Extended formulations, nonnegative factorizations, and randomized communication protocols

An extended formulation of a polyhedron P is a linear description of a polyhedron Q together with a linear map π such that π(Q)=P. These objects are of fundamental importance in polyhedral combinatorics and optimization theory, and the subject of a number of studies. Yannakakis’ factorization theorem (Yannakakis in J Comput Syst Sci 43(3):441–466, 1991) provides a surprising connection between extended formulations and communication complexity, showing that the smallest size of an extended formulation of $$P$$P equals the nonnegative rank of its slack matrix S. Moreover, Yannakakis also shows that the nonnegative rank of S is at most 2^c, where c is the complexity of any deterministic protocol computing S. In this paper, we show that the latter result can be strengthened when we allow protocols to be randomized. In particular, we prove that the base-2 logarithm of the nonnegative rank of any nonnegative matrix equals the minimum complexity of a randomized communication protocol computing the matrix in expectation. Using Yannakakis’ factorization theorem, this implies that the base-2 logarithm of the smallest size of an extended formulation of a polytope P equals the minimum complexity of a randomized communication protocol computing the slack matrix of P in expectation. We show that allowing randomization in the protocol can be crucial for obtaining small extended formulations. Specifically, we prove that for the spanning tree and perfect matching polytopes, small variance in the protocol forces large size in the extended formulation.

Paclitaxel versus doxorubicin as first-line single-agent chemotherapy for metastatic breast cancer: a European Organization for Research and Treatment of Cancer Randomized Study with cross-over.

PURPOSE: To compare the efficacy of paclitaxel versus doxorubicin given as single agents in first-line therapy of advanced breast cancer (primary end point, progression-free survival ¿PFS) and to explore the degree of cross-resistance between the two agents. PATIENTS AND METHODS: Three hundred thirty-one patients were randomized to receive either paclitaxel 200 mg/m(2), 3-hour infusion every 3 weeks, or doxorubicin 75 mg/m(2), intravenous bolus every 3 weeks. Seven courses were planned unless progression or unacceptable toxicity occurred before the seven courses were finished. Patients who progressed within the seven courses underwent early cross-over to the alternative drug, while a delayed cross-over was optional for the remainder of patients at the time of disease progression. RESULTS: Objective response in first-line therapy was significantly better (P =.003) for doxorubicin (response rate ¿RR, 41%) than for paclitaxel (RR, 25%), with doxorubicin achieving a longer median PFS (7.5 months for doxorubicin v 3.9 months for paclitaxel, P <.001). In second-line therapy, cross-over to doxorubicin (91 patients) and to paclitaxel (77 patients) gave response rates of 30% and 16%, respectively. The median survival durations of 18.3 months for doxorubicin and 15.6 months for paclitaxel were not significantly different (P =.38). The doxorubicin arm had greater toxicity, but this was counterbalanced by better symptom control. CONCLUSION: At the dosages and schedules used in the present study, doxorubicin achieves better disease and symptom control than paclitaxel in first-line treatment. Doxorubicin and paclitaxel are not totally cross-resistant, which supports further investigation of these drugs in combination or in sequence, both in advanced disease and in the adjuvant setting.

Randomized, controlled trial investigating short-term health-related quality of life with doxorubicin and paclitaxel versus doxorubicin and cyclophosphamide as first-line chemotherapy in patients with metastatic breast cancer: European Organization for Research and Treatment of Cancer Breast Cancer Group, Investigational Drug Branch for Breast Cancer and the New Drug Development Group Study.

PURPOSE: To compare health-related quality of life (HRQOL) in patients with metastatic breast cancer receiving the combination of doxorubicin and paclitaxel (AT) or doxorubicin and cyclophosphamide (AC) as first-line chemotherapy treatment. PATIENTS AND METHODS: Eligible patients (n = 275) with anthracycline-naive measurable metastatic breast cancer were randomly assigned to AT (doxorubicin 60 mg/m(2) as an intravenous bolus plus paclitaxel 175 mg/m(2) as a 3-hour infusion) or AC (doxorubicin 60 mg/m(2) plus cyclophosphamide 600 mg/m(2)) every 3 weeks for a maximum of six cycles. Dose escalation of paclitaxel (200 mg/m(2)) and cyclophosphamide (750 mg/m(2)) was planned at cycle 2 to reach equivalent myelosuppression in the two groups. HRQOL was assessed with the European Organization for Research and Treatment of Cancer (EORTC) Quality of Life Questionnaire C30 and the EORTC Breast Module at baseline and the start of cycles 2, 4, and 6, and 3 months after the last cycle. RESULTS: Seventy-nine percent of the patients (n = 219) completed a baseline measure. However, there were no statistically significant differences in HRQOL between the two treatment groups. In both groups, selected aspects of HRQOL were impaired over time, with increased fatigue, although some clinically significant improvements in emotional functioning were seen, as well as a reduction in pain over time. Overall, global quality of life was maintained in both treatment groups. CONCLUSION: This information is important when advising women patients of the expected HRQOL consequences of treatment regimens and should help clinicians and their patients make informed treatment decisions.

Mature results of a randomized phase II multicenter study of exemestane versus tamoxifen as first-line hormone therapy for postmenopausal women with metastatic breast cancer.

BACKGROUND: Women with hormone-responsive metastatic breast cancer (MBC) may respond to or have stable disease with a number of hormone therapies. We explored the efficacy and safety of the steroidal aromatase inactivator exemestane as first-line hormonal therapy in MBC in postmenopausal women. PATIENTS AND METHODS: Patients with measurable disease were eligible if they had received no prior hormone therapy for metastatic disease and had hormone receptor positive disease or hormone receptor unknown disease with a long disease-free interval from adjuvant therapy. They were randomized to tamoxifen 20 mg/day or exemestane 25 mg/day in this open-label study. RESULTS: Blinded independently reviewed response rates for exemestane and tamoxifen were 41% and 17%, respectively. Fifty-seven per cent of exemestane- and 42% of tamoxifen-treated patients experienced clinical benefit, defined as complete or partial response, or disease stabilization lasting at least 6 months. There was a low incidence of severe flushing, sweating, nausea and edema in women who received exemestane. One exemestane-treated patient had a pulmonary embolism with grade 4 dyspnea. CONCLUSIONS: Exemestane is well tolerated and active in the first-line treatment of hormone-responsive MBC. An ongoing EORTC phase III trial is comparing the efficacy, measuring time-to-disease progression, of exemestane and tamoxifen.

Promising results with exemestane in the first-line treatment of metastatic breast cancer: a randomized phase II EORTC trial with a tamoxifen control.

Because tamoxifen (TAM), a nonsteroidal antiestrogen, is routinely used in the adjuvant setting, other hormone therapies are needed as alternatives for first-line treatment of metastatic breast cancer (MBC). Currently, exemestane (EXE) and other antiaromatase agents are indicated for use in patients who experience failure of TAM. In this multicenter, randomized, open-label, TAM-controlled (20 mg/day), phase II trial, we examined the activity and tolerability of EXE 25 mg/day for the first-line treatment of MBC in postmenopausal women. Exemestane was well tolerated and demonstrated substantial first-line antitumor activity based on intent-to-treat analysis of peer-reviewed responses. In the EXE arm, values for complete, partial, and objective response, clinical benefit, and time to tumor progression (TTP) exceeded those reported for TAM although no statistical comparison was made. Based on these encouraging results, a phase III trial will compare EXE and TAM.

The effect of exemestane on serum lipid profile in postmenopausal women with metastatic breast cancer: a companion study to EORTC Trial 10951, 'Randomized phase II study in first line hormonal treatment for metastatic breast cancer with exemestane or tamoxifen in postmenopausal patients'.

BACKGROUND: The impact of aromatase inhibitors (AIs) on non-cancer-related outcomes, which are known to be affected by oestrogens, has become increasingly important in postmenopausal women with hormone-dependent breast cancer. So far, data related to the effect of AIs on lipid profile in postmenopausal women is scarce. This study, as a companion substudy of an EORTC phase II trial (10951), evaluated the impact of exemestane, a steroidal aromatase inactivator, on the lipid profile of postmenopausal metastatic breast cancer (MBC) patients. PATIENTS AND METHODS: The EORTC trial 10951 randomised 122 postmenopausal breast cancer patients to exemestane (E) 25 mg (n = 62) or tamoxifen (T) 20 mg (n = 60) once daily as a first-line treatment in the metastatic setting. Exemestane showed promising results in all the primary efficacy end points of the trial (response rate, clinical benefit rate and response duration), and it was well tolerated with low incidence of serious toxicity. As a secondary end point of this phase II trial, serum triglycerides (TRG), high-density lipoprotein cholesterol (HDL), total cholesterol (TC), lipoprotein a (Lip a), and apolipoproteins (Apo) B and A1 were measured at baseline and while on therapy (at 8, 24 and 48 weeks) to assess the impact of exemestane and tamoxifen on serum lipid profiles. Of the 122 randomised patients, those who had baseline and at least one other lipid assessment are included in the present analysis. The patients who received concomitant drugs that could affect lipid profile are included only if these drugs were administered throughout the study treatment. Increase or decrease in lipid parameters within 20% of baseline were considered as non-significant and thus unchanged. RESULTS: Seventy-two patients (36 in both arms) were included in the statistical analysis. The majority of patients had abnormal TC and normal TRG, HDL, Apo A1, Apo B and Lip a levels at baseline. Neither exemestane nor tamoxifen had adverse effects on TC, HDL, Apo A1, Apo B or Lip a levels at 8, 24 and 48 weeks of treatment. Exemestane and tamoxifen had opposite effects on TRG levels: exemestane lowered while tamoxifen increased TRG levels over time. There were too few patients with normal baseline TC and abnormal TRG, HDL, Apo A1, Apo B and Lip a levels to allow for assessment of E's impact on these subsets. The atherogenic risk determined by Apo A1:Apo B and TC:HDL ratios remained unchanged throughout the treatment period in both the E and T arms. CONCLUSIONS: Overall, exemestane has no detrimental effect on cholesterol levels and the atherogenic indices, which are well-known risk factors for coronary artery disease. In addition, it has a beneficial effect on TRG levels. These data, coupled with E's excellent efficacy and tolerability, support further exploration of its potential in the metastatic, adjuvant and chemopreventive setting.

Clinical staging versus laparotomy and combined modality with MOPP versus ABVD in early-stage hodgkin's disease: the H6 twin randomized trials from the european organization for research and treatment of cancer lymphoma cooperative group

info:eu-repo/semantics/published

Prevention of recurrences in frequently relapsing herpes labialis with thymopentin a randomized double-blind placebo-controlled multicenter study

The present randomized, placebo-controlled double-blind multicenter study included a population of 36 subjects with frequent recurrences (at least once a month) of herpes labialis. Most of the patients had failed to respond adequately to previous treatment with other therapeutic tools, including acyclovir. Either 50 mg of thymopentin or of placebo was administered 3 times a week, by the subcutaneous route, for 6 weeks. Subsequently, the patients were observed for nearly 6 months on the average. The results achieved with thymopentin for the individual parameters were significantly superior to those obtained with placebo; thus significant improvement was seen in patients on thymopentin in the duration of the longest symptomfree period (prolonged from 2.1 weeks to 20.9 weeks, p = 0.000), in the number of relapses (reduced from 1.6 to 0.4 episodes/month, p = 0.001), and in the total duration of herpes symptoms per month (shortened from 2.0 to 0.3 weeks, p = 0.000). Placebo treatment also resulted in considerable improvement (p < 0.05 or 0.01), but was significantly inferior to the improvement obtained with thymopentin. The longest symptomfree period in the placebo group was prolonged from 2.4 to 11.2 weeks. The number of relapses per month was reduced from 1.4 to 0.8, and the total duration of herpes symptoms per month from 2 to 0.9 weeks. The results of intergroup analyses, in which the observed parameters and the improvement achieved in either group were compared, significantly favored thymopentin treatment. The effect of thymopentin was in all but one parameters superior to that of placebo and highly significant (p < 0.01). © 1985 Humana Press Inc.

International guidelines for management of metastatic breast cancer: Can metastatic breast cancer be cured?

A distinctive subset of metastatic breast cancer (MBC) is oligometastatic disease, which is characterized by single or few detectable metastatic lesions. The existing treatment guidelines for patients with localized MBC include surgery, radiotherapy, and regional chemotherapy. The European School of Oncology-Metastatic Breast Cancer Task Force addressed the management of these patients in its first consensus recommendations published in 2007. The Task Force endorsed the possibility of a more aggressive and multidisciplinary approach for patients with oligometastatic disease, stressing also the need for clinical trials in this patient population. At the sixth European Breast Cancer Conference, held in Berlin in March 2008, the second public session on MBC guidelines addressed the controversial issue of whether MBC can be cured. In this commentary, we summarize the discussion and related recommendations regarding the available therapeutic options that are possibly associated with cure in these patients. In particular, data on local (surgery and radiotherapy) and chemotherapy options are discussed. Large retrospective series show an association between surgical removal of the primary tumor or of lung metastases and improved long-term outcome in patients with oligometastatic disease. In the absence of data from prospective randomized studies, removal of the primary tumor or isolated metastatic lesions may be an attractive therapeutic strategy in this subset of patients, offering rapid disease control and potential for survival benefit. Some improvement in outcome may also be achieved with optimization of systemic therapies, possibly in combination with optimal local treatment. © 2010. Published by Oxford University Press.

Multicenter randomized trial of dacarbazine alone or in combination with two different doses and schedules of interferon alfa-2a in the treatment of advanced melanoma

Purpose: Some phase II studies have suggested that the combination of interferons (IFNs) with dacarbazine (DTIC) in the treatment of malignant melanoma (MM) increases the antitumor activity of DTIC alone. In an attempt to confirm this hypothesis, a randomized study was performed with the further intent of observing whether low doses of recombinant interferon alfa-2a (rIFNα2a) could be as effective as intermediate doses. Patients and Methods: Two hundred sixty-six patients were randomized onto three different treatment arms: DTIC 800 mg/m 2 intravenously (IV) days 1 and 21; DTIC plus rIFNα2a 9 mIU intramuscularly (IM) daily; and DTIC plus rIFNα2a 3 mIU IM three times per week. Major prognostic factors were well balanced among the three arms. Chemotherapy was administered for a maximum of eight cycles. After 6 months of therapy, rIFNα2a was continued until disease progression at 3 mIU three times per week in responding patients who had received the combined treatment. Results: The percentage of objective responses did not differ among the three groups (20%, 28%, and 23%, respectively), although a significant prolongation of response duration was observed when rIFNα2a was added to DTIC (2.6 v 8.4 v 5.5 months, respectively). However, this improvement in response duration did not translate into an amelioration of overall survival. The addition of rIFNα2a led to the onset of flu-like syndrome, but in no case was it necessary to withdraw the treatment program and no toxic deaths or life-threatening toxicities were reported. Conclusion: In this study, rIFNα2a significantly prolonged response duration, whereas no effects on response rate and survival were observed; rIFNα2a 3 mIU appeared to be equally effective and better tolerated than 9 mIU.