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Concept: Approximation


Women comprise a minority of the Science, Technology, Engineering, Mathematics, and Medicine (STEMM) workforce. Quantifying the gender gap may identify fields that will not reach parity without intervention, reveal underappreciated biases, and inform benchmarks for gender balance among conference speakers, editors, and hiring committees. Using the PubMed and arXiv databases, we estimated the gender of 36 million authors from >100 countries publishing in >6000 journals, covering most STEMM disciplines over the last 15 years, and made a web app allowing easy access to the data ( Despite recent progress, the gender gap appears likely to persist for generations, particularly in surgery, computer science, physics, and maths. The gap is especially large in authorship positions associated with seniority, and prestigious journals have fewer women authors. Additionally, we estimate that men are invited by journals to submit papers at approximately double the rate of women. Wealthy countries, notably Japan, Germany, and Switzerland, had fewer women authors than poorer ones. We conclude that the STEMM gender gap will not close without further reforms in education, mentoring, and academic publishing.

Concepts: Physics, Statistics, Computer science, Wealth, Science, Approximation, Estimation, Mathematics


Estimating the case-fatality risk (CFR)-the probability that a person dies from an infection given that they are a case-is a high priority in epidemiologic investigation of newly emerging infectious diseases and sometimes in new outbreaks of known infectious diseases. The data available to estimate the overall CFR are often gathered for other purposes (e.g., surveillance) in challenging circumstances. We describe two forms of bias that may affect the estimation of the overall CFR-preferential ascertainment of severe cases and bias from reporting delays-and review solutions that have been proposed and implemented in past epidemics. Also of interest is the estimation of the causal impact of specific interventions (e.g., hospitalization, or hospitalization at a particular hospital) on survival, which can be estimated as a relative CFR for two or more groups. When observational data are used for this purpose, three more sources of bias may arise: confounding, survivorship bias, and selection due to preferential inclusion in surveillance datasets of those who are hospitalized and/or die. We illustrate these biases and caution against causal interpretation of differential CFR among those receiving different interventions in observational datasets. Again, we discuss ways to reduce these biases, particularly by estimating outcomes in smaller but more systematically defined cohorts ascertained before the onset of symptoms, such as those identified by forward contact tracing. Finally, we discuss the circumstances in which these biases may affect non-causal interpretation of risk factors for death among cases.

Concepts: Infection, Scientific method, Mathematics, Approximation, Statistics, Estimation, Infectious disease, Epidemiology


BACKGROUND: Obstetric fistula is a severe condition which can have devastating consequences for a woman’s life. Despite a considerable literature, very little is known about its prevalence. This project was conducted to carry out a situational analysis of fistula services in South Sudan and to pilot test the Key Informant Method (KIM) to estimate the prevalence of fistula in a region of South Sudan. METHODS: Key stakeholder interviews, document reviews and fistula surgery record reviews were undertaken. A KIM survey was conducted in a district of Western Bahr-el-Ghazal in January 2012. One hundred sixty-six community-based distributors, traditional birth attendants and village midwives were trained as key informants to identify women with fistula in the community. Women identified were subsequently examined by an obstetrician and nurse to verify whether they had a fistula. RESULTS: There were limited fistula repair services in South Sudan. Approximately 50–80 women per year attend periodic campaigns, with around half having a fistula and receiving a repair. On average a further 5 women a year received fistula repair from hospital services. Ten women with potential fistula were identified via KIM; all confirmed by the obstetrician. Of these, three were from the survey area, which had 8,865 women of reproductive age (15–49 years). This gives a minimal estimated prevalence of at least 30 fistulas per 100,000 women of reproductive age (95% CI 10–100). CONCLUSIONS: Routine fistula repair services available do not meet the population’s needs. The pilot study suggests that KIM can be used to identify women with fistula in the community. Data on fistula are generally poor; the KIM methodology we used in South Sudan yielded a lower fistula prevalence than estimates reported previously in the region.

Concepts: Rectovaginal fistula, Approximation, Sudan, Southern Sudan, Obstetrics, Vesicovaginal fistula, Childbirth, Fistula


Assessing oil pollution using traditional field-based methods over large areas is difficult and expensive. Remote sensing technologies with good spatial and temporal coverage might provide an alternative for monitoring oil pollution by recording the spectral signals of plants growing in polluted soils. Total petroleum hydrocarbon concentrations of soils and the hyperspectral canopy reflectance were measured in wetlands dominated by reeds (Phragmites australis) around oil wells that have been producing oil for approximately 10 years in the Yellow River Delta, eastern China to evaluate the potential of vegetation indices and red edge parameters to estimate soil oil pollution. The detrimental effect of oil pollution on reed communities was confirmed by the evidence that the aboveground biomass decreased from 1076.5 g m(-2) to 5.3 g m(-2) with increasing total petroleum hydrocarbon concentrations ranging from 9.45 mg kg(-1) to 652 mg kg(-1). The modified chlorophyll absorption ratio index (MCARI) best estimated soil TPH concentration among 20 vegetation indices. The linear model involving MCARI had the highest coefficient of determination (R(2) = 0.73) and accuracy of prediction (RMSE = 104.2 mg kg(-1)). For other vegetation indices and red edge parameters, the R(2) and RMSE values ranged from 0.64 to 0.71 and from 120.2 mg kg(-1) to 106.8 mg kg(-1) respectively. The traditional broadband normalized difference vegetation index (NDVI), one of the broadband multispectral vegetation indices (BMVIs), produced a prediction (R(2) = 0.70 and RMSE = 110.1 mg kg(-1)) similar to that of MCARI. These results corroborated the potential of remote sensing for assessing soil oil pollution in large areas. Traditional BMVIs are still of great value in monitoring soil oil pollution when hyperspectral data are unavailable.

Concepts: Landfill, Approximation, Yellow River, Hyperspectral imaging, Estimation, People's Republic of China, Remote sensing, Petroleum


The oxygen status of a tumor has significant clinical implications for treatment prognosis, with well-oxygenated subvolumes responding markedly better to radiotherapy than poorly supplied regions. Oxygen is essential for tumor growth, yet estimation of local oxygen distribution can be difficult to ascertain in situ, due to chaotic patterns of vasculature. It is possible to avoid this confounding influence by using avascular tumor models, such as tumor spheroids, a much better approximation of realistic tumor dynamics than monolayers, where oxygen supply can be described by diffusion alone. Similar to in situ tumours, spheroids exhibit an approximately sigmoidal growth curve, often approximated and fitted by logistic and Gompertzian sigmoid functions. These describe the basic rate of growth well, but do not offer an explicitly mechanistic explanation. This work examines the oxygen dynamics of spheroids and demonstrates that this growth can be derived mechanistically with cellular doubling time and oxygen consumption rate (OCR) being key parameters. The model is fitted to growth curves for a range of cell lines and derived values of OCR are validated using clinical measurement. Finally, we illustrate how changes in OCR due to gemcitabine treatment can be directly inferred using this model.

Concepts: Gompertz function, Oncology, Approximation, Cancer, Population growth, Estimation, Exponentials, Sigmoid function


How often do people visit the world’s protected areas (PAs)? Despite PAs covering one-eighth of the land and being a major focus of nature-based recreation and tourism, we don’t know. To address this, we compiled a globally-representative database of visits to PAs and built region-specific models predicting visit rates from PA size, local population size, remoteness, natural attractiveness, and national income. Applying these models to all but the very smallest of the world’s terrestrial PAs suggests that together they receive roughly 8 billion (8 x 109) visits/y-of which more than 80% are in Europe and North America. Linking our region-specific visit estimates to valuation studies indicates that these visits generate approximately US $600 billion/y in direct in-country expenditure and US $250 billion/y in consumer surplus. These figures dwarf current, typically inadequate spending on conserving PAs. Thus, even without considering the many other ecosystem services that PAs provide to people, our findings underscore calls for greatly increased investment in their conservation.

Concepts: Estimation, Approximation, North America, The Wild, Conservation, Europe, World, Biodiversity


Insufficient data exist for accurate estimation of global nutrient supplies. Commonly used global datasets contain key weaknesses: 1) data with global coverage, such as the FAO food balance sheets, lack specific information about many individual foods and no information on micronutrient supplies nor heterogeneity among subnational populations, while 2) household surveys provide a closer approximation of consumption, but are often not nationally representative, do not commonly capture many foods consumed outside of the home, and only provide adequate information for a few select populations. Here, we attempt to improve upon these datasets by constructing a new model-the Global Expanded Nutrient Supply (GENuS) model-to estimate nutrient availabilities for 23 individual nutrients across 225 food categories for thirty-four age-sex groups in nearly all countries. Furthermore, the model provides historical trends in dietary nutritional supplies at the national level using data from 1961-2011. We determine supplies of edible food by expanding the food balance sheet data using FAO production and trade data to increase food supply estimates from 98 to 221 food groups, and then estimate the proportion of major cereals being processed to flours to increase to 225. Next, we estimate intake among twenty-six demographic groups (ages 20+, both sexes) in each country by using data taken from the Global Dietary Database, which uses nationally representative surveys to relate national averages of food consumption to individual age and sex-groups; for children and adolescents where GDD data does not yet exist, average calorie-adjusted amounts are assumed. Finally, we match food supplies with nutrient densities from regional food composition tables to estimate nutrient supplies, running Monte Carlo simulations to find the range of potential nutrient supplies provided by the diet. To validate our new method, we compare the GENuS estimates of nutrient supplies against independent estimates by the USDA for historical US nutrition and find very good agreement for 21 of 23 nutrients, though sodium and dietary fiber will require further improvement.

Concepts: Approximation, Eating, Food security, Micronutrient, Nutrient, Estimation, Food, Nutrition


Sound produced by fish spawning aggregations (FSAs) permits the use of passive acoustic methods to identify the timing and location of spawning. However, difficulties in relating sound levels to abundance have impeded the use of passive acoustics to conduct quantitative assessments of biomass. Here we show that models of measured fish sound production versus independently measured fish density can be generated to estimate abundance and biomass from sound levels at FSAs. We compared sound levels produced by spawning Gulf Corvina (Cynoscion othonopterus) with simultaneous measurements of density from active acoustic surveys in the Colorado River Delta, Mexico. During the formation of FSAs, we estimated peak abundance at 1.53 to 1.55 million fish, which equated to a biomass of 2,133 to 2,145 metric tons. Sound levels ranged from 0.02 to 12,738 Pa(2), with larger measurements observed on outgoing tides. The relationship between sound levels and densities was variable across the duration of surveys but stabilized during the peak spawning period after high tide to produce a linear relationship. Our results support the use of active acoustic methods to estimate density, abundance, and biomass of fish at FSAs; using appropriately scaled empirical relationships, sound levels can be used to infer these estimates.

Concepts: Cynoscion, Sound pressure, Approximation, Tide, Estimation, Colorado River, Sound, Acoustics


Falls are the leading cause of fatal and nonfatal injuries among adults aged ≥65 years (older adults). During 2014, approximately 27,000 older adults died because of falls; 2.8 million were treated in emergency departments for fall-related injuries, and approximately 800,000 of these patients were subsequently hospitalized.* To estimate the numbers, percentages, and rates of falls and fall injuries among older adults by selected characteristics and state, CDC analyzed data from the 2014 Behavioral Risk Factor Surveillance System (BRFSS) survey. In 2014, 28.7% of older adults reported falling; the estimated 29.0 million falls resulted in 7.0 million injuries. Known effective strategies for reducing the number of older adult falls include a multifactorial clinical approach (e.g., gait and balance assessment, strength and balance exercises, and medication review). Health care providers can play an important role in fall prevention by screening older adults for fall risk, reviewing and managing medications linked to falls, and recommending vitamin D supplements to improve bone, muscle, and nerve health and reduce the risk for falls.

Concepts: Muscle, Health care provider, Medicine, Approximation, Behavioral Risk Factor Surveillance System, Death, Estimation, Health care


Establishing the time since death is critical in every death investigation, yet existing techniques are susceptible to a range of errors and biases. For example, forensic entomology is widely used to assess the postmortem interval (PMI), but errors can range from days to months. Microbes may provide a novel method for estimating PMI that avoids many of these limitations. Here we show that postmortem microbial community changes are dramatic, measurable, and repeatable in a mouse model system, allowing PMI to be estimated within approximately 3 days over 48 days. Our results provide a detailed understanding of bacterial and microbial eukaryotic ecology within a decomposing corpse system and suggest that microbial community data can be developed into a forensic tool for estimating PMI. DOI:

Concepts: Archaea, Death, Eukaryote, Mathematics, Microorganism, Bacteria, Approximation, Estimation