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

Event-Free Survival, a Prostate-Specific Antigen-Based Composite End Point, Is Not a Surrogate for Overall Survival in Men With Localized Prostate Cancer Treated With Radiation

PURPOSE: Recently, we have shown that metastasis-free survival is a strong surrogate for overall survival (OS) in men with intermediate- and high-risk localized prostate cancer and can accelerate the evaluation of new (neo)adjuvant therapies. Event-free survival (EFS), an earlier prostate-specific antigen (PSA)-based composite end point, may further expedite trial completion. METHODS: EFS was defined as the time from random assignment to the date of first evidence of disease recurrence, including biochemical failure, local or regional recurrence, distant metastasis, or death from any cause, or was censored at the date of last PSA assessment. Individual patient data from trials within the Intermediate Clinical Endpoints in Cancer of the Prostate-ICECaP-database with evaluable PSA and disease follow-up data were analyzed. We evaluated the surrogacy of EFS for OS using a 2-stage meta-analytic validation model by determining the correlation of EFS with OS (patient level) and the correlation of treatment effects (hazard ratios [HRs]) on both EFS and OS (trial level). A clinically relevant surrogacy was defined a priori as an R2 ≥ 0.7. RESULTS: Data for 10,350 patients were analyzed from 15 radiation therapy-based trials enrolled from 1987 to 2011 with a median follow-up of 10 years. At the patient level, the correlation of EFS with OS was 0.43 (95% CI, 0.42 to 0.44) as measured by Kendall's tau from a copula model. At the trial level, the R2 was 0.35 (95% CI, 0.01 to 0.60) from the weighted linear regression of log(HR)-OS on log(HR)-EFS. CONCLUSION: EFS is a weak surrogate for OS and is not suitable for use as an intermediate clinical end point to substitute for OS to accelerate phase III (neo)adjuvant trials of prostate cancer therapies for primary radiation therapy-based trials

Global Retinoblastoma Presentation and Analysis by National Income Level

Importance: Early diagnosis of retinoblastoma, the most common intraocular cancer, can save both a child's life and vision. However, anecdotal evidence suggests that many children across the world are diagnosed late. To our knowledge, the clinical presentation of retinoblastoma has never been assessed on a global scale. Objectives: To report the retinoblastoma stage at diagnosis in patients across the world during a single year, to investigate associations between clinical variables and national income level, and to investigate risk factors for advanced disease at diagnosis. Design, Setting, and Participants: A total of 278 retinoblastoma treatment centers were recruited from June 2017 through December 2018 to participate in a cross-sectional analysis of treatment-naive patients with retinoblastoma who were diagnosed in 2017. Main Outcomes and Measures: Age at presentation, proportion of familial history of retinoblastoma, and tumor stage and metastasis. Results: The cohort included 4351 new patients from 153 countries; the median age at diagnosis was 30.5 (interquartile range, 18.3-45.9) months, and 1976 patients (45.4%) were female. Most patients (n = 3685 [84.7%]) were from low- A nd middle-income countries (LMICs). Globally, the most common indication for referral was leukocoria (n = 2638 [62.8%]), followed by strabismus (n = 429 [10.2%]) and proptosis (n = 309 [7.4%]). Patients from high-income countries (HICs) were diagnosed at a median age of 14.1 months, with 656 of 666 (98.5%) patients having intraocular retinoblastoma and 2 (0.3%) having metastasis. Patients from low-income countries were diagnosed at a median age of 30.5 months, with 256 of 521 (49.1%) having extraocular retinoblastoma and 94 of 498 (18.9%) having metastasis. Lower national income level was associated with older presentation age, higher proportion of locally advanced disease and distant metastasis, and smaller proportion of familial history of retinoblastoma. Advanced disease at diagnosis was more common in LMICs even after adjusting for age (odds ratio for low-income countries vs upper-middle-income countries and HICs, 17.92 [95% CI, 12.94-24.80], and for lower-middle-income countries vs upper-middle-income countries and HICs, 5.74 [95% CI, 4.30-7.68]). Conclusions and Relevance: This study is estimated to have included more than half of all new retinoblastoma cases worldwide in 2017. Children from LMICs, where the main global retinoblastoma burden lies, presented at an older age with more advanced disease and demonstrated a smaller proportion of familial history of retinoblastoma, likely because many do not reach a childbearing age. Given that retinoblastoma is curable, these data are concerning and mandate intervention at national and international levels. Further studies are needed to investigate factors, other than age at presentation, that may be associated with advanced disease in LMICs

Increasing the dose intensity of chemotherapy by more frequent administration or sequential scheduling: a patient-level meta-analysis of 37 298 women with early breast cancer in 26 randomised trials

Background Increasing the dose intensity of cytotoxic therapy by shortening the intervals between cycles, or by giving individual drugs sequentially at full dose rather than in lower-dose concurrent treatment schedules, might enhance efficacy. Methods To clarify the relative benefits and risks of dose-intense and standard-schedule chemotherapy in early breast cancer, we did an individual patient-level meta-analysis of trials comparing 2-weekly versus standard 3-weekly schedules, and of trials comparing sequential versus concurrent administration of anthracycline and taxane chemotherapy. The primary outcomes were recurrence and breast cancer mortality. Standard intention-to-treat log-rank analyses, stratified by age, nodal status, and trial, yielded dose-intense versus standard-schedule first-event rate ratios (RRs). Findings Individual patient data were provided for 26 of 33 relevant trials identified, comprising 37 298 (93%) of 40 070 women randomised. Most women were aged younger than 70 years and had node-positive disease. Total cytotoxic drug usage was broadly comparable in the two treatment arms; colony-stimulating factor was generally used in the more dose-intense arm. Combining data from all 26 trials, fewer breast cancer recurrences were seen with dose-intense than with standard-schedule chemotherapy (10-year recurrence risk 28·0% vs 31·4%; RR 0·86, 95% CI 0·82–0·89; p<0·0001). 10-year breast cancer mortality was similarly reduced (18·9% vs 21·3%; RR 0·87, 95% CI 0·83–0·92; p<0·0001), as was all-cause mortality (22·1% vs 24·8%; RR 0·87, 95% CI 0·83–0·91; p<0·0001). Death without recurrence was, if anything, lower with dose-intense than with standard-schedule chemotherapy (10-year risk 4·1% vs 4·6%; RR 0·88, 95% CI 0·78–0·99; p=0·034). Recurrence reductions were similar in the seven trials (n=10 004) that compared 2-weekly chemotherapy with the same chemotherapy given 3-weekly (10-year risk 24·0% vs 28·3%; RR 0·83, 95% CI 0·76–0·91; p<0·0001), in the six trials (n=11 028) of sequential versus concurrent anthracycline plus taxane chemotherapy (28·1% vs 31·3%; RR 0·87, 95% CI 0·80–0·94; p=0·0006), and in the six trials (n=6532) testing both shorter intervals and sequential administration (30·4% vs 35·0%; RR 0·82, 95% CI 0·74–0·90; p<0·0001). The proportional reductions in recurrence with dose-intense chemotherapy were similar and highly significant (p<0·0001) in oestrogen receptor (ER)-positive and ER-negative disease and did not differ significantly by other patient or tumour characteristics. Interpretation Increasing the dose intensity of adjuvant chemotherapy by shortening the interval between treatment cycles, or by giving individual drugs sequentially rather than giving the same drugs concurrently, moderately reduces the 10-year risk of recurrence and death from breast cancer without increasing mortality from other causes. Funding Cancer Research UK, Medical Research Council

20-Year Risks of Breast-Cancer Recurrence after Stopping Endocrine Therapy at 5 Years

The administration of endocrine therapy for 5 years substantially reduces recurrence rates during and after treatment in women with early-stage, estrogen-receptor (ER)-positive breast cancer. Extending such therapy beyond 5 years offers further protection but has additional side effects. Obtaining data on the absolute risk of subsequent distant recurrence if therapy stops at 5 years could help determine whether to extend treatment

Global Retinoblastoma Presentation and Analysis by National Income Level.

Importance: Early diagnosis of retinoblastoma, the most common intraocular cancer, can save both a child's life and vision. However, anecdotal evidence suggests that many children across the world are diagnosed late. To our knowledge, the clinical presentation of retinoblastoma has never been assessed on a global scale. Objectives: To report the retinoblastoma stage at diagnosis in patients across the world during a single year, to investigate associations between clinical variables and national income level, and to investigate risk factors for advanced disease at diagnosis. Design, Setting, and Participants: A total of 278 retinoblastoma treatment centers were recruited from June 2017 through December 2018 to participate in a cross-sectional analysis of treatment-naive patients with retinoblastoma who were diagnosed in 2017. Main Outcomes and Measures: Age at presentation, proportion of familial history of retinoblastoma, and tumor stage and metastasis. Results: The cohort included 4351 new patients from 153 countries; the median age at diagnosis was 30.5 (interquartile range, 18.3-45.9) months, and 1976 patients (45.4%) were female. Most patients (n = 3685 [84.7%]) were from low- and middle-income countries (LMICs). Globally, the most common indication for referral was leukocoria (n = 2638 [62.8%]), followed by strabismus (n = 429 [10.2%]) and proptosis (n = 309 [7.4%]). Patients from high-income countries (HICs) were diagnosed at a median age of 14.1 months, with 656 of 666 (98.5%) patients having intraocular retinoblastoma and 2 (0.3%) having metastasis. Patients from low-income countries were diagnosed at a median age of 30.5 months, with 256 of 521 (49.1%) having extraocular retinoblastoma and 94 of 498 (18.9%) having metastasis. Lower national income level was associated with older presentation age, higher proportion of locally advanced disease and distant metastasis, and smaller proportion of familial history of retinoblastoma. Advanced disease at diagnosis was more common in LMICs even after adjusting for age (odds ratio for low-income countries vs upper-middle-income countries and HICs, 17.92 [95% CI, 12.94-24.80], and for lower-middle-income countries vs upper-middle-income countries and HICs, 5.74 [95% CI, 4.30-7.68]). Conclusions and Relevance: This study is estimated to have included more than half of all new retinoblastoma cases worldwide in 2017. Children from LMICs, where the main global retinoblastoma burden lies, presented at an older age with more advanced disease and demonstrated a smaller proportion of familial history of retinoblastoma, likely because many do not reach a childbearing age. Given that retinoblastoma is curable, these data are concerning and mandate intervention at national and international levels. Further studies are needed to investigate factors, other than age at presentation, that may be associated with advanced disease in LMICs

Metabolite profiling in retinoblastoma identifies novel clinicopathological subgroups

BACKGROUND: Tumour classification, based on histopathology or molecular pathology, is of value to predict tumour behaviour and to select appropriate treatment. In retinoblastoma, pathology information is not available at diagnosis and only exists for enucleated tumours. Alternative methods of tumour classification, using noninvasive techniques such as magnetic resonance spectroscopy, are urgently required to guide treatment decisions at the time of diagnosis. METHODS: High-resolution magic-angle spinning magnetic resonance spectroscopy (HR-MAS MRS) was undertaken on enucleated retinoblastomas. Principal component analysis and cluster analysis of the HR-MAS MRS data was used to identify tumour subgroups. Individual metabolite concentrations were determined and were correlated with histopathological risk factors for each group. RESULTS: Multivariate analysis identified three metabolic subgroups of retinoblastoma, with the most discriminatory metabolites being taurine, hypotaurine, total-choline and creatine. Metabolite concentrations correlated with specific histopathological features: taurine was correlated with differentiation, total-choline and phosphocholine with retrolaminar optic nerve invasion, and total lipids with necrosis. CONCLUSIONS: We have demonstrated that a metabolite-based classification of retinoblastoma can be obtained using ex vivo magnetic resonance spectroscopy, and that the subgroups identified correlate with histopathological features. This result justifies future studies to validate the clinical relevance of these subgroups and highlights the potential of in vivo MRS as a noninvasive diagnostic tool for retinoblastoma patient stratification