High tumor budding stratifies breast cancer with metastatic properties.

Tumor budding refers to single or small cluster of tumor cells detached from the main tumor mass. In colon cancer high tumor budding is associated with positive lymph nodes and worse prognosis. Therefore, we investigated the value of tumor budding as a predictive feature of lymph node status in breast cancer (BC). Whole tissue sections from 148 surgical resection specimens (SRS) and 99 matched preoperative core biopsies (CB) with invasive BC of no special type were analyzed on one slide stained with pan-cytokeratin. In SRS, the total number of intratumoral (ITB) and peripheral tumor buds (PTB) in ten high-power fields (HPF) were counted. A bud was defined as a single tumor cell or a cluster of up to five tumor cells. High tumor budding equated to scores averaging >4 tumor buds across 10HPFs. In CB high tumor budding was defined as ≥10 buds/HPF. The results were correlated with pathological parameters. In SRS high PTB stratified BC with lymph node metastases (p ≤ 0.03) and lymphatic invasion (p ≤ 0.015). In CB high tumor budding was significantly (p = 0.0063) associated with venous invasion. Pathologists are able, based on morphology, to categorize BC into a high and low risk groups based in part on lymph node status. This risk assessment can be easily performed during routine diagnostics and it is time and cost effective. These results suggest that high PTB is associated with loco-regional metastasis, highlighting the possibility that this tumor feature may help in therapeutic decision-making.

Temporal variability of damage potential on roads as a conceptual contribution towards a short-term avalanche risk simulation

The fatality risk caused by avalanches on road networks can be analysed using a long-term approach, resulting in a mean value of risk, and with emphasis on short-term fluctuations due to the temporal variability of both, the hazard potential and the damage potential. In this study, the approach for analysing the long-term fatality risk has been adapted by modelling the highly variable short-term risk. The emphasis was on the temporal variability of the damage potential and the related risk peaks. For defined hazard scenarios resulting from classified amounts of snow accumulation, the fatality risk was calculated by modelling the hazard potential and observing the traffic volume. The avalanche occurrence probability was calculated using a statistical relationship between new snow height and observed avalanche releases. The number of persons at risk was determined from the recorded traffic density. The method resulted in a value for the fatality risk within the observed time frame for the studied road segment. The long-term fatality risk due to snow avalanches as well as the short-term fatality risk was compared to the average fatality risk due to traffic accidents. The application of the method had shown that the long-term avalanche risk is lower than the fatality risk due to traffic accidents. The analyses of short-term avalanche-induced fatality risk provided risk peaks that were 50 times higher than the statistical accident risk. Apart from situations with high hazard level and high traffic density, risk peaks result from both, a high hazard level combined with a low traffic density and a high traffic density combined with a low hazard level. This provided evidence for the importance of the temporal variability of the damage potential for risk simulations on road networks. The assumed dependence of the risk calculation on the sum of precipitation within three days is a simplified model. Thus, further research is needed for an improved determination of the diurnal avalanche probability. Nevertheless, the presented approach may contribute as a conceptual step towards a risk-based decision-making in risk management.

Elicitable distortion risk measures: A concise proof

Elicitability has recently been discussed as a desirable property for risk measures. Kou and Peng (2014) showed that an elicitable distortion risk measure is either a Value-at-Risk or the mean. We give a concise alternative proof of this result, and discuss the conflict between comonotonic additivity and elicitability.