Mathematical formulation of a dynamical system with dry friction subjected to external forces

We consider the response of a one-dimensional system with friction. S.W. Shaw (Journal of Sound and Vibration, 1986) introduced the set up of different coefficients for the static and dynamic phases (also called stick and slip phases). He constructs a step by step solution, corresponding to an harmonic forcing. In this paper, we show that the theory of variational inequalities provides an elegant and synthetic approach to obtain the existence and uniqueness of the solution, avoiding the step by step construction. We then apply the theory to a real structure with real data and show that the model is quite accurate. In our case, the forcing motion comes from dilatation, due to temperature

Soft tissue sarcomas of the trunk wall (STS-TW): a study of 343 patients from the French Sarcoma Group (FSG) database

Background: Soft tissue sarcomas of the trunk wall (STS-TW) are usually studied together with soft tissue sarcomas of other locations. We report a study on STS-TW forming part of the French Sarcoma Group database. Patients and methods: Three hundred and forty-three adults were included. We carried out univariate and multivariate analysis for overall survival (OS), metastasis-free survival (MFS) and local recurrence-free survival (LRFS). Results: Tumor locations were as follows: thoracic wall, 82.5%; abdominal wall, 12.3% and pelvic wall, 5.2%. Median tumor size was 6.0 cm. The most frequent tumor types were unclassified sarcoma (27.7%) and myogenic sarcoma (19.2%). A total of 44.6% of cases were grade 3. In all, 21.9% of patients had a previous medical history of radiotherapy (PHR). Median follow-up was 7.6 years. The 5-year OS, MFS and LRFS rates were 60.4%, 68.9% and 58.4%, respectively. Multivariate analysis retained PHR and grade for predicting LRFS and PHR, size and grade as prognostic factors of MFS. Factors influencing OS were age, size, PHR, depth, grade and surgical margins. The predictive factors of incomplete response were PHR, size and T3. Conclusions: Our results suggest similar classical prognostic factors as compared with sarcomas of other locations. However, a separate analysis of STS-TW revealed a significant poor prognosis subgroup of patients with PH

Performance status is the most powerful risk factor for early death among patients with advanced soft tissue sarcoma The European Organisation for Research and Treatment of Cancer – Soft Tissue and Bone Sarcoma Group (STBSG) and French Sarcoma Group (FSG) study

BACKGROUND: We investigated prognostic factors (PFs) for 90-day mortality in a large cohort of advanced/metastatic soft tissue sarcoma (STS) patients treated with first-line chemotherapy. METHODS: The PFs were identified by both logistic regression analysis and probability tree analysis in patients captured in the Soft Tissue and Bone Sarcoma Group (STBSG) database (3002 patients). Scores derived from the logistic regression analysis and algorithms derived from probability tree analysis were subsequently validated in an independent study cohort from the French Sarcoma Group (FSG) database (404 patients). RESULTS: The 90-day mortality rate was 8.6 and 4.5% in both cohorts. The logistic regression analysis retained performance status (PS; odds ratio (OR) = 3.83 if PS = 1, OR = 12.00 if PS >= 2), presence of liver metastasis (OR = 2.37) and rare site metastasis (OR = 2.00) as PFs for early death. The CHAID analysis retained PS as a major discriminator followed by histological grade (only for patients with PS >= 2). In both models, PS was the most powerful PF for 90-day mortality. CONCLUSION: Performance status has to be taken into account in the design of further clinical trials and is one of the most important parameters to guide patient management. For those patients with poor PS, expected benefits from therapy should be weighed up carefully against the anticipated toxicities. British Journal of Cancer (2011) 104, 1544-1550. doi: 10.1038/bjc.2011.136 www.bjcancer.com Published online 19 April 2011 (C) 2011 Cancer Research U

Variables with time-varying effects and the Cox model: Some statistical concepts illustrated with a prognostic factor study in breast cancer

International audienceBACKGROUND: The Cox model relies on the proportional hazards (PH) assumption, implying that the factors investigated have a constant impact on the hazard - or risk - over time. We emphasize the importance of this assumption and the misleading conclusions that can be inferred if it is violated; this is particularly essential in the presence of long follow-ups. METHODS: We illustrate our discussion by analyzing prognostic factors of metastases in 979 women treated for breast cancer with surgery. Age, tumour size and grade, lymph node involvement, peritumoral vascular invasion (PVI), status of hormone receptors (HRec), Her2, and Mib1 were considered. RESULTS: Median follow-up was 14 years; 264 women developed metastases. The conventional Cox model suggested that all factors but HRec, Her2, and Mib1 status were strong prognostic factors of metastases. Additional tests indicated that the PH assumption was not satisfied for some variables of the model. Tumour grade had a significant time-varying effect, but although its effect diminished over time, it remained strong. Interestingly, while the conventional Cox model did not show any significant effect of the HRec status, tests provided strong evidence that this variable had a non-constant effect over time. Negative HRec status increased the risk of metastases early but became protective thereafter. This reversal of effect may explain non-significant hazard ratios provided by previous conventional Cox analyses in studies with long follow-ups. CONCLUSIONS: Investigating time-varying effects should be an integral part of Cox survival analyses. Detecting and accounting for time-varying effects provide insights on some specific time patterns, and on valuable biological information that could be missed otherwise

Mathematical formulation of a dynamical system with dry friction subjected to external forces

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