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This paper proposes a conceptual revisiting of population dynamics to include heterogeneous behaviors of individuals, mutations, and selection. The first part of the paper focuses on the derivation of a general mathematical structure which permits to describe systems composed of individuals whose interactions are stochastic. Hybrid models where some of the populations follow a deterministic dynamics are also discussed. The second part deals with two specific applications, namely the effect of the cellular aging in the virus infection process and the dynamics of virus mutation and competition with the immune system. Sample simulations are presented and classical models of population dynamics are critically analyzed in light of the proposed approach.

Objective: To evaluate the association between vitamin supplements and the incidence and progression of radiographic knee osteoarthritis (OA). Study Design: Prospective cohort. Methods: Men and women aged 40 years and older (N = 2239) participating in the community-based Clearwater Osteoarthritis Study (1988–current) with biennial, sequential radiographs. The Lawrence & Kellgren ordinal scale was used to determine evidence of the study outcome, radiographic knee OA, and progression of radiographic knee OA. The study exposure was baseline history of self-reported vitamin supplement usage. Results: Individuals without baseline knee OA who self-reported vitamin supplement usage were 12% less likely to develop knee OA than were those individuals who self-reported no vitamin supplement usage (RR = 0.88; 95% C.I. 0.86–0.89). Those with baseline knee OA who self-reported vitamin supplement usage were 7% less likely to experience knee OA progression than were those individuals who self-reported no vitamin supplement usage (RR = 0.93; 95% C.I. 0.87–0.99). Conclusion: After consideration of BMI, gender, age, history of knee trauma, exercise and vitamin supplement usage prior to study baseline, these findings suggest that vitamin supplement usage may play a protective role in knee OA. Vitamin supplements may be a cost-effective strategy to reduce the incidence and/or slow the progression of knee OA. As many approved OA drugs are accompanied by adverse side effects, the role of vitamin supplements in the development and progression of knee OA warrants further investigation.

We describe a new method based on principal component analysis and robust consensus ensemble clustering to identify and elucidate the subtypes of breast cancer disease. The method was applied to microarray gene expression data using micro-dissection of samples from 36 breast cancer patients with at least two of three pathological stages of disease. Controls were normal breast epithelial cells from 3 disease free patients. Our method identified an optimum set of genes and strong, stable clusters which correlated well with clinical classification into Luminal, Basal and Her2+ subtypes based on ER, PR and Her2 status. It also revealed a hierarchical portrait of disease progression through various grades and stages and identified genes and functional pathways for each stage, grade and disease subtype. We found that gene expression heterogeneity across subtypes is much greater than the heterogeneity of progression from DCIS to IDC within a subtype, suggesting that the disease subtypes are distinct disease processes. The averaging over data perturbations and clustering methods is critical in the robust identification of subtypes and gene markers for grade and progression.

Melanoma is one of the most aggressive human neoplasms, and its incidence is still increasing. To estimate the risk of possible progression and overall survival, Breslow tumor thickness and the invasion level (Clark level) are the most established markers for melanomas at the time of primary diagnosis. In the last decades, overexpression of immunohistochemically labeled metallothioneins (MTs) on paraffin-embedded tissues has turned out to be a highly significant prognostic marker in different tumors. We report the results of a large prospective study on melanoma patients in which MT overexpression was a highly significant marker for progression and survival. In contrast to most other markers, MT overexpression was independent from tumor thickness, and was highly specific even in thin (lowrisk) melanoma patients. In high-risk melanoma patients, sentinel lymph node (SLN) biopsy — a surgical technique with predictive value for progression — was performed. The benefit of this procedure for the individual patient's overall survival remains unclear. Our results corroborate the validity of MT overexpression in primary melanoma as a useful prognostic marker: its accuracy is comparable,and to some degree supplementary to, the results of SLN biopsy.