Recent trends and components of change in fertility in Nepal

The objectives of this article are, first, to provide improved estimates of recent fertility levels and trends in Nepal and, second, to analyse the components of fertility change. The analysis is based on data from Nepal's 1996 and 2001 Demographic and Health Surveys. Total fertility rates (TFR) are derived by the own-children method. They incorporate additional adjustments to compensate for displacement of births, and they are compared with estimates derived by the birth-history method. Fertility is estimated not only for the whole country but also by urban/rural residence and by woman's education. The own-children estimates for the whole country indicate that the TFR declined from 4.96 to 4.69 births per woman between the 3-year period preceding the 1996 survey and the 3-year period preceding the 2001 survey. About three-quarters of the decline stems from reductions in age-specific marital fertility rates and about one-quarter from changes in age-specific proportions currently married. Further decomposition of the decline in marital fertility, as measured by births per currently married woman during the 5-year period before each survey, indicates that almost half of the decline in marital fertility is accounted for by changes in population composition by ecological region, development region, urban/rural residence, education, age at first cohabitation with husband, time elapsed since first cohabitation, number of living children at the start of the 5-year period and media exposure. With these variables controlled, another one-third of the decline is accounted for by increase in the proportion sterilized at the start of the 5-year period before each survey.     

Bayesian inference on age-specific survival for censored and truncated data

1. Traditional estimation of age-specific survival and mortality rates in vertebrates is limited to individuals with known age. Although this subject has been studied extensively using effective capture-recapture and capture-recovery models, inference remains challenging because of large numbers of incomplete records (i.e. unknown age of many individuals) and because of the inadequate duration of the studies. 2. Here, we present a hierarchical model for capture-recapture/recovery (CRR) data sets with large proportions of unknown times of birth and death. The model uses a Bayesian framework to draw inference on population-level age-specific demographic rates using parametric survival functions and applies this information to reconstruct times of birth and death for individuals with unknown age. 3. We simulated a set of CRR data sets with varying study span and proportions of individuals with known age, and varying recapture and recovery probabilities. We used these data sets to compare our method to a traditional CRR model, which requires knowledge of individual ages. Subsequently, we applied our method to a subset of a long-term CRR data set on Soay sheep. 4. Our results show that this method performs better than the common CRR model when sample sizes are low. Still, our model is sensitive to the choice of priors with low recapture probability and short studies. In such cases, priors that overestimate survival perform better than those that underestimate it. Also, the model was able to estimate accurately ages at death for Soay sheep, with an average error of 0.94 years and to identify differences in mortality rate between sexes. 5. Although many of the problems in the estimation of age-specific survival can be reduced through more efficient sampling schemes, most ecological data sets are still sparse and with a large proportion of missing records. Thus, improved sampling needs still to be combined with statistical models capable of overcoming the unavoidable limitations of any fieldwork. We show that our approach provides reliable estimates of parameters and unknown times of birth and death even with the most incomplete data sets while being flexible enough to accommodate multiple recapture probabilities and covariates.     

Using Lifetime Risk Estimates in Personal Genomic Profiles: Estimation of Uncertainty

Personal genome tests are now offered direct-to-consumer (DTC) via genetic variants identified by genome-wide association studies (GWAS) for common diseases. Tests report risk estimates (age-specific and lifetime) for various diseases based on genotypes at multiple loci. However, uncertainty surrounding such risk estimates has not been systematically investigated. With breast cancer as an example, we examined the combined effect of uncertainties in population incidence rates, genotype frequency, effect sizes, and models of joint effects among genetic variants on lifetime risk estimates. We performed simulations to estimate lifetime breast cancer risk for carriers and noncarriers of genetic variants. We derived population-based cancer incidence rates from Surveillance, Epidemiology, and End Results (SEER) Program and comparative international data. We used data for non-Hispanic white women from 2003 to 2005. We derived genotype frequencies and effect sizes from published GWAS and meta-analyses. For a single genetic variant in FGFR2 gene (rs2981582), combination of uncertainty in these parameters produced risk estimates where upper and lower 95% simulation intervals differed by more than 3-fold. Difference in population incidence rates was the largest contributor to variation in risk estimates. For a panel of five genetic variants, estimated lifetime risk of developing breast cancer before age 80 for a woman that carried all risk variants ranged from 6.1% to 21%, depending on assumptions of additive or multiplicative joint effects and breast cancer incidence rates. Epidemiologic parameters involved in computation of disease risk have substantial uncertainty, and cumulative uncertainty should be properly recognized. Reliance on point estimates alone could be seriously misleading.     

Uncertainty calculations for theoretical flight power curves

The comparison of theoretical and experimental estimates of the mechanical power requirement for flight is currently impossible owing to the absence of complete experimental data based on mechanical power, as opposed to measurements of metabolic rates. Nevertheless, comparisons of measured and predicted characteristic speeds, and inferred power curves are frequently made, despite the total absence of uncertainty estimates of the theoretically predicted quantities. Here the method for correct calculation of uncertainty estimates in mechanical power models is outlined in detail, and analytical and numerical results are derived for realistic examples. The sensitivity of the calculated variations in power requirement varies greatly among the independent variables, and the practical and theoretical consequences of this variation are discussed. Pending the arrival of appropriate experimental measurements, it is now possible, in principle, to make quantitative comparisons with theoretical predictions.     

Cumulative Risks of Foster Care Placement for Danish Children

Although recent research suggests that the cumulative risk of foster care placement is far higher for American children than originally suspected, little is known about the cumulative risk of foster care placement in other countries, which makes it difficult to gauge the degree to which factor foster care placement is salient in other contexts. In this article, we provide companion estimates to those provided in recent work on the US by using Danish registry data and synthetic cohort life tables to show how high and unequally distributed the cumulative risk of foster care placement is for Danish children. Results suggest that at the beginning of the study period (in 1998) the cumulative risk of foster care placement for Danish children was roughly in line with the risk for American children. Yet, by the end of the study period (2010), the risk had declined to half the risk for American children. Our results also show some variations by parental ethnicity and sex, but these differences are small. Indeed, they appear quite muted relative to racial/ethnic differences in these risks in the United States. Last, though cumulative risks are similar between Danish and American children (especially at the beginning of the study period), the age-specific risk profiles are markedly different, with higher risks for older Danish children than for older American children.     

Demographic window to aging in the wild: constructing life tables and estimating survival functions from marked individuals of unknown age

Summary We address the problem of establishing a survival schedule for wild populations. A demographic key identity is established, leading to a method whereby age-specific survival and mortality can be deduced from a marked cohort life table established for individuals that are randomly sampled at unknown age and marked, with subsequent recording of time-to-death. This identity permits the construction of life tables from data where the birth date of subjects is unknown. An analogous key identity is established for the continuous case in which the survival schedule of the wild population is related to the density of the survival distribution in the marked cohort. These identities are explored for both life tables and continuous lifetime data. For the continuous case, they are implemented with statistical methods using non-parametric density estimation methods to obtain flexible estimates for the unknown survival distribution of the wild population. The analytical model provided here serves as a starting point to develop more complex models for residual demography, i.e. models for estimating survival of wild populations in which age-at-entry is unknown and using remaining information in randomly encountered individuals. This is a first step towards a broad new concept of 'expressed demographic information content of marked or captured individuals'.     

Analysis of covariance: an alternative to nutritional indices

Some statistical problems are added to the growing list of cautionary tales regarding the use of the conventional, ratio-based nutritional indices (RCR, RGR, ECI, AD and ECD). Analysis of ratios is based on the, probably unrealistic, assumption of an isometric relationship between denominator and numerator variables. Analysis of covariance (ANCOVA) makes less restrictive assumptions, and additionally provides important information about the data which is lost by using ratio variables. We demonstrate, using computer-generated data sets, some of the pitfalls of statistical analysis of ratios and illustrate how these may be avoided using ANCOVA. Some possible consequences of such statistical iniquities for biological interpretations are discussed.     

Uncertainty in Calculations of Net Primary Production for Grasslands

Net primary production (NPP) is a fundamental characteristic of all ecosystems and foundational to understanding the fluxes of energy and nutrients. Because NPP cannot be measured directly, researchers use field-measured surrogates as input variables in various equations designed to estimate ‘true NPP’. This has led to considerable debate concerning which equations most accurately estimate ‘true NPP’. This debate has influenced efforts to assess NPP in grasslands, with researchers often advocating more complex equations to avoid underestimation. However, this approach ignores the increase in statistical error associated with NPP estimates as a greater number of parameters and more complex mathematical functions are introduced into the equation. Using published grassland data and Monte Carlo simulation techniques, we assessed the relative variability in NPP estimates obtained using six different NPP estimation equations that varied in both the number of parameters and intricacy of mathematical operations. Our results indicated that more complex equations may result in greater uncertainty without reducing the probability of underestimation. The amount of uncertainty associated with estimates of NPP was influenced by the number of parameters as well as the variability in the data and the nature of the mathematical operations. For example, due to greater variability in the field-measured belowground data than aboveground data, estimates of belowground NPP tended to have more uncertainty than estimates of aboveground NPP. An analysis in which the input data were standardized allowed us to isolate the details of the calculations from the variability in the data in assessing the propagation of uncertainty. This analysis made clear that equations with product terms have the potential to magnify the uncertainty of the inputs in the estimates of NPP although this relationship was complicated by interactions with data variability and number of parameters. Our results suggest that more complex NPP estimation equations can increase uncertainty without necessarily reducing risk of underestimation. Because estimates can never be tested by comparison to “true NPP”, we recommend that researchers include an assessment of propagation of statistical error when evaluating the ‘best’ estimation method.     

Mixed-effects statistical model for comparative LC-MS proteomics studies

Comparing a protein's concentrations across two or more treatments is the focus of many proteomics studies. A frequent source of measurements for these comparisons is a mass spectrometry (MS) analysis of a protein's peptide ions separated by liquid chromatography (LC) following its enzymatic digestion. Alas, LC-MS identification and quantification of equimolar peptides can vary significantly due to their unequal digestion, separation, and ionization. This unequal measurability of peptides, the largest source of LC-MS nuisance variation, stymies confident comparison of a protein's concentration across treatments. Our objective is to introduce a mixed-effects statistical model for comparative LC-MS proteomics studies. We describe LC-MS peptide abundance with a linear model featuring pivotal terms that account for unequal peptide LC-MS measurability. We advance fitting this model to an often incomplete LC-MS data set with REstricted Maximum Likelihood (REML) estimation, producing estimates of model goodness-of-fit, treatment effects, standard errors, confidence intervals, and protein relative concentrations. We illustrate the model with an experiment featuring a known dilution series of a filamentous ascomycete fungus Trichoderma reesei protein mixture. For 781 of the 1546 T. reesei proteins with sufficient data coverage, the fitted mixed-effects models capably described the LC-MS measurements. The LC-MS measurability terms effectively accounted for this major source of uncertainty. Ninety percent of the relative concentration estimates were within 0.5-fold of the true relative concentrations. Akin to the common ratio method, this model also produced biased estimates, albeit less biased. Bias decreased significantly, both absolutely and relative to the ratio method, as the number of observed peptides per protein increased. Mixed-effects statistical modeling offers a flexible, well-established methodology for comparative proteomics studies integrating common experimental designs with LC-MS sample processing plans. It favorably accounts for the unequal LC-MS measurability of peptides and produces informative quantitative comparisons of a protein's concentration across treatments with objective measures of uncertainties.     

ProbCD: enrichment analysis accounting for categorization uncertainty

Background  

As in many other areas of science, systems biology makes extensive use of statistical association and significance estimates in contingency tables, a type of categorical data analysis known in this field as enrichment (also over-representation or enhancement) analysis. In spite of efforts to create probabilistic annotations, especially in the Gene Ontology context, or to deal with uncertainty in high throughput-based datasets, current enrichment methods largely ignore this probabilistic information since they are mainly based on variants of the Fisher Exact Test.     

Dimensions of global population projections: what do we know about future population trends and structures?

The total size of the world population is likely to increase from its current 7 billion to 8–10 billion by 2050. This uncertainty is because of unknown future fertility and mortality trends in different parts of the world. But the young age structure of the population and the fact that in much of Africa and Western Asia, fertility is still very high makes an increase by at least one more billion almost certain. Virtually, all the increase will happen in the developing world. For the second half of the century, population stabilization and the onset of a decline are likely. In addition to the future size of the population, its distribution by age, sex, level of educational attainment and place of residence are of specific importance for studying future food security. The paper provides a detailed discussion of different relevant dimensions in population projections and an evaluation of the methods and assumptions used in current global population projections and in particular those produced by the United Nations and by IIASA.     

Power for detecting genetic divergence: differences between statistical methods and marker loci

Information on statistical power is critical when planning investigations and evaluating empirical data, but actual power estimates are rarely presented in population genetic studies. We used computer simulations to assess and evaluate power when testing for genetic differentiation at multiple loci through combining test statistics or P values obtained by four different statistical approaches, viz. Pearson's chi-square, the log-likelihood ratio G-test, Fisher's exact test, and an F(ST)-based permutation test. Factors considered in the comparisons include the number of samples, their size, and the number and type of genetic marker loci. It is shown that power for detecting divergence may be substantial for frequently used sample sizes and sets of markers, also at quite low levels of differentiation. The choice of statistical method may be critical, though. For multi-allelic loci such as microsatellites, combining exact P values using Fisher's method is robust and generally provides a high resolving power. In contrast, for few-allele loci (e.g. allozymes and single nucleotide polymorphisms) and when making pairwise sample comparisons, this approach may yield a remarkably low power. In such situations chi-square typically represents a better alternative. The G-test without Williams's correction frequently tends to provide an unduly high proportion of false significances, and results from this test should be interpreted with great care. Our results are not confined to population genetic analyses but applicable to contingency testing in general.     

Bayesian Modeling of Age-Specific Survival in Nesting Studies Under Dirichlet Priors

There has been much work done in nest survival analysis using the maximum likelihood (ML) method. The ML method suffers from the instability of numerical calculations when models having a large number of unknown parameters are used. A Bayesian approach of model fitting is developed to estimate age-specific survival rates for nesting studies using a large class of prior distributions. The computation is done by Gibbs sampling. Some latent variables are introduced to simplify the full conditional distributions. The method is illustrated using both a real and a simulated data set. Results indicate that Bayesian analysis provides stable and accurate estimates of nest survival rates.     

Dealing with uncertainty in landscape genetic resistance models: a case of three co‐occurring marsupials

Landscape genetics lacks explicit methods for dealing with the uncertainty in landscape resistance estimation, which is particularly problematic when sample sizes of individuals are small. Unless uncertainty can be quantified, valuable but small data sets may be rendered unusable for conservation purposes. We offer a method to quantify uncertainty in landscape resistance estimates using multimodel inference as an improvement over single model‐based inference. We illustrate the approach empirically using co‐occurring, woodland‐preferring Australian marsupials within a common study area: two arboreal gliders (Petaurus breviceps, and Petaurus norfolcensis) and one ground‐dwelling antechinus (Antechinus flavipes). First, we use maximum‐likelihood and a bootstrap procedure to identify the best‐supported isolation‐by‐resistance model out of 56 models defined by linear and non‐linear resistance functions. We then quantify uncertainty in resistance estimates by examining parameter selection probabilities from the bootstrapped data. The selection probabilities provide estimates of uncertainty in the parameters that drive the relationships between landscape features and resistance. We then validate our method for quantifying uncertainty using simulated genetic and landscape data showing that for most parameter combinations it provides sensible estimates of uncertainty. We conclude that small data sets can be informative in landscape genetic analyses provided uncertainty can be explicitly quantified. Being explicit about uncertainty in landscape genetic models will make results more interpretable and useful for conservation decision‐making, where dealing with uncertainty is critical.     

Estimating Uncertainty in Ecosystem Budget Calculations

Ecosystem nutrient budgets often report values for pools and fluxes without any indication of uncertainty, which makes it difficult to evaluate the significance of findings or make comparisons across systems. We present an example, implemented in Excel, of a Monte Carlo approach to estimating error in calculating the N content of vegetation at the Hubbard Brook Experimental Forest in New Hampshire. The total N content of trees was estimated at 847 kg ha⁻¹ with an uncertainty of 8%, expressed as the standard deviation divided by the mean (the coefficient of variation). The individual sources of uncertainty were as follows: uncertainty in allometric equations (5%), uncertainty in tissue N concentrations (3%), uncertainty due to plot variability (6%, based on a sample of 15 plots of 0.05 ha), and uncertainty due to tree diameter measurement error (0.02%). In addition to allowing estimation of uncertainty in budget estimates, this approach can be used to assess which measurements should be improved to reduce uncertainty in the calculated values. This exercise was possible because the uncertainty in the parameters and equations that we used was made available by previous researchers. It is important to provide the error statistics with regression results if they are to be used in later calculations; archiving the data makes resampling analyses possible for future researchers. When conducted using a Monte Carlo framework, the analysis of uncertainty in complex calculations does not have to be difficult and should be standard practice when constructing ecosystem budgets.     

Bayesian estimation of ancestral character states on phylogenies

Biologists frequently attempt to infer the character states at ancestral nodes of a phylogeny from the distribution of traits observed in contemporary organisms. Because phylogenies are normally inferences from data, it is desirable to account for the uncertainty in estimates of the tree and its branch lengths when making inferences about ancestral states or other comparative parameters. Here we present a general Bayesian approach for testing comparative hypotheses across statistically justified samples of phylogenies, focusing on the specific issue of reconstructing ancestral states. The method uses Markov chain Monte Carlo techniques for sampling phylogenetic trees and for investigating the parameters of a statistical model of trait evolution. We describe how to combine information about the uncertainty of the phylogeny with uncertainty in the estimate of the ancestral state. Our approach does not constrain the sample of trees only to those that contain the ancestral node or nodes of interest, and we show how to reconstruct ancestral states of uncertain nodes using a most-recent-common-ancestor approach. We illustrate the methods with data on ribonuclease evolution in the Artiodactyla. Software implementing the methods (BayesMultiState) is available from the authors.     

Estimating biomarker-based HIV incidence using prevalence data in high risk groups with missing outcomes

The novel two-step serologic sensitive/less sensitive testing algorithm for detecting recent HIV seroconversion (STARHS) provides a simple and practical method to estimate HIV-1 incidence using cross-sectional HIV seroprevalence data. STARHS has been used increasingly in epidemiologic studies. However, the uncertainty of incidence estimates using this algorithm has not been well described, especially for high risk groups or when missing data is present because a fraction of sensitive enzyme immunoassay (EIA) positive specimens are not tested by the less sensitive EIA. Ad hoc methods used in practice provide incorrect confidence limits and thus may jeopardize statistical inference. In this report, we propose maximum likelihood and Bayesian methods for correctly estimating the uncertainty in incidence estimates obtained using prevalence data with a fraction missing, and extend the methods to regression settings. Using a study of injection drug users participating in a drug detoxification program in New York city as an example, we demonstrated the impact of underestimating the uncertainty in incidence estimates using ad hoc methods. Our methods can be applied to estimate the incidence of other diseases from prevalence data using similar testing algorithms when missing data is present.     

Extrapolation in Risk Assessment: Improving the Quantification of Uncertainty,and Improving Information to Reduce the Uncertainty

Risk assessments inevitably extrapolate from the known to the unknown. The resulting calculation of risk involves two fundamental kinds of uncertainty: uncertainty owing to intrinsically unpredictable (random) components of the future events, and uncertainty owing to imperfect prediction formulas (parameter uncertainty and error in model structure) that are used to predict the component that we think is predictable. Both types of uncertainty weigh heavily both in health and ecological risk assessments. Our first responsibility in conducting risk assessments is to ensure that the reported risks correctly reflect our actual level of uncertainty (of both types). The statistical methods that lend themselves to correct quantification of the uncertainty are also effective for combining different sources of information. One way to reduce uncertainty is to use all the available data. To further sharpen future risk assessments, it is useful to partition the uncertainty between the random component and the component due to parameter uncertainty, so that we can quantify the expected reduction in uncertainty that can be achieved by investing in a given amount of future data. An example is developed to illustrate the potential for use of comparative data, from toxicity testing on other species or other chemicals, to improve the estimates of low-effect concentration in a particular case with sparse case-specific data.     

Genetic analysis of the predisposition to uterine myoma. Prevalence and morbidity

Prevalence of uterine myoma (MU) was estimated in several Moscow districts. The overall average estimate of the MU prevalence is 2.45% among women of all groups. The prevalence MU estimates increase with the age, its maximum value reaching 8.31% at the age of 50 years. The morbidity risk estimates increased with the age as well, the maximum value being 2.98% at the age of 40-44 years. The value of "cumulative" morbidity risks, i. e. the probability to be affected, is 9.74% for a population living long enough, this value being based on the age-specific estimates of morbidity risks. Taking into consideration the autopsy data, indicating that frequency of MU, including small myomatous nodes, is 20%, the conclusion is made that MU is manifested by clinically expressed disturbances (urging a woman to address to a doctor) in 50% of cases only. Epidemiological data obtained are to be used later for genetic analysis of familial data on MU.