for 3 years. Follow-up prostate biopsies occurred at 6, 12, 24, and 36 months postrandomization. The primary end point was time to development of invasive PCa. Kaplan-Meier plots and log-rank tests were used to compare two treatment groups for this end point. RESULTS: For all patients, the median age was 62.8 years. The median baseline prostate-specific antigen (PSA; n = 302) was 5.41 ug/L; total testosterone (n = 291) was 13.4 nmol/L. Invasive PCa developed among 26.4% of patients. The hazard ratio for the nutritional supplement to prevent PCa was 1.03 (95% CI, 0.67 to 1.60; P = .88). Gleason score distribution was similar in both groups with 83.5% of cancers graded Gleason sum of 6. Baseline age, weight, PSA, and testosterone did not predict for development of PCa. The supplement was well tolerated with flatulence reported more frequently (27% v 17%) among men receiving micronutrients. CONCLUSION: This trial does not support the hypothesis that combination vitamin E, selenium, and soy prevents progression from HGPIN to PCa

Predictive model for survival in patients having repeat radiation treatment for painful bone metastases

Item does not contain fulltextPURPOSE: To establish a survival prediction model in the setting of a randomized trial of re-irradiation for painful bone metastases. METHODS: Data were randomly divided into training and testing sets with an approximately 3:2 ratio. Baseline factors of gender, primary cancer site, KPS, worst-pain score and age were included with backward variable selection to derive a model using the training set. A partial score was assigned by dividing the value of each statistically significant regression coefficient by the smallest statistically significant regression coefficient. The survival prediction score (SPS) was obtained by adding together partial scores for the variables that were statistically significant. Three risk groups were modelled. RESULTS: The training set included 460 patients and the testing set 351 patients. Only KPS and primary cancer site reached the 5%-significance level. Summing up the partial scores assigned to KPS (90-100, 0; 70-80, 1; 50-60, 2) and primary cancer site (breast, 0; prostate, 1.3; other, 2.6; lung, 3) totalled the SPS. The 1/3 and 2/3 percentiles of the SPS were 2 and 3.6. For the testing set, the median survival of the 3 groups was not reached, 11.3 (95% C.I. 8.5 - not reached) and 5.2months (95% C.I. 3.7-6.5). The 3, 6 and 12month survival rates for the worst group were 64.4% (95% C.I. 55.3-72.1%), 43.0% (95% C.I. 34.0-51.8%) and 19.7% (95% C.I. 12.4-28.1%) respectively, similar to that in the training set. CONCLUSION: This survival prediction model will assist in choosing dose fractionation. We recommend a single 8Gy in the worst group identified

Health-Related Quality of Life in Metastatic, Hormone-Sensitive Prostate Cancer: ENZAMET (ANZUP 1304), an International, Randomized Phase III Trial Led by ANZUP

Purpose: We previously reported that enzalutamide improved overall survival when added to standard of care in metastatic, hormone-sensitive prostate cancer. Here, we report its effects on aspects of health-related quality of life (HRQL). Methods: HRQL was assessed with the European Organisation for Research and Treatment of Cancer core quality-of-life questionnaire and QLM-PR25 at weeks 0, 4, 12, and then every 12 weeks until progression. Scores from week 4 to 156 were analyzed with repeated measures modeling to calculate group means and differences. Deterioration-free survival was from random assignment until the earliest of death, clinical progression, discontinuation of study treatment, or a worsening of 10 points or more from baseline in fatigue, physical function, cognitive function, or overall health and quality of life (OHQL). HRQL scores range from 0 (lowest possible) to 100 (highest possible). Results: HRQL was assessed in 1,042 of 1,125 participants (93%). Differences in means favored control over enzalutamide for fatigue (5.2, 95% CI, 3.6 to 6.9; P , .001), cognitive function (4.0, 95% CI, 2.5 to 5.5; P , .001), and physical function (2.6, 95% CI, 1.3 to 3.9; P , .001), but not OHQL (1.2, 95% CI, 20.2 to 2.7; P 5 .1). Deterioration-free survival rates at 3 years, and log-rank P values comparing the whole distributions, favored enzalutamide over control for OHQL (31% v 17%; P , .0001), cognitive function (31% v 20%; P 5 .001), and physical function (31% v 22%; P , .001), but not fatigue (24% v 18%; P 5 .16). The effects of enzalutamide on HRQL were independent of baseline characteristics. Conclusion: Enzalutamide was associated with worsening of self-reported fatigue, cognitive function, and physical function, but not OHQL. Enzalutamide was associated with improved deterioration-free survival for OHQL, physical function, and cognitive function because delays in disease progression outweighed early deteriorations in these aspects of HRQL.Martin R. Stockler ... Christopher J. Sweeney ... et. a

Health-related quality of life in metastatic, hormone-sensitive prostate cancer : ENZAMET (ANZUP 1304), an international, randomized phase iii trial led by ANZUP

PURPOSE We previously reported that enzalutamide improved overall survival when added to standard of care in metastatic, hormone-sensitive prostate cancer. Here, we report its effects on aspects of health-related quality of life (HRQL). METHODS HRQL was assessed with the European Organisation for Research and Treatment of Cancer core quality-of-life questionnaire and QLM-PR25 at weeks 0, 4, 12, and then every 12 weeks until progression. Scores from week 4 to 156 were analyzed with repeated measures modeling to calculate group means and differences. Deterioration-free survival was from random assignment until the earliest of death, clinical progression, discontinuation of study treatment, or a worsening of 10 points or more from baseline in fatigue, physical function, cognitive function, or overall health and quality of life (OHQL). HRQL scores range from 0 (lowest possible) to 100 (highest possible). RESULTS HRQL was assessed in 1,042 of 1,125 participants (93%). Differences in means favored control over enzalutamide for fatigue (5.2, 95% CI, 3.6 to 6.9; P, .001), cognitive function (4.0, 95% CI, 2.5 to 5.5; P, .001), and physical function (2.6, 95% CI, 1.3 to 3.9; P, .001), but not OHQL (1.2, 95% CI, 20.2 to 2.7; P 5 .1). Deterioration-free survival rates at 3 years, and log-rank P values comparing the whole distributions, favored enzalutamide over control for OHQL (31% v 17%; P, .0001), cognitive function (31% v 20%; P 5 .001), and physical function (31% v 22%; P, .001), but not fatigue (24% v 18%; P 5 .16). The effects of enzalutamide on HRQL were independent of baseline characteristics. CONCLUSION Enzalutamide was associated with worsening of self-reported fatigue, cognitive function, and physical function, but not OHQL. Enzalutamide was associated with improved deterioration-free survival for OHQL, physical function, and cognitive function because delays in disease progression outweighed early deteriorations in these aspects of HRQL