Simplified population data analysis using gamma distribution for nutritional requirements and its application to the estimation of iron requirements for women of child-bearing age

BackgroundEstimation of nutritional requirements is a difficult task, especially for nutrients whose requirements have skewed distribution like iron in menstruating women.ObjectiveTo mathematically develop a simplified population data analysis using gamma distribution for the estimation of nutritional requirements, not depending on extensive numerical calculation.MethodsThe required equations for the estimation of requirements were devised and solved. Existing data of iron intakes and iron losses in literature were fitted to cumulative distribution curves including gamma distribution. The proposed method was applied to the estimation of iron requirements in women using the National Health and Nutrition Survey data from 2003 to 2007 in Japan.ResultsThe type 2 equation of nutritional state is first introduced: prevalence of inadequate nutritional state = Σ(individuals with intake/requirement <1)/(total number of individuals). The prevalence of inadequate nutritional status is determined by F-distribution with positive real number parameters, if the intake and the requirement have independent gamma distributions. The sum of basal and menstrual iron losses is well approximated by gamma distribution, if the basal and menstrual iron losses have independent gamma distributions. Using these relationships, an approximate estimate of iron requirements was determined. Iron intakes and losses were found to be well approximated by gamma distribution. The median of the coefficient of variation (CV) of basal iron loss was 34 %. A new correction method for intra-individual variation in gamma distribution under constant CV is presented also. The median of the estimated median iron requirement was 8.12 mg, 8.15 mg and 8.18 mg for women aged 18−29 years, respectively, as the exact numerical estimate, the approximate estimate using BETA.INV in Excel and the approximate estimate using F.INV in Excel. For women aged 30−49 years, it was 9.15 mg, 9.17 mg and 9.14 mg. The intake covering the needs of 97.7 % women was 14.55 mg, 14.44 mg and 14.49 mg for women aged 18−29 years, and 15.70 mg, 15.77 mg and 15.60 mg for women aged 30−49 years.ConclusionThe approximate estimates of iron requirements agreed well with the exact numerical estimate. The proposed method is useful for the estimation of iron requirements in menstruating women that usually requires extensive numerical calculations.     

Estimation of iron requirements for women by numerical analysis of population-based data from the National Health and Nutrition Surveys of Japan 2003–2007

Iron requirements were estimated from the results of the National Health and Nutrition Surveys of Japan 2003–2007 using the numerical analysis of requirements based on an integral equation. The numerical analysis used population-based data on iron nutriture, the prevalence of inadequate iron status, and the distribution of iron intakes. The cutoff value for inadequate iron status was defined as a serum ferritin concentration <30 ng/mL. Iron intakes and menstrual blood losses followed a log-normal distribution and published values were corrected accordingly to calculate usual values. For women aged 18–29 years old, the median of the estimated median iron requirement (corresponding to the estimated average requirement by using the terminology of the dietary reference intakes) was 7.59 mg (range, 6.86–8.11). The median of the estimated usual iron intake covering the needs of women with 80 mL per cycle of menstrual blood loss was 11.27 mg (range, 10.16–12.00), and the median of the usual iron intake covering the needs of 97.7% of women was 13.93 mg (range, 12.55–14.81). For women aged 30–49 years old, the corresponding figures were 8.13 mg (range, 7.96–8.69), 11.95 mg (range, 11.72–12.77), and 14.71 mg (range, 14.44–15.72).     

Combination of Soy Protein,Amylopectin, and Chromium Stimulates Muscle Protein Synthesis by Regulation of Ubiquitin–Proteasome Proteolysis Pathway after Exercise

This review discusses the development of studies that evaluated the essentiality and requirements of iron from the ancient to the present. The therapeutic effects of iron compounds were recognized by the ancient Greeks and Romans. The earliest recognition of the essentiality of iron was stated by Paracelsus, a distinguished physician alchemist, in the sixteenth century. Iron was included in the earliest nutritional standard prepared for the Royal Army by E. A. Parkes, the first professor of hygiene. The League of Nations Health Organisation determined average iron requirements based on literature review. In the first US Recommended Dietary Allowances (RDA), the RDA of iron was determined from the results of iron balance studies. In the current Dietary Reference Intakes, iron requirements were determined based on the factorial method with the aid of Monte Carlo simulation for combining basal and menstrual iron losses. Population data analysis is a recently developed alternative that does not use the pre-estimated iron absorption rate and requires the prevalence of inadequacy instead. Population data analysis uses the convolution integral for combining basal and menstrual iron losses to ensure the required accuracy. This review also provides new estimates of hair and nail iron losses.

     

Iron requirements

Absorbed iron (Fe) requirements are partly recalculated based on new figures for Fe requirements in menstruating women. The new higher figures were obtained by including in the calculation of the total requirements the effect of variations in hemoglobin concentration, which influences the variation in menstrual Fe losses and the variation in basal Fe losses. Higher figures were also found for menstruating teenage girls. Dietary iron requirements were also recalculated based on a critical examination of data available allowing estimations of bioavailability of the dietary iron in Western-type diets. In borderline Fe-deficient subjects, with optimal hemoglobin levels but no iron stores, the 95th percentile range for the bioavailability was estimated to 14–16% of the fraction of the dietary Fe that is potentially available for absorption (correction for partially available fortification Fe).     

Estimation of Dietary Iron Bioavailability from Food Iron Intake and Iron Status

Currently there are no satisfactory methods for estimating dietary iron absorption (bioavailability) at a population level, but this is essential for deriving dietary reference values using the factorial approach. The aim of this work was to develop a novel approach for estimating dietary iron absorption using a population sample from a sub-section of the UK National Diet and Nutrition Survey (NDNS). Data were analyzed in 873 subjects from the 2000–2001 adult cohort of the NDNS, for whom both dietary intake data and hematological measures (hemoglobin and serum ferritin (SF) concentrations) were available. There were 495 men aged 19–64 y (mean age 42.7±12.1 y) and 378 pre-menopausal women (mean age 35.7±8.2 y). Individual dietary iron requirements were estimated using the Institute of Medicine calculations. A full probability approach was then applied to estimate the prevalence of dietary intakes that were insufficient to meet the needs of the men and women separately, based on their estimated daily iron intake and a series of absorption values ranging from 1–40%. The prevalence of SF concentrations below selected cut-off values (indicating that absorption was not high enough to maintain iron stores) was derived from individual SF concentrations. An estimate of dietary iron absorption required to maintain specified SF values was then calculated by matching the observed prevalence of insufficiency with the prevalence predicted for the series of absorption estimates. Mean daily dietary iron intakes were 13.5 mg for men and 9.8 mg for women. Mean calculated dietary absorption was 8% in men (50^th percentile for SF 85 µg/L) and 17% in women (50^th percentile for SF 38 µg/L). At a ferritin level of 45 µg/L estimated absorption was similar in men (14%) and women (13%). This new method can be used to calculate dietary iron absorption at a population level using data describing total iron intake and SF concentration.     

Dietary molar ratios of phytate: Zinc and millimolar ratios of phytate × calcium: Zinc in South Koreans

The zinc nutritional status in south Koreans was established by evaluation of zinc, calcium and phytate intakes, the molar ratio of phytate: zinc, and the millimolar ratio of phytate × calcium: zinc. The intakes of iron and magnesium were also estimated. Sampling was designed so that it was representative of the national population. Two-day food records were used for the calculation of nutrient intakes, using food consumption data from the 1995 National Nutrition Survey (’95NNS) for South Korea. Daily intakes of zinc and calcium were estimated to be 10.1 mg/d and 426.5 mg/d, respectively, and those of iron and magnesium were 15.2 mg/d and 268.0 mg/d, respectively. The estimated daily phytate intake was 1676.6 mg/d. The ratio of phytate: zinc was 15.9 mol/d and that of phytate × calcium: zinc was 168.9 mmol/d. The ratio in millimoles per 4.2 MJ (1000 kcal) of phytate × calcium: zinc was 91.8. The major food groups for zinc intake were meat, poultry and their products (43%), and cereals and grain products (18%). Sixty-two percent of zinc was from animal food sources. Cereal and grain products supplied most of the phytate intake (46%) followed by seasonings, fruits, and legumes and their products. The major food source of phytate was rice (39%). The results of the study raise concern about the suboptimal zinc status in relation to the Western diet.     

Linking population dynamics models with empirically derived models through phytoplankton primary production

There are alternative methods for estimation of phytoplankton primary production (PP) that are fundamentally different in the calculation approach. The process‐oriented PP model is a mechanistic, empirically derived method based on the photosynthesis–light relationships. The population dynamics‐based PP calculation, which is a synthetic method, provides a production estimate based on population dynamics of phytoplankton. These alternative methods were here compared with regard to production estimates and linked to enhance the performance of the existing models of population dynamics applied to a wide variety of lakes worldwide in terms of morphometry, nutrient status, and light environments. Estimates of PP were shown to be sensitive to changes in phytoplankton sinking and zooplankton grazing rates in both methods. Production estimates in the process‐oriented PP model were also sensitive to light‐associated parameters such as day length. Although the production estimated from the population dynamics‐based PP calculation tended to be lower than that from the process‐oriented PP model irrespective of lake morphometry, production estimates calculated from both methods with standard parameterization were comparable when production was estimated on an annual timescale. However, it was also shown that the alternative methods could produce different production estimates when estimated on shorter timescales such as cyanobacterial blooms in summer. Cyanobacteria with low mortality due to grazing and sinking losses have been considered as trophic bottlenecks, but there is increasing evidence that their mortality is, to a considerable extent, due to parasitic pathogens. In the case of cyanobacterial blooms, an addition of parasite‐related loss term (19%–33% of standing stock) resulted in a resolution of the difference in production estimates between the methods. These analyses theoretically support the critical role of parasitism and resolve the bottleneck problem in aquatic ecosystem metabolism.     

Inferring parturition and neonate survival from movement patterns of female ungulates: a case study using woodland caribou

Analyses of animal movement data have primarily focused on understanding patterns of space use and the behavioural processes driving them. Here, we analyzed animal movement data to infer components of individual fitness, specifically parturition and neonate survival. We predicted that parturition and neonate loss events could be identified by sudden and marked changes in female movement patterns. Using GPS radio‐telemetry data from female woodland caribou (Rangifer tarandus caribou), we developed and tested two novel movement‐based methods for inferring parturition and neonate survival. The first method estimated movement thresholds indicative of parturition and neonate loss from population‐level data then applied these thresholds in a moving‐window analysis on individual time‐series data. The second method used an individual‐based approach that discriminated among three a priori models representing the movement patterns of non‐parturient females, females with surviving offspring, and females losing offspring. The models assumed that step lengths (the distance between successive GPS locations) were exponentially distributed and that abrupt changes in the scale parameter of the exponential distribution were indicative of parturition and offspring loss. Both methods predicted parturition with near certainty (>97% accuracy) and produced appropriate predictions of parturition dates. Prediction of neonate survival was affected by data quality for both methods; however, when using high quality data (i.e., with few missing GPS locations), the individual‐based method performed better, predicting neonate survival status with an accuracy rate of 87%. Understanding ungulate population dynamics often requires estimates of parturition and neonate survival rates. With GPS radio‐collars increasingly being used in research and management of ungulates, our movement‐based methods represent a viable approach for estimating rates of both parameters.     

Dietary copper and human health: Current evidence and unresolved issues

Although copper (Cu) is recognized as an essential trace element, uncertainties remain regarding Cu reference values for humans, as illustrated by discrepancies between recommendations issued by different national authorities. This review examines human studies published since 1990 on relationships between Cu intake, Cu balance, biomarkers of Cu status, and health. It points out several gaps and unresolved issues which make it difficult to assess Cu requirements. Results from balance studies suggest that daily intakes below 0.8 mg/day lead to net Cu losses, while net gains are consistently observed above 2.4 mg/day. However, because of an incomplete collection of losses in all studies, a precise estimation of Cu requirements cannot be derived from available data. Data regarding the relationship between Cu intake and potential biomarkers are either too preliminary or inconclusive because of low specificity or low sensitivity to change in dietary Cu over a wide range of intakes. Results from observation and intervention studies do not support a link between Cu and a risk of cardiovascular disease, cognitive decline, arthritis or cancer for intakes ranging from 0.6 to 3 mg/day, and limited evidence exists for impaired immune function in healthy subjects with a very low (0.38 mg/day) Cu intake. However, data from observation studies should be regarded with caution because of uncertainties regarding Cu concentration in various foods and water. Further studies that accurately evaluate Cu exposure based on reliable biomarkers of Cu status are needed.     

Combining species distribution modeling and distance sampling to assess wildlife population size: A case study with the northern yellow-cheeked gibbon (Nomascus annamensis)

Population size and distribution data for wildlife species play an important role in conservation and management, especially for endangered species. However, scientists seriously lack data on the population status of many species. The northern yellow-cheeked gibbon (Nomascus annamensis) is found in southern Lao PDR, central Vietnam, and northeastern Cambodia. The population of the species has significantly declined due to hunting, habitat loss, and the wildlife trade. To examine the population size and distribution of N. annamensis, we conducted a field survey in Song Thanh Nature Reserve, Quang Nam Province, central Vietnam from February to April 2019 using the audio point count method. We combined Distance Sampling and Ecological Niche Modeling to estimate the population of the gibbons. Results showed that the total suitable area for the gibbons was about 302.32 km², with the two most important variables of the habitat model being the distance-to-villages and forest type. We detected 36 gibbon groups through field surveys and estimated 443 (95% CI, 278–707) gibbon groups in Song Thanh Nature Reserve. Our results indicate that the gibbon population in Song Thanh Nature Reserve is the largest known population of N. annamensis in Vietnam. In addition, our study was the first to combine species distribution modeling with distance sampling to estimate gibbon density and population size. This approach might be useful in surveying and monitoring gibbon populations because it takes imperfect detection probability into account in estimating gibbon population density while estimating the area of potential habitat using environmental variables.     

Dispersal kernel of green rice leafhopper estimated from truncated data

Characterizing dispersal kernels from truncated data is important for managing and predicting population dynamics. We used mark-recapture data from 10 previously published replicated experiments at three host plant development stages (seedling, tillering, and heading) to estimate parameters of the normal and exponential dispersal kernels for green rice leafhopper, Nephotettix cincticeps (Uhler). We compared classic statistical methods for estimating untruncated distribution parameters from truncated data with maximum likelihood (MLE) and the method of statistical moments for simulated and empirical data. Simulations showed that both methods provided accurate parameter estimates with similar precision. The method of moments is algebraically complex, but simple to calculate, while the MLE methods require numerical solutions of nonlinear equations. Simulations also showed that accurate, precise estimates of the parameters of the untruncated distributions could be attained even under severe truncation with sufficient numbers of recaptures. Both diffusivity and the exponential mean were higher with later plant growth stage, showing that insects moved farther and faster at the heading stage. Precision of the estimates was not strongly related to percent capture, size of the experimental field, or the number of leafhoppers captured. The leptokurtic exponential kernel fit the data better than the normal kernel for all the experiments. These results support an alternative explanation for the strong density-dependent population regulation of this species at the heading stage. Instead of leafhopper density per se, the increase in movement at this stage could integrate the populations in the separate fields, leveling densities throughout the landscape.     

Menstrual Cycle Phase Does Not Predict Political Conservatism

Recent authors have reported a relationship between women''s fertility status, as indexed by menstrual cycle phase, and conservatism in moral, social and political values. We conducted a survey to test for the existence of a relationship between menstrual cycle day and conservatism.2213 women reporting regular menstrual cycles provided data about their political views. Of these women, 2208 provided information about their cycle date, 1260 provided additional evidence of reliability in self-reported cycle date, and of these, 750 also indicated an absence of hormonal disruptors such as recent hormonal contraception use, breastfeeding or pregnancy. Cycle day was used to estimate day-specific fertility rate (probability of conception); political conservatism was measured via direct self-report and via responses to the "Moral Foundations” questionnaire. We also recorded relationship status, which has been reported to interact with menstrual cycle phase in determining political preferences.We found no evidence of a relationship between estimated cyclical fertility changes and conservatism, and no evidence of an interaction between relationship status and cyclical fertility in determining political attitudes. Our findings were robust to multiple inclusion/exclusion criteria and to different methods of estimating fertility and measuring conservatism. In summary, the relationship between cycle-linked reproductive parameters and conservatism may be weaker or less reliable than previously thought.     

A Multilevel Model for Continuous Time Population Estimation

Summary .  Statistical methods have been developed and applied to estimating populations that are difficult or too costly to enumerate. Known as multilist methods in epidemiological settings, individuals are matched across lists and estimation of population size proceeds by modeling counts in incomplete multidimensional contingency tables (based on patterns of presence/absence on lists). As multilist methods typically assume that lists are compiled instantaneously, there are few options available for estimating the unknown size of a closed population based on continuously (longitudinally) compiled lists. However, in epidemiological settings, continuous time lists are a routine byproduct of administrative functions. Existing methods are based on time-to-event analyses with a second step of estimating population size. We propose an alternative approach to address the twofold epidemiological problem of estimating population size and of identifying patient factors related to duration (in days) between visits to a health care facility. A Bayesian framework is proposed to model interval lengths because, for many patients, the data are sparse; many patients were observed only once or twice. The proposed method is applied to the motivating data to illustrate the methods' applicability. Then, a small simulation study explores the performance of the estimator under a variety of conditions. Finally, a small discussion section suggests opportunities for continued methodological development for continuous time population estimation.     

The estimation of the fitness function from two samples taken from a population

The fitness of animals subjected to natural selection can be defined as the probability of surviving selection for a given interval of time, or some convenient multiple of this probability. If the fitness of animals is related to some quantitative variable X (such as size) then this relationship is expressed mathematically in the fitness function w(x) and this function can be estimated by comparing the distribution of X in samples taken before and after selection. In this note five methods for estimating the fitness function on the basis of samples from a large population are discussed. They are compared on three previously published sets of data and as a result estimation according to weighted multiple regression is recommended.     

Maximum-likelihood estimation of coalescence times in genealogical trees

We develop a method for maximum-likelihood estimation of coalescence times in genealogical trees, based on population genetics data. For this purpose, a Viterbi-type algorithm is constructed to maximize the joint likelihood of the coalescence times. Marginal confidence intervals for the coalescence times based on the profile likelihoods are also computed. Our method of finding MLEs and calculating C.I.'s appears to be more accurate than alternative numerical maximization methods, and maximum-likelihood inference appears to be more accurate than other existing model-free approaches to estimating coalescent times. We demonstrate the method on two different data sets: human Y chromosome DNA data and fungus DNA data.     

Nutritional status of a select group of free-living elderly people in Vancouver

A study was conducted to determine the nutritional status of the free-living elderly population in Vancouver. The response rate of the sample was low. Dietary information from 104 single men and women and 23 couples was collected by the 24-hour recall method. Biochemical tests in 56 single individuals and 13 couples included measurement of hemoglobin concentration and hematocrit, plasma analysis for concentrations of total protein, iron, carotene, vitamin A, ascorbic acid, vitamin E and cholesterol and for transferrin saturation, and urine analysis for concentrations of creatinine, thiamin, riboflavin and N¹-methylnicotinamide.Mean energy intakes were considerably below the Dietary Standard for Canada. However, mean intakes of individual nutrients were similar to or in excess of the Dietary Standard for Canada for single men and women and for married men. Married women had low average intakes of calcium, iron, thiamin and riboflavin but adequate intakes of other nutrients. Mean values for biochemical variables were within the accepted range as defined by the Interdepartmental Committee of Nutrition for National Defense in the United States. According to the Nutrition Canada definitions of “high risk” there were no individuals in high-risk categories for any biochemical variable except plasma cholesterol concentration and transferrin saturation. The dietary and biochemical data indicated that the nutritional status in this select group of elderly persons was good except for intake of total energy and, in married women, of calcium, iron, thiamin and riboflavin.     

Hemorrhage-Adjusted Iron Requirements,Hematinics and Hepcidin Define Hereditary Hemorrhagic Telangiectasia as a Model of Hemorrhagic Iron Deficiency

Background

Iron deficiency anemia remains a major global health problem. Higher iron demands provide the potential for a targeted preventative approach before anemia develops. The primary study objective was to develop and validate a metric that stratifies recommended dietary iron intake to compensate for patient-specific non-menstrual hemorrhagic losses. The secondary objective was to examine whether iron deficiency can be attributed to under-replacement of epistaxis (nosebleed) hemorrhagic iron losses in hereditary hemorrhagic telangiectasia (HHT).

Methodology/Principal Findings

The hemorrhage adjusted iron requirement (HAIR) sums the recommended dietary allowance, and iron required to replace additional quantified hemorrhagic losses, based on the pre-menopausal increment to compensate for menstrual losses (formula provided). In a study population of 50 HHT patients completing concurrent dietary and nosebleed questionnaires, 43/50 (86%) met their recommended dietary allowance, but only 10/50 (20%) met their HAIR. Higher HAIR was a powerful predictor of lower hemoglobin (p = 0.009), lower mean corpuscular hemoglobin content (p<0.001), lower log-transformed serum iron (p = 0.009), and higher log-transformed red cell distribution width (p<0.001). There was no evidence of generalised abnormalities in iron handling Ferritin and ferritin² explained 60% of the hepcidin variance (p<0.001), and the mean hepcidinferritin ratio was similar to reported controls. Iron supplement use increased the proportion of individuals meeting their HAIR, and blunted associations between HAIR and hematinic indices. Once adjusted for supplement use however, reciprocal relationships between HAIR and hemoglobin/serum iron persisted. Of 568 individuals using iron tablets, most reported problems completing the course. For patients with hereditary hemorrhagic telangiectasia, persistent anemia was reported three-times more frequently if iron tablets caused diarrhea or needed to be stopped.

Conclusions/significance

HAIR values, providing an indication of individuals’ iron requirements, may be a useful tool in prevention, assessment and management of iron deficiency. Iron deficiency in HHT can be explained by under-replacement of nosebleed hemorrhagic iron losses.     

Spatial pattern and sequential sampling of squash bug (Heteroptera: Coreidae) adults in watermelon

Spatial distribution patterns of adult squash bugs were determined in watermelon, Citrullus lanatus (Thunberg) Matsumura and Nakai, during 2001 and 2002. Results of analysis using Taylor's power law regression model indicated that squash bugs were aggregated in watermelon. Taylor's power law provided a good fit with r2 = 0.94. A fixed precision sequential sampling plan was developed for estimating adult squash bug density at fixed precision levels in watermelon. The plan was tested using a resampling simulation method on nine and 13 independent data sets ranging in density from 0.15 to 2.52 adult squash bugs per plant. Average estimated means obtained in 100 repeated simulation runs were within the 95% CI of the true means for all the data. Average estimated levels of precision were similar to the desired level of precision, particularly when the sampling plan was tested on data having an average mean density of 1.19 adult squash bugs per plant. Also, a sequential sampling for classifying adult squash bug density as below or above economic threshold was developed to assist in the decision-making process. The classification sampling plan is advantageous in that it requires smaller sample sizes to estimate the population status when the population density differs greatly from the action threshold. However, the plan may require excessively large sample sizes when the density is close to the threshold. Therefore, an integrated sequential sampling plan was developed using a combination of a fixed precision and classification sequential sampling plans. The integration of sampling plans can help reduce sampling requirements.     

Overestimates of maternity and population growth rates in multi-annual breeders

There has been limited attention to estimating maternity rate because it appears to be relatively simple. However, when used for multi-annual breeder species, such as the largest carnivores, the most common estimators introduce an upward bias by excluding unproductive females. Using a simulated dataset based on published data, we compare the accuracy of maternity estimates derived from standard methods against estimates derived from an alternative method. We show that standard methods overestimate maternity rates in the presence of unsuccessful pregnancies. Importantly, population growth rates derived from a matrix model parameterized with the biased estimates may indicate increasing populations although the populations are stable or even declining. We recommend the abandonment of the biased standard methods and to instead use the unbiased alternative method for population projections and assessments of population viability.     

Iron status,malaria parasite loads and food policies: Evidence from sub-Saharan Africa

This brief article investigates the consequences of improving children's iron status for malaria parasite loads by analyzing data from Cote d’Ivoire, Zambia, and Tanzania; the treatment of iron deficiencies has been argued to flare up malaria in under-nourished populations. The data from a randomized controlled trial in Cote d’Ivoire showed statistically insignificant effects of the consumption of iron-fortified biscuits on children's malaria parasite loads. Second, nutrient intakes data from Zambia showed insignificant correlations and associations between children's iron and folate intakes and malaria parasite loads. Third, malaria parasite loads did not change significantly for Tanzanian children receiving anthelmintic treatment; malaria loads were lower for older children and for those using bed nets. Overall, the evidence from sub-Saharan African countries suggests that small improvements in iron status achieved via suitable food policies are unlikely to have detrimental effects for children's malaria parasite loads.