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Concept: Extrapolation


The persistence of chemicals is a key parameter for their environmental risk assessment. Extrapolating their biodegradability potential in aqueous systems to soil systems would improve the environmental impact assessment. This study compares the fate of (14/13)C-labelled 2,4-D (2,4-dichlorophenoxyacetic acid) and ibuprofen in OECD tests 301 (ready biodegradability in aqueous systems) and 307 (soil). 85% of 2,4-D and 68% of ibuprofen were mineralised in aqueous systems, indicating ready biodegradability, but only 57% and 45% in soil. Parent compounds and metabolites decreased to <2% of the spiked amounts in both systems. In soil, 36% of 2,4-D and 30% of ibuprofen were bound in non-extractable residues (NER). NER formation in the abiotic controls was half as high as in the biotic treatments. However, mineralisation, biodegradation and abiotic residue formation are competing processes. Assuming the same extent of abiotic NER formation in abiotic and biotic systems may therefore overestimate the abiotic contribution in the biotic systems. Mineralisation was described by a logistic model for the aquatic systems and by a two-pool first order degradation model for the soil systems. This agrees with the different abundance of microorganisms in the two systems, but precludes direct comparison of the fitted parameters. Nevertheless, the maximum mineralisable amounts determined by the models were similar in both systems, although the maximum mineralisation rate was about 3.5 times higher in the aqueous systems than in the soil system for both compounds; these parameters may thus be extrapolated from aqueous to soil systems. However, the maximum mineralisable amount is calculated by extrapolation to infinite times and includes intermediately formed biomass derived from the labelled carbon. The amount of labelled carbon within microbial biomass residues is higher in the soil system, resulting in lower degradation rates. Further evaluation of these relationships requires comparison data on more chemicals and from different soils.

Concepts: Evaluation, Soil, Environmental remediation, C, Bioremediation, Impact assessment, Extrapolation, Environmental impact assessment


As human activities expand beyond national jurisdictions to the high seas, there is increasing need to consider anthropogenic impacts to species that inhabit these waters. The current scarcity of scientific observations of cetaceans in the high seas impedes the assessment of population-level impacts of these activities. This study is directed towards an important management need in the high seas-the development of plausible density estimates to facilitate a quantitative assessment of anthropogenic impacts on cetacean populations in these waters. Our study region extends from a well-surveyed region within the United States Exclusive Economic Zone into a large region of the western North Atlantic sparsely surveyed for cetaceans. We modeled densities of 15 cetacean taxa using available line transect survey data and habitat covariates and extrapolated predictions to sparsely surveyed regions. We formulated models carefully to reduce the extent of extrapolation beyond covariate ranges, and constrained them to model simple and generalizable relationships. To evaluate confidence in the predictions, we performed several qualitative assessments, such as mapping where predictions were made outside sampled covariate ranges, and comparing them with maps of sightings from a variety of sources that could not be integrated into our models. Our study revealed a range of confidence levels for the model results depending on the taxon and geographic area, and highlights the need for additional surveying in environmentally distinct areas. Combined with their explicit confidence levels and necessary caution, our density estimates can inform a variety of management needs in the high seas, such as the quantification of potential cetacean interactions with military training exercises, shipping, fisheries, deep-sea mining, as well as delineation of areas of special biological significance in international waters. Our approach is generally applicable to other marine taxa and geographic regions for which management will be implemented but data are sparse. This article is protected by copyright. All rights reserved.

Concepts: Scientific method, Water, Sociology, Assessment, Qualitative research, Quantitative research, Social sciences, Extrapolation


Modern soil mapping is characterised by the need to interpolate point referenced (geostatistical) observations and the availability of large numbers of environmental characteristics for consideration as covariates to aid this interpolation. Modelling tasks of this nature also occur in other fields such as biogeography and environmental science. This analysis employs the Least Angle Regression (LAR) algorithm for fitting Least Absolute Shrinkage and Selection Operator (LASSO) penalized Multiple Linear Regressions models. This analysis demonstrates the efficiency of the LAR algorithm at selecting covariates to aid the interpolation of geostatistical soil carbon observations. Where an exhaustive search of the models that could be constructed from 800 potential covariate terms and 60 observations would be prohibitively demanding, LASSO variable selection is accomplished with trivial computational investment.

Concepts: Scientific method, Regression analysis, Linear regression, Dimension, Numerical analysis, Interpolation, Extrapolation, Soil science


(1) Estimate age, period and cohort effects for motorcyclist traffic casualties 1979-2008 in New Zealand and (2) forecast the incidence of New Zealand motorcycle traffic casualties for the period 2019-2023 assuming future age, cohort and period effects, and compare these with an estimate based on simple linear extrapolation.

Concepts: Regression analysis, Forecasting, Trend estimation, Extrapolation


BACKGROUND: Absorption factors are required to convert physiologic requirements for iron into Dietary Reference Values, but the absorption from single meals cannot be used to estimate dietary iron absorption. OBJECTIVE: The objective was to conduct a systematic review of iron absorption from whole diets. DESIGN: A structured search was completed by using the Medline, EMBASE, and Cochrane CENTRAL databases from inception to November 2011. Formal inclusion and exclusion criteria were applied, and data extraction, validity assessment, and meta-analyses were undertaken. RESULTS: Nineteen studies from the United States, Europe, and Mexico were included. Absorption from diets was higher with an enhancer (standard mean difference: 0.53; 95% CI: 0.21, 0.85; P = 0.001) and was also higher when compared with low-bioavailability diets (standard mean difference: 0.96; 95% CI: 0.51, 1.41; P < 0.0001); however, single inhibitors did not reduce absorption (possibly because of the limited number of studies and participants and their heterogeneity). A regression equation to calculate iron absorption was derived by pooling data for iron status (serum and plasma ferritin) and dietary enhancers and inhibitors from 58 individuals (all from US studies): log[nonheme-iron absorption, %] = -0.73 log[ferritin, μg/L] + 0.11 [modifier] + 1.82. In individuals with serum ferritin concentrations from 6 to 80 μg/L, predicted absorption ranged from 2.1% to 23.0%. CONCLUSIONS: Large variations were observed in mean nonheme-iron absorption (0.7-22.9%) between studies, which depended on iron status (diet had a greater effect at low serum and plasma ferritin concentrations) and dietary enhancers and inhibitors. Iron absorption was predicted from serum ferritin concentrations and dietary modifiers by using a regression equation. Extrapolation of these findings to developing countries and to men and women of different ages will require additional high-quality controlled trials.

Concepts: Regression analysis, Statistics, Mathematics, Arithmetic mean, Iron deficiency anemia, Prediction interval, Forecasting, Extrapolation


BACKGROUND: In health technology assessments (HTAs) of interventions that affect survival, it is essential to accurately estimate the survival benefit associated with the new treatment. Generally, trial data must be extrapolated, and many models are available for this purpose. The choice of extrapolation model is critical because different models can lead to very different cost-effectiveness results. A failure to systematically justify the chosen model creates the possibility of bias and inconsistency between HTAs. OBJECTIVE: To demonstrate the limitations and inconsistencies associated with the survival analysis component of HTAs and to propose a process guide that will help exclude these from future analyses. METHODS: We reviewed the survival analysis component of 45 HTAs undertaken for the National Institute for Health and Clinical Excellence (NICE) in the cancer disease area. We drew upon our findings to identify common limitations and to develop a process guide. RESULTS: The chosen survival models were not systematically justified in any of the HTAs reviewed. The range of models considered was usually insufficient, and the rationale for the chosen model was universally limited: In particular, the plausibility of the extrapolated portion of fitted survival curves was very rarely explicitly considered. Limitations. We do not seek to describe and review all methods available for performing survival analysis-several approaches exist that are not mentioned in this article. Instead we seek to analyze methods commonly used in HTAs and limitations associated with their application. CONCLUSIONS: Survival analysis has not been conducted systematically in HTAs. A systematic approach such as the one proposed here is required to reduce the possibility of bias in cost-effectiveness results and inconsistency between technology assessments.

Concepts: Critical thinking, Survival analysis, Model, Unified Modeling Language, Analysis, Proposal, Extrapolation, National Institute for Health and Clinical Excellence


Apply methods of damped trend analysis to forecast inpatient glycemic control.

Concepts: Regression analysis, Weather, Forecasting, Trend estimation, Extrapolation, Weather forecasting


Ultrasonography is a useful technique to study muscle contractions in vivo, however larger muscles like vastus lateralis may be difficult to visualise with smaller, commonly used transducers. Fascicle length is often estimated using linear trigonometry to extrapolate fascicle length to regions where the fascicle is not visible. However, this approach has not been compared to measurements made with a larger field of view for dynamic muscle contractions. Here we compared two different single-transducer extrapolation methods to measure VL muscle fascicle length to a direct measurement made using two synchronised, in-series transducers. The first method used pennation angle and muscle thickness to extrapolate fascicle length outside the image (extrapolate method). The second method determined fascicle length based on the extrapolated intercept between a fascicle and the aponeurosis (intercept method). Nine participants performed maximal effort, isometric, knee extension contractions on a dynamometer at 10° increments from 50 to 100° of knee flexion. Fascicle length and torque were simultaneously recorded for offline analysis. The dual transducer method showed similar patterns of fascicle length change (overall mean coefficient of multiple correlation was 0.76 and 0.71 compared to extrapolate and intercept methods respectively), but reached different absolute lengths during the contractions. This had the effect of producing force-length curves of the same shape, but each curve was shifted in terms of absolute length. We concluded that dual transducers are beneficial for studies that examine absolute fascicle lengths, whereas either of the single transducer methods may produce similar results for normalised length changes, and repeated measures experimental designs.

Concepts: Knee, Medical ultrasonography, Units of measurement, Length, Vastus lateralis muscle, Extrapolation, Perimysium, Muscle fascicle


The interpretation of the effect of predictors in projected normal regression models is not straight-forward. The main aim of this paper is to make this interpretation easier such that these models can be employed more readily by social scientific researchers. We introduce three new measures: the slope at the inflection point (bc ), average slope (AS) and slope at mean (SAM) that help us assess the marginal effect of a predictor in a Bayesian projected normal regression model. The SAM or AS are preferably used in situations where the data for a specific predictor do not lie close to the inflection point of a circular regression curve. In this case bc is an unstable and extrapolated effect. In addition, we outline how the projected normal regression model allows us to distinguish between an effect on the mean and spread of a circular outcome variable. We call these types of effects location and accuracy effects, respectively. The performance of the three new measures and of the methods to distinguish between location and accuracy effects is investigated in a simulation study. We conclude that the new measures and methods to distinguish between accuracy and location effects work well in situations with a clear location effect. In situations where the location effect is not clearly distinguishable from an accuracy effect not all measures work equally well and we recommend the use of the SAM.

Concepts: Regression analysis, Linear regression, Statistics, Prediction, Arithmetic mean, Errors and residuals in statistics, Extrapolation, Bayesian linear regression


Although molecular dynamics (MD) simulations are commonly used to predict the structure and properties of glasses, they are intrinsically limited to short time scales, necessitating the use of fast cooling rates. It is therefore challenging to compare results from MD simulations to experimental results for glasses cooled on typical laboratory time scales. Based on MD simulations of a sodium silicate glass with varying cooling rate (from 0.01 to 100 K/ps), here we show that thermal history primarily affects the medium-range order structure, while the short-range order is largely unaffected over the range of cooling rates simulated. This results in a decoupling between the enthalpy and volume relaxation functions, where the enthalpy quickly plateaus as the cooling rate decreases, whereas density exhibits a slower relaxation. Finally, we show that, using the proper extrapolation method, the outcomes of MD simulations can be meaningfully compared to experimental values when extrapolated to slower cooling rates.

Concepts: Time, Regression analysis, Molecular dynamics, Chemistry, Experiment, Monte Carlo method, Forecasting, Extrapolation