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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


(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


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


Antibiotics are often used in neonates despite the absence of relevant dosing information in drug labels. For neonatal dosing, clinicians must extrapolate data from studies for adults and older children, who have strikingly different physiologies. As a result, dosing extrapolation can lead to increased toxicity or efficacy failures in neonates. Driven by these differences and recent legislation mandating the study of drugs in children and neonates, an increasing number of pharmacokinetic studies of antibiotics are being performed in neonates. These studies have led to new dosing recommendations with particular consideration for neonate body size and maturation. Herein, we highlight the available pharmacokinetic data for commonly used systemic antibiotics in neonates.

Concepts: Pharmacology, Infant, Drug, Drug addiction, Antibiotic, Cultural studies, Interpolation, Extrapolation


The laboratory mouse has become the predominant test species in biomedical research. The number of papers that translate or extrapolate data from mouse to human has grown exponentially since the year 2000. There are many physiological and anatomical factors to consider in the process of extrapolating data from one species to another. Body temperature is, of course, a critical determinant in extrapolation because it has a direct impact on metabolism, cardiovascular function, drug efficacy, pharmacokinetics of toxins and drugs, and many other effects. While most would consider the thermoregulatory system of mice to be sufficiently stable and predictable as to not be a cause for concern, the thermal physiology of mice does in fact present unique challenges to the biomedical researcher. A variable and unstable core temperature, high metabolic rate, preference for warm temperatures, large surface area: body mass ratio, and high rate of thermal conductance, are some of the key factors of mice that can affect the interpretation and translation of data to humans. It is the intent of this brief review to enlighten researchers studying interspecies translation of biomedical data on the salient facets of the mouse thermal physiology and show how extrapolation in fields such as physiology, psychology, nutrition, pharmacology, toxicology, and pathology.

Concepts: Biology, Physiology, Temperature, Human anatomy, Mouse, Basal metabolic rate, Interpolation, Extrapolation


This paper develops a means of more easily and less invasively estimating ventricular dead space volume (Vd), an important, but difficult to measure physiological parameter. Vd represents a subject and condition dependent portion of measured ventricular volume that is not actively participating in ventricular function. It is employed in models based on the time varying elastance concept, which see widespread use in haemodynamic studies, and may have direct diagnostic use. The proposed method involves linear extrapolation of a Frank-Starling curve (stroke volume vs end-diastolic volume) and its end-systolic equivalent (stroke volume vs end-systolic volume), developed across normal clinical procedures such as recruitment manoeuvres, to their point of intersection with the y-axis (where stroke volume is 0) to determine Vd. To demonstrate the broad applicability of the method, it was validated across a cohort of six sedated and anaesthetised male Pietrain pigs, encompassing a variety of cardiac states from healthy baseline behaviour to circulatory failure due to septic shock induced by endotoxin infusion. Linear extrapolation of the curves was supported by strong linear correlation coefficients of R = 0.78 and R = 0.80 average for pre- and post- endotoxin infusion respectively, as well as good agreement between the two linearly extrapolated y-intercepts (Vd) for each subject (no more than 7.8% variation). Method validity was further supported by the physiologically reasonable Vd values produced, equivalent to 44.3-53.1% and 49.3-82.6% of baseline end-systolic volume before and after endotoxin infusion respectively. This method has the potential to allow Vd to be estimated without a particularly demanding, specialised protocol in an experimental environment. Further, due to the common use of both mechanical ventilation and recruitment manoeuvres in intensive care, this method, subject to the availability of multi-beat echocardiography, has the potential to allow for estimation of Vd in a clinical environment.

Concepts: Cardiology, Heart, Estimation, End-diastolic volume, End-systolic volume, Extrapolation, Stroke volume, Frank-Starling law of the heart