Hidden population size estimation and diagnostics using two respondent-driven samples with applications in Armenia

Estimating the size of hidden populations is essential to understand the magnitude of social and healthcare needs, risk behaviors, and disease burden. However, due to the hidden nature of these populations, they are difficult to survey, and there are no gold standard size estimation methods. Many different methods and variations exist, and diagnostic tools are needed to help researchers assess method-specific assumptions as well as compare between methods. Further, because many necessary mathematical assumptions are unrealistic for real survey implementation, assessment of how robust methods are to deviations from the stated assumptions is essential. We describe diagnostics and assess the performance of a new population size estimation method, capture–recapture with successive sampling population size estimation (CR-SS-PSE), which we apply to data from 3 years of studies from three cities and three hidden populations in Armenia. CR-SS-PSE relies on data from two sequential respondent-driven sampling surveys and extends the successive sampling population size estimation (SS-PSE) framework by using the number of individuals in the overlap between the two surveys and a model for the successive sampling process to estimate population size. We demonstrate that CR-SS-PSE is more robust to violations of successive sampling assumptions than SS-PSE. Further, we compare the CR-SS-PSE estimates to population size estimations using other common methods, including unique object and service multipliers, wisdom of the crowd, and two-source capture–recapture to illustrate volatility across estimation methods.     

Residual-based diagnostics for structural equation models

Summary .  Classical diagnostics for structural equation models are based on aggregate forms of the data and are ill suited for checking distributional or linearity assumptions. We extend recently developed goodness-of-fit tests for correlated data based on subject-specific residuals to structural equation models with latent variables. The proposed tests lend themselves to graphical displays and are designed to detect misspecified distributional or linearity assumptions. To complement graphical displays, test statistics are defined; the null distributions of the test statistics are approximated using computationally efficient simulation techniques. The properties of the proposed tests are examined via simulation studies. We illustrate the methods using data from a study of in utero lead exposure.     

Bayesian case influence diagnostics for survival models

We propose Bayesian case influence diagnostics for complex survival models. We develop case deletion influence diagnostics for both the joint and marginal posterior distributions based on the Kullback-Leibler divergence (K-L divergence). We present a simplified expression for computing the K-L divergence between the posterior with the full data and the posterior based on single case deletion, as well as investigate its relationships to the conditional predictive ordinate. All the computations for the proposed diagnostic measures can be easily done using Markov chain Monte Carlo samples from the full data posterior distribution. We consider the Cox model with a gamma process prior on the cumulative baseline hazard. We also present a theoretical relationship between our case-deletion diagnostics and diagnostics based on Cox's partial likelihood. A simulated data example and two real data examples are given to demonstrate the methodology.     

Deletion diagnostics for alternating logistic regressions

Deletion diagnostics are introduced for the regression analysis of clustered binary outcomes estimated with alternating logistic regressions, an implementation of generalized estimating equations (GEE) that estimates regression coefficients in a marginal mean model and in a model for the intracluster association given by the log odds ratio. The diagnostics are developed within an estimating equations framework that recasts the estimating functions for association parameters based upon conditional residuals into equivalent functions based upon marginal residuals. Extensions of earlier work on GEE diagnostics follow directly, including computational formulae for one‐step deletion diagnostics that measure the influence of a cluster of observations on the estimated regression parameters and on the overall marginal mean or association model fit. The diagnostic formulae are evaluated with simulations studies and with an application concerning an assessment of factors associated with health maintenance visits in primary care medical practices. The application and the simulations demonstrate that the proposed cluster‐deletion diagnostics for alternating logistic regressions are good approximations of their exact fully iterated counterparts.     

Linear and nonlinear mixed-effects models for censored HIV viral loads using normal/independent distributions

HIV RNA viral load measures are often subjected to some upper and lower detection limits depending on the quantification assays. Hence, the responses are either left or right censored. Linear (and nonlinear) mixed-effects models (with modifications to accommodate censoring) are routinely used to analyze this type of data and are based on normality assumptions for the random terms. However, those analyses might not provide robust inference when the normality assumptions are questionable. In this article, we develop a Bayesian framework for censored linear (and nonlinear) models replacing the Gaussian assumptions for the random terms with normal/independent (NI) distributions. The NI is an attractive class of symmetric heavy-tailed densities that includes the normal, Student's-t, slash, and the contaminated normal distributions as special cases. The marginal likelihood is tractable (using approximations for nonlinear models) and can be used to develop Bayesian case-deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated with two HIV AIDS studies on viral loads that were initially analyzed using normal (censored) mixed-effects models, as well as simulations.     

Uncertainties in the application of the species area relationship for characterisation factors of land occupation in life cycle assessment

Purpose  

Uncertainties in land use damage modeling are recognized, but hardly quantified in life cycle assessment (LCA). The objective of this study is to analyze the influence of various key assumptions and uncertainties within the development of characterisation factors (CFs) for land use in LCA. We assessed the influence on land use CFs of (1) parameter uncertainty and (2) the choice for a constant or land use-specific species accumulation factor z and including or excluding regional effects.     

Robust two-stage estimation in hierarchical nonlinear models

Hierarchical models encompass two sources of variation, namely within and among individuals in the population; thus, it is important to identify outliers that may arise at each sampling level. A two-stage approach to analyzing nonlinear repeated measurements naturally allows parametric modeling of the respective variance structure for the intraindividual random errors and interindividual random effects. We propose a robust two-stage procedure based on Huber's (1981, Robust Statistics) theory of M-estimation to accommodate separately aberrant responses within an experimental unit and subjects deviating from the study population when the usual assumptions of normality are violated. A toxicology study of chronic ozone exposure in rats illustrates the impact of outliers on the population inference and hence the advantage of adopting the robust methodology. The robust weights generated by the two-stage M-estimation process also serve as diagnostics for gauging the relative influence of outliers at each level of the hierarchical model. A practical appeal of our proposal is the computational simplicity since the estimation algorithm may be implemented using standard statistical software with a nonlinear least squares routine and iterative capability.     

Methylation microarray-based detection of clinical copy-number aberrations in CLL benchmarked to standard FISH analysis

Copy-number aberrations (CNAs) are assessed using FISH analysis in diagnostics of chronic lymphocytic leukemia (CLL), but CNAs can also be extrapolated from Illumina BeadChips developed for genome-wide methylation microarray screening. Increasing numbers of microarray data-sets are available from diagnostic samples, making it useful to assess the potential in CNA diagnostics.We benchmarked the limitations of CNA testing from two Illumina BeadChips (EPIC and 450k) and using two common packages for analysis (conumee and ChAMP) to FISH-based assessment of 11q, 13q, and 17p deletions in 202 CLL samples.Overall, the two packages predicted CNAs with similar accuracy regardless of the microarray type, but lower than FISH-based assessment. We showed that the bioinformatics analysis needs to be adjusted to the specific CNA, as no general settings were identified. Altogether, we were able to predict CNAs using methylation microarray data, however, with limited accuracy, making FISH-based assessment of deletions the superior diagnostic choice.     

Landscape analysis of NTD diagnostics and considerations on the development of a strategy for regulatory pathways

Access to quality-assured, accurate diagnostics is critical to ensure that the 2021–2030 neglected tropical disease (NTD) road map targets can be achieved. Currently, however, there is limited regulatory oversight and few quality assurance mechanisms for NTD diagnostic tools. In attempting to address such challenges and the changing environment in regulatory requirements for diagnostics, a landscape analysis was conducted, to better understand the availability of NTD diagnostics and inform future regulatory frameworks. The list of commercially available diagnostics was compiled from various sources, including WHO guidance, national guidelines for case detection and management, diagnostic target product profiles and the published literature. The inventory was analyzed according to diagnostic type, intended use, regulatory status, and risk classification. To estimate the global need and size of the market for each type of diagnostic, annual procurement data were collected from WHO, procurement agencies, NGOs and international organizations, where available and global disease prevalence. Expert interviews were also conducted to ensure a better understanding of how diagnostics are procured and used. Of 125 diagnostic tools included in this analysis, rapid diagnostic tools accounted for 33% of diagnostics used for NTDs and very few diagnostics had been subjected to regulatory assessment. The number of tests needed for each disease was less than 1 million units per annum, except in the case of two diseases, suggesting limited commercial value. Despite the nature of the market, and presumed insufficient return on commercial investment, acceptable levels of assurance on performance, quality and safety of diagnostics are still required. Priority actions include setting up an agile, interim, stepwise risk assessment mechanism, in particular for diagnostics of lower risk, in order to support national NTD programmes and their partners with the selection and procurement of the diagnostics needed to control, eliminate and eradicate NTDs.     

海洋甲壳类生物资源评估方法研究进展

目前甲壳类生物资源,如蟹、龙虾、对虾及南极磷虾等组成了全球庞大且极具商业价值的渔业.虽然这些渔业的重要性逐步提升,规模也在扩大,但相对于其他渔业,适合且有效的海洋甲壳类资源评估与管理方法仍需进一步发展.本文回顾和评价了各种用于甲壳类生物资源评估的方法与模型,对剩余产量模型、时滞差分模型、损耗模型及体长结构模型等应用到甲壳类生物资源评估的4种主要模型进行了归纳和分析,简要地总结了这几种模型在应用时所需要的假设前提以及对所需数据的要求等,并对比分析了几种模型的优、缺点.此外,本文还列举了关于资源评估方法中模型的假设要求.参数的估算方法、不确定性来源及一般性解决办法等.最后,本文对甲壳类资源评估方法的发展方向和前景进行了展望.     

Local influence diagnostics for hierarchical count data models with overdispersion and excess zeros

We consider models for hierarchical count data, subject to overdispersion and/or excess zeros. Molenberghs et al. ( 2007 ) and Molenberghs et al. ( 2010 ) extend the Poisson‐normal generalized linear‐mixed model by including gamma random effects to accommodate overdispersion. Excess zeros are handled using either a zero‐inflation or a hurdle component. These models were studied by Kassahun et al. ( 2014 ). While flexible, they are quite elaborate in parametric specification and therefore model assessment is imperative. We derive local influence measures to detect and examine influential subjects, that is subjects who have undue influence on either the fit of the model as a whole, or on specific important sub‐vectors of the parameter vector. The latter include the fixed effects for the Poisson and for the excess‐zeros components, the variance components for the normal random effects, and the parameters describing gamma random effects, included to accommodate overdispersion. Interpretable influence components are derived. The method is applied to data from a longitudinal clinical trial involving patients with epileptic seizures. Even though the data were extensively analyzed in earlier work, the insight gained from the proposed diagnostics, statistically and clinically, is considerable. Possibly, a small but important subgroup of patients has been identified.     

Skew‐normal/independent linear mixed models for censored responses with applications to HIV viral loads

Often in biomedical studies, the routine use of linear mixed‐effects models (based on Gaussian assumptions) can be questionable when the longitudinal responses are skewed in nature. Skew‐normal/elliptical models are widely used in those situations. Often, those skewed responses might also be subjected to some upper and lower quantification limits (QLs; viz., longitudinal viral‐load measures in HIV studies), beyond which they are not measurable. In this paper, we develop a Bayesian analysis of censored linear mixed models replacing the Gaussian assumptions with skew‐normal/independent (SNI) distributions. The SNI is an attractive class of asymmetric heavy‐tailed distributions that includes the skew‐normal, skew‐t, skew‐slash, and skew‐contaminated normal distributions as special cases. The proposed model provides flexibility in capturing the effects of skewness and heavy tail for responses that are either left‐ or right‐censored. For our analysis, we adopt a Bayesian framework and develop a Markov chain Monte Carlo algorithm to carry out the posterior analyses. The marginal likelihood is tractable, and utilized to compute not only some Bayesian model selection measures but also case‐deletion influence diagnostics based on the Kullback–Leibler divergence. The newly developed procedures are illustrated with a simulation study as well as an HIV case study involving analysis of longitudinal viral loads.     

Predictive influence in the accelerated failure time model

We develop case deletion diagnostics for prediction of future observations in the accelerated failure time model. We view prediction to be an important inferential goal in a survival analysis and thus it is important to identify whether particular observations may be influencing the quality of predictions. We use the Kullback-Leibler divergence as a measure of the discrepancy between the estimated probability distributions for the full and the case-deleted samples. In particular, we focus on the effect of case deletion on estimated survival curves but where we regard the survival curve estimate as a vehicle for prediction. We also develop a diagnostic for assessing the effect of case deletion on inferences for the median time to failure. The estimated median can be used with both predictive and estimative purposes in mind. We also discuss the relationship between our suggested measures and the corresponding Cook distance measure, which was designed with the goal of assessing estimative influence. Several applications of the proposed diagnostics are presented.     

Bayesian influence measures for joint models for longitudinal and survival data

Summary This article develops a variety of influence measures for carrying out perturbation (or sensitivity) analysis to joint models of longitudinal and survival data (JMLS) in Bayesian analysis. A perturbation model is introduced to characterize individual and global perturbations to the three components of a Bayesian model, including the data points, the prior distribution, and the sampling distribution. Local influence measures are proposed to quantify the degree of these perturbations to the JMLS. The proposed methods allow the detection of outliers or influential observations and the assessment of the sensitivity of inferences to various unverifiable assumptions on the Bayesian analysis of JMLS. Simulation studies and a real data set are used to highlight the broad spectrum of applications for our Bayesian influence methods.     

Mixture models for estimating the size of a closed population when capture rates vary among individuals

We develop a parameterization of the beta-binomial mixture that provides sensible inferences about the size of a closed population when probabilities of capture or detection vary among individuals. Three classes of mixture models (beta-binomial, logistic-normal, and latent-class) are fitted to recaptures of snowshoe hares for estimating abundance and to counts of bird species for estimating species richness. In both sets of data, rates of detection appear to vary more among individuals (animals or species) than among sampling occasions or locations. The estimates of population size and species richness are sensitive to model-specific assumptions about the latent distribution of individual rates of detection. We demonstrate using simulation experiments that conventional diagnostics for assessing model adequacy, such as deviance, cannot be relied on for selecting classes of mixture models that produce valid inferences about population size. Prior knowledge about sources of individual heterogeneity in detection rates, if available, should be used to help select among classes of mixture models that are to be used for inference.     

Biological methods of ecological diagnostics as an effective qualitative assessment of environmental pollution

The existing methods for environment quality assessment do not meet current requirements because they are based on the comparison of quantitative pollution indices with the maximum allowable concentration (MAC), which significantly reduces the reliability of results. Biological methods of ecological diagnostics become priority-oriented since they provide a qualitative assessment of the environment and are based on the study of the response of living organisms to pollution.     

Properties of Markov Chain Monte Carlo Performance across Many Empirical Alignments

Nearly all current Bayesian phylogenetic applications rely on Markov chain Monte Carlo (MCMC) methods to approximate the posterior distribution for trees and other parameters of the model. These approximations are only reliable if Markov chains adequately converge and sample from the joint posterior distribution. Although several studies of phylogenetic MCMC convergence exist, these have focused on simulated data sets or select empirical examples. Therefore, much that is considered common knowledge about MCMC in empirical systems derives from a relatively small family of analyses under ideal conditions. To address this, we present an overview of commonly applied phylogenetic MCMC diagnostics and an assessment of patterns of these diagnostics across more than 18,000 empirical analyses. Many analyses appeared to perform well and failures in convergence were most likely to be detected using the average standard deviation of split frequencies, a diagnostic that compares topologies among independent chains. Different diagnostics yielded different information about failed convergence, demonstrating that multiple diagnostics must be employed to reliably detect problems. The number of taxa and average branch lengths in analyses have clear impacts on MCMC performance, with more taxa and shorter branches leading to more difficult convergence. We show that the usage of models that include both Γ-distributed among-site rate variation and a proportion of invariable sites is not broadly problematic for MCMC convergence but is also unnecessary. Changes to heating and the usage of model-averaged substitution models can both offer improved convergence in some cases, but neither are a panacea.     

Metagenomic abundance estimation and diagnostic testing on species level

One goal of sequencing-based metagenomic community analysis is the quantitative taxonomic assessment of microbial community compositions. In particular, relative quantification of taxons is of high relevance for metagenomic diagnostics or microbial community comparison. However, the majority of existing approaches quantify at low resolution (e.g. at phylum level), rely on the existence of special genes (e.g. 16S), or have severe problems discerning species with highly similar genome sequences. Yet, problems as metagenomic diagnostics require accurate quantification on species level. We developed Genome Abundance Similarity Correction (GASiC), a method to estimate true genome abundances via read alignment by considering reference genome similarities in a non-negative LASSO approach. We demonstrate GASiC’s superior performance over existing methods on simulated benchmark data as well as on real data. In addition, we present applications to datasets of both bacterial DNA and viral RNA source. We further discuss our approach as an alternative to PCR-based DNA quantification.     

Local Influence for Generalized Linear Models with Missing Covariates

Summary In the analysis of missing data, sensitivity analyses are commonly used to check the sensitivity of the parameters of interest with respect to the missing data mechanism and other distributional and modeling assumptions. In this article, we formally develop a general local influence method to carry out sensitivity analyses of minor perturbations to generalized linear models in the presence of missing covariate data. We examine two types of perturbation schemes (the single‐case and global perturbation schemes) for perturbing various assumptions in this setting. We show that the metric tensor of a perturbation manifold provides useful information for selecting an appropriate perturbation. We also develop several local influence measures to identify influential points and test model misspecification. Simulation studies are conducted to evaluate our methods, and real datasets are analyzed to illustrate the use of our local influence measures.     

Hardy-Weinberg equilibrium diagnostics

We propose two diagnostics for the statistical assessment of Hardy-Weinberg equilibrium. One diagnostic is the posterior probability of the complement of the smallest highest posterior density credible region that includes points in the parameter space consistent with the hypothesis of equilibrium. The null hypothesis of equilibrium is to be rejected if this probability is less than a pre-selected critical level. The second diagnostic is the proportion of the parameter space occupied by the highest posterior density credible region associated with the critical level. These Bayesian diagnostics can be interpreted as analogues of the classical types I and II error probabilities. They are broadly applicable: they can be computed for any hypothesis test, using samples of any size generated according to any distribution.