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Causal variance decompositions for a given disease-specific quality indicator can be used to quantify differences in performance between hospitals or health care providers. While variance decompositions can demonstrate variation in quality of care, causal mediation analysis can be used to study care pathways leading to the differences in performance between the institutions. This raises the question of whether the two approaches can be combined to decompose between-hospital variation in an outcome type indicator to that mediated through a given process (indirect effect) and remaining variation due to all other pathways (direct effect). For this purpose, we derive a causal mediation analysis decomposition of between-hospital variance, discuss its interpretation, and propose an estimation approach based on generalized linear mixed models for the outcome and the mediator. We study the performance of the estimators in a simulation study and demonstrate its use in administrative data on kidney cancer care in Ontario.

Plant breeding, like other fields in applied quantitative genetics, has embraced large-scale phenotype data as a way to rapidly and accurately create the next generations of crops. High-throughput phenotyping technologies and large-scale multi-environment breeding trials generate an unprecedented scale of data for breeders to use to make selections and crosses in breeding programs. However, the statistical foundation of multi-trait breeding is based on the multivariate linear mixed effect model, a tool notorious for its fragility when applied to more than a handful of traits. We present MegaLMM, a statistical framework and associated software package that facilitates flexible mixed model analyses on a virtually unlimited number of traits. Using three examples with real plant data, we show that MegaLMM can efficiently model the genetic architecture of thousands of traits at once while significantly improving genetic value prediction accuracy.

Obesity is considered to be one of the primary health risks in modern industrialized societies. Estimating the evolution of its prevalence over time is an essential element of public health reporting. This requires the application of suitable statistical methods on epidemiologic data with substantial local detail. Generalized linear-mixed models with medical treatment records as covariates mark a powerful combination for this purpose. However, the task is methodologically challenging. Disease frequencies are subject to both regional and temporal heterogeneity. Medical treatment records often show strong internal correlation due to diagnosis-related grouping. This frequently causes excessive variance in model parameter estimation due to rank-deficiency problems. Further, generalized linear-mixed models are often estimated via approximate inference methods as their likelihood functions do not have closed forms. These problems combined lead to unacceptable uncertainty in prevalence estimates over time. We propose an l2-penalized temporal logit-mixed model to solve these issues. We derive empirical best predictors and present a parametric bootstrap to estimate their mean-squared errors. A novel penalized maximum approximate likelihood algorithm for model parameter estimation is stated. With this new methodology, the regional obesity prevalence in Germany from 2009 to 2012 is estimated. We find that the national prevalence ranges between 15 and 16%, with significant regional clustering in eastern Germany.

In this paper, we introduce a new ridge-type estimator/predictor called the weighted mixed ridge estimator/predictor (WMRE/P) by unifying the sample and prior information in a linear mixed model wi...

Summary Collecting information on multiple longitudinal outcomes is increasingly common in many clinical settings. In many cases, it is desirable to model these outcomes jointly. However, in large data sets, with many outcomes, computational burden often prevents the simultaneous modeling of multiple outcomes within a single model. We develop a mean field variational Bayes algorithm, to jointly model multiple Gaussian, Poisson, or binary longitudinal markers within a multivariate generalized linear mixed model. Through simulation studies and clinical applications (in the fields of sight threatening diabetic retinopathy and primary biliary cirrhosis), we demonstrate substantial computational savings of our approximate approach when compared to a standard Markov Chain Monte Carlo, while maintaining good levels of accuracy of model parameters.

Existing studies on spatial linear mixed models typically assume a normal distribution for the random error components. However, such an assumption may not be appropriate in many applications. This...

When designing repeated measures studies, both the amount and the pattern of missing outcome data can affect power. The chance that an observation is missing may vary across measurements, and missingness may be correlated across measurements. For example, in a physiotherapy study of patients with Parkinson’s disease, increasing intermittent dropout over time yielded missing measurements of physical function. In this example, we assume data are missing completely at random, since the chance that a data point was missing appears to be unrelated to either outcomes or covariates. For data missing completely at random, we propose noncentral F power approximations for the Wald test for balanced linear mixed models with Gaussian responses. The power approximations are based on moments of missing data summary statistics. The moments were derived assuming a conditional linear missingness process. The approach provides approximate power for both complete-case analyses, which include independent sampling units where all measurements are present, and observed-case analyses, which include all independent sampling units with at least one measurement. Monte Carlo simulations demonstrate the accuracy of the method in small samples. We illustrate the utility of the method by computing power for proposed replications of the Parkinson’s study.

Key message Genomic prediction with special weight of major genes is a valuable tool to populate bio-digital resource centers. Abstract Phenotypic information of crop genetic resources is a prerequisite for an informed selection that aims to broaden the genetic base of the elite breeding pools. We investigated the potential of genomic prediction based on historical screening data of plant responses against the Barley yellow mosaic viruses for populating the bio-digital resource center of barley. Our study includes dense marker data for 3838 accessions of winter barley, and historical screening data of 1751 accessions for Barley yellow mosaic virus (BaYMV) and of 1771 accessions for Barley mild mosaic virus (BaMMV). Linear mixed models were fitted by considering combinations for the effects of genotypes, years, and locations. The best linear unbiased estimations displayed a broad spectrum of plant responses against BaYMV and BaMMV. Prediction abilities, computed as correlations between predictions and observed phenotypes of accessions, were low for the marker-assisted selection approach amounting to 0.42. In contrast, prediction abilities of genomic best linear unbiased predictions were high, with values of 0.62 for BaYMV and 0.64 for BaMMV. Prediction abilities of genomic prediction were improved by up to ~ 5% using W-BLUP, in which more weight is given to markers with significant major effects found by association mapping. Our results outline the utility of historical screening data and W-BLUP model to predict the performance of the non-phenotyped individuals in genebank collections. The presented strategy can be considered as part of the different approaches used in genebank genomics to valorize genetic resources for their usage in disease resistance breeding and research.

This study aimed to identify the spatial patterns of lower respiratory tract infections (LRIs) and their association with fine particulate matter (PM2.5). The disability-adjusted life year (DALY) database was used to represent the burden each country experiences as a result of LRIs. PM2.5 data obtained from the Atmosphere Composition Analysis Group was assessed as the source for main exposure. Global Moran’s I and Getis-Ord Gi* were applied to identify the spatial patterns and for hotspots analysis of LRIs. A generalized linear mixed model was coupled with a sensitivity test after controlling for covariates to estimate the association between LRIs and PM2.5. Subgroup analyses were performed to determine whether LRIs and PM2.5 are correlated for various ages and geographic regions. A significant spatial auto-correlated pattern was identified for global LRIs with Moran’s Index 0.79, and the hotspots of LRIs were clustered in 35 African and 4 Eastern Mediterranean countries. A consistent significant positive association between LRIs and PM2.5 with a coefficient of 0.21 (95% CI 0.06–0.36) was identified. Furthermore, subgroup analysis revealed a significant effect of PM2.5 on LRI for children (0–14 years) and the elderly (≥ 70 years), and this effect was confirmed to be significant in all regions except for those comprised of Eastern Mediterranean countries.

Finite mixture models are a widely known method for modelling data that arise from a heterogeneous population. Within the family of mixtures of regression models, mixtures of linear mixed models have also been applied in different areas since, besides taking into consideration the heterogeneity in the population, they also allow to take into account the correlation between observations from the same individual. One of the main issues in mixture models concerns the estimation of the parameters. Maximum likelihood estimation is one of the most used methods in the estimation of the parameters for mixture models. However, the maximization of the log-likelihood function in mixture models is complex, producing in many cases infinite solutions whereby the maximum likelihood estimator may not exist, at least globally. For this reason, it is common to resort to iterative methods, in particular to the Expectation-Maximization (EM) algorithm. However, the slow convergence and the selection of initial values are two of biggest issues of the EM algorithm, the reason why some modified versions of this algorithm have been developed over the years. In this article we compare the performance of the EM, Classification EM (CEM) and Stochastic EM (SEM) algorithms in the estimation of the parameters for mixtures of linear mixed models. In order to evaluate their performance, we carry out a simulation study and a real data application. The results show that the CEM algorithm is the least computationally demanding algorithm, although the three algorithms provide similar maximum likelihood estimates for the parameters., The research of L. Novais was financed by FCT - Fundacao para a Ciencia e a Tecnologia, through the PhD scholarship with reference SFRH/BD/139121/2018.

Hidden Markov and semi-Markov models (H(S)MMs) constitute useful tools for modeling observations subject to certain dependency structures. The hidden states render these models very flexible and allow them to capture many different types of latent patterns and dynamics present in the data. This has led to the increased popularity of these models, which have been applied to a variety of problems in various domains and settings, including longitudinal data. In many longitudinal studies, the response variable is categorical or count-type. Generalized linear mixed models (GLMMs) can be used to analyze a wide range of variables, including categorical and count. The present study proposes a model that combines HSMMs with GLMMs, leading to generalized linear mixed hidden semi-Markov models (GLM-HSMMs). These models can account for time-varying unobserved heterogeneity and handle different response types. Parameter estimation is achieved using a Monte Carlo Newton-Raphson (MCNR)-like algorithm. In our proposed model, the distribution of the random effects depends on hidden states. We illustrate the applicability of GLM-HSMMs with an example in the field of occupational health, where the response variable consists of count values. Furthermore, we assess the performance of our MCNR-like algorithm through a simulation study.

A wide array of technologies are available for gaining insight into the movement of wild aquatic animals. Although acoustic telemetry can lack the fine‐scale spatial resolution of some satellite tracking technologies, the substantially longer battery life can yield important long‐term data on individual behavior and movement for low per‐unit cost. Typically, however, receiver arrays are designed to maximize spatial coverage at the cost of positional accuracy leading to potentially longer detection gaps as individuals move out of range between monitored locations. This is particularly true when these technologies are deployed to monitor species in hard‐to‐access locations.Here, we develop a novel approach to analyzing acoustic telemetry data, using the timing and duration of gaps between animal detections to infer different behaviors. Using the durations between detections at the same and different receiver locations (i.e., detection gaps), we classify behaviors into “restricted” or potential wider “out‐of‐range” movements synonymous with longer distance dispersal. We apply this method to investigate spatial and temporal segregation of inferred movement patterns in two sympatric species of reef shark within a large, remote, marine protected area (MPA). Response variables were generated using network analysis, and drivers of these movements were identified using generalized linear mixed models and multimodel inference.Species, diel period, and season were significant predictors of “out‐of‐range” movements. Silvertip sharks were overall more likely to undertake “out‐of‐range” movements, compared with gray reef sharks, indicating spatial segregation, and corroborating previous stable isotope work between these two species. High individual variability in “out‐of‐range” movements in both species was also identified.We present a novel gap analysis of telemetry data to help infer differential movement and space use patterns where acoustic coverage is imperfect and other tracking methods are impractical at scale. In remote locations, inference may be the best available tool and this approach shows that acoustic telemetry gap analysis can be used for comparative studies in fish ecology, or combined with other research techniques to better understand functional mechanisms driving behavior., Financial and logistical constraints may lead to imperfect in‐field acoustic receiver array designs which can result in acoustic telemetry data with long detection gaps. We present a novel gap analysis of telemetry data to help infer differential movement and space use patterns where acoustic coverage is imperfect and other tracking methods impractical

Multi-regional clinical trials have a hierarchical data structure because several regions form a patient population and individual patients are nested within their own regions. Data are obtained fr...

SummaryTo elucidate the molecular mechanisms underlying genetic variants identified from genome-wide association studies (GWAS) for a variety of phenotypic traits encompassing binary, continuous, count, and survival outcomes, we propose a novel and flexible method to test for mediation that can simultaneously accommodate multiple genetic variants and different types of outcome variables. Specifically, we employ the intersection-union test approach combined with likelihood ratio test to detect mediation effect of multiple genetic variants via some mediator (for example, the expression of a neighboring gene) on outcome. We fit high-dimensional generalized linear mixed models under the mediation framework, separately under the null and alternative hypothesis. We leverage Laplace approximation to compute the marginal likelihood of outcome and use coordinate descent algorithm to estimate corresponding parameters. Our extensive simulations demonstrate the validity of our proposed method and substantial, up to 97%, power gains over alternative methods. Applications to real data for the study of Chlamydia trachomatis infection further showcase advantages of our method. We believe our proposed method will be of value and general interest in this post-GWAS era to disentangle the potential causal mechanism from DNA to phenotype for new drug discovery and personalized medicine.

The connection between regularization and min–max robustification in the presence of unobservable covariate measurement errors in linear mixed models is addressed. We prove that regularized model parameter estimation is equivalent to robust loss minimization under a min–max approach. On the example of the LASSO, Ridge regression, and the Elastic Net, we derive uncertainty sets that characterize the feasible noise that can be added to a given estimation problem. These sets allow us to determine measurement error bounds without distribution assumptions. A conservative Jackknife estimator of the mean squared error in this setting is proposed. We further derive conditions under which min-max robust estimation of model parameters is consistent. The theoretical findings are supported by a Monte Carlo simulation study under multiple measurement error scenarios.

We study robust designs for generalized linear mixed models (GLMMs) with protections against possible departures from underlying model assumptions. Among various types of model departures, an imprecision in the assumed linear predictor or the link function has a great impact on predicting the conditional mean response function in a GLMM. We develop methods for constructing adaptive sequential designs when the fitted mean response or the link function is possibly of an incorrect parametric form. We adopt the maximum likelihood method for estimating the parameters in GLMMs and investigate both I-optimal and D-optimal design criteria for the construction of robust sequential designs. To study the empirical properties of these sequential designs, we ran a series of simulations using both logistic and Poisson mixed models. As indicated in the simulation results, the I-optimal design generally outperforms the D-optimal design for all scenarios considered. Both designs are more efficient than the conventionally used uniform design and the classical D-optimal design obtained under the assumption that the fitted models are correctly specified. The proposed designs are also illustrated in an example using actual data from a dose–response experiment.

In this paper, we introduce stochastic-restricted Liu predictors which will be defined by combining in a special way the two approaches followed in obtaining the mixed predictors and the Liu predictors in the linear mixed models. Superiorities of the linear combination of the new predictor to the Liu and mixed predictors are done in the sense of mean square error matrix criterion. Finally, numerical examples and a simulation study are done to illustrate the findings. In numerical examples, we took some arbitrary observations from the data as the prior information since we did not have historical data or additional information about the data sets. The results show that this case does the new estimator gain efficiency over the constituent estimators and provide accurate estimation and prediction of the data.

Linear mixed models (LMMs) are popular to analyze repeated measurements with a Gaussian response. For longitudinal studies, the LMMs consist of a fixed part expressing the effect of covariates on the mean evolution in time and a random part expressing the variation of the individual curves around the mean curve. Selecting the appropriate fixed and random effect parts is an important modeling exercise. In a Bayesian framework, there is little agreement on the appropriate selection criteria. This paper compares the performance of the deviance information criterion (DIC), the pseudo-Bayes factor and the widely applicable information criterion (WAIC) in LMMs, with an extension to LMMs with skew-normal distributions. We focus on the comparison between the conditional criteria (given random effects) versus the marginal criteria (averaged over random effects). In spite of theoretical arguments, there is not much enthusiasm among applied statisticians to make use of the marginal criteria. We show in an extensive simulation study that the three marginal criteria are superior in choosing the appropriate longitudinal model. In addition, the marginal criteria selected most appropriate model for growth curves of Nigerian chicken. A self-written R function can be combined with standard Bayesian software packages to obtain the marginal selection criteria.

Count outcomes are commonly encountered in health sector data. The occurrence of count outcomes that exhibit many zeros has necessitated the extension of the ubiquitous Poisson regression model to accommodate the zero inflation and overdispersion as a result of the extra dispersion. We explored different extensions of the Poisson model including mixed models within the generalized linear mixed model framework to account for the repeated measurement of outcomes. These models are applied to maternal mortality data from fifty-six health facilities in four regions of Ghana. The objective is to identify factors associated with maternal mortality. The best-fitting model, the zero-inflated Poisson generalized linear mixed model, revealed that maternal mortality in hospital facilities is influenced by the number of referrals (into and out) of the hospital facility, number of antenatal visits exceeding four, number of midwives, and number of medical doctors at the facility. To be able to achieve targeted results in reducing maternal mortality and achieve the Sustainable Development Goal 3, the government, together with the ministry of health, should provide adequate maternal health services, especially at the district and community level. Additionally, there is a need for increased investment in Community Health Planning Services and related healthcare infrastructure and systems within the context of the Ouagadougou Declaration, that is, improve the training of skilled birth workers (midwives and doctors) and employ them at clinics to deal with labour complications without referring them to major hospitals. Furthermore, a well-structured awareness campaign is needed with importance given to avoiding adolescent pregnancy and improving antenatal care attendance to, at least, four, the gold standard, before delivery. Also, we recommend quality assessment form an essential part of all services that are directed towards improving maternal health and that more emphasis is needed to be given on research with multiple allied partners.

Background The blue shark Prionace glauca is a highly migratory species with a circumglobal distribution. Mean movement rate, defined by the horizontal tracking distance between two data points over the duration of time, is commonly used to understand the horizontal displacement of highly migratory species across a wide range. However, the estimation of mean movement rates for blue sharks has never been conducted using a statistical model. We therefore investigated the mean movement rates using a generalized linear mixed model with data from satellite tags to estimate the range of mean movement rates for 10 blue sharks in the northwestern Pacific Ocean and to reveal the interaction of mean movement rate with several factors. Results (1) Estimations of mean movement rates for the 10 blue sharks were significantly influenced by behavioral differences among individuals; (2) uncertainty in the estimation (i.e., predictive and confidence intervals) of mean movement rates for these blue sharks was larger over shorter time periods, and (3) the predictive intervals of mean movement rates for the sharks ranged widely from 0.33 to 5.02 km/h. Conclusion Blue sharks are considered to opportunistically change their mean movement rates regardless of differences in sex, movement direction, or season.

Premise With digitization and data sharing initiatives underway over the last 15 years, an important need has been prioritizing specimens to digitize. Because duplicate specimens are shared among herbaria in exchange and gift programs, we investigated the extent to which unique biogeographic data are held in small herbaria vs. these data being redundant with those held by larger institutions. We evaluated the unique specimen contributions that small herbaria make to biogeographic understanding at county, locality, and temporal scales. Methods We sampled herbarium specimens of 40 plant taxa from each of eight states of the United States of America in four broad status categories: extremely rare, very rare, common native, and introduced. We gathered geographic information from specimens held by large (≥100,000 specimens) and small (

Whether or not biogeographic rules dealing with spatial patterns of animal body sizes are valid for ectotherms is controversial. As the ectotherms grow all their lives, we explored the role of age and annual growth rate in body size variation in Phrynocephalus przewalskii in northern China. Morphological data were collected from 11 populations across a broad geographic gradient. Correlations between age, sex, climatic factors, and body size were analyzed using generalized linear model (GLM) and generalized linear mixed model (GLMM). GLM analysis indicated that the general body size of both sexes and the appendage size of females increased significantly with increasing temperature; however, the coefficient of determination was very small. GLMM analysis indicated that body size only correlated with age, whereas appendage size was affected by age, temperature, rainfall, and sunshine. Annual growth rates were positively correlated with temperature. We concluded that body size variation was mainly caused by age structure and plasticity of the growth rate in P. przewalskii and did not follow Bergmann's rule; however, females followed Allen's rule. Future studies to investigate the effect of energy restriction are needed to further understand the relationship between growth rate and body size. We also suggest that further studies on thermal advantage and sexual selection may be helpful to understand appendage size variation in P. przewalskii., This study explores the validity of Bergmann's rule and Allen's rule in Phrynocephalus przewalskii, a small sand lizard prevalent in the deserts of northern China. Analysis of correlations between climatic factors and body size enabled us to conclude that body size trends were mainly caused by plasticity of growth rates, whereas appendage size trends were due to heat balance in females. We believe that our study makes a significant contribution to literature because we have shown that age should be considered, along with general body size, when testing biogeographic rules; we also recommend the use of temperature instead of latitude or altitude in such studies.

Research on prominence perception has made use of animated agents and controlled speech in experimental settings, but these methodologies have disregarded some aspects of the acoustic and visual correlates of prominence. To overcome these limitations we propose a new methodological approach using spontaneous speech data. For this, we created a small database with extracts from a television talent show and neutralised the prominence-lending properties of the acoustic cues of prominence in the speech signal. In our pilot study twelve naive listeners marked words for binary prominence (prominent vs. non-prominent) in two modalities, i.e. audio-only and audiovisual, under three conditions involving neutralisation of (a) fundamental frequency, (b) intensity, and (c) both fundamental frequency and intensity. Additionally, the marks of two trained listeners served as control condition. Different generalised linear mixed models were estimated and compared using the Akaike Information Criterion (AIC). The most parsimonious model was then examined using traditional null-hypothesis testing in order to provisionally establish the effects of our independent variables on prominence marking. We argue that spontaneous speech can be successfully applied to the study of the multimodal perception of prominence.

1. In mixed stands, species complementarity (e.g. facilitation and competition reduction) may enhance forest tree productivity. Although positive mixture effects have been identified in forests world‐wide, the majority of studies have focused on two‐species interactions in managed systems with high functional diversity. We extended this line of research to examine mixture effects on tree productivity across landscape‐scale compositional and environmental gradients in the low functional diversity, fire‐suppressed, mixed‐conifer forests of the U.S. Interior West. 2. We investigated mixture effects on the productivity of Pinus ponderosa, Pseudotsuga menziesii and Abies concolor. Using region‐wide forest inventory data, we created individual‐tree generalized linear mixed models and examined the growth of these species across community gradients. We compared the relative influences of stand structure, age, competition and environmental stress on mixture effects using multi‐model inference. We analysed growth of neighbouring tree species to infer whether a mixture effect in a single species translated to the stand‐level. 3. We found support for a positive mixture effect in P. menziesii, although our results were equivocal in light of a weaker but still plausible alternative model. Growth of P. menziesii neighbouring species in mixed stands declined or held constant depending on aridity, suggesting that a positive mixture effect in P. menziesii does not necessarily extend to the stand level. We found no evidence for mixture effects in P. ponderosa, A. concolor or their neighbouring species. 4. Complementarity appears to have a limited influence on tree growth in the mixed‐conifer systems of the U.S. Interior West, reflecting limited functional diversity. Historical changes in stand structure following fire exclusion, particularly high stand densities, may limit the potential for positive species mixture effects. The limited species pool of Interior West forests increases the risk that, without careful management, what functional diversity exists could be lost to compositional changes resulting from stand dynamics or disturbance.

Change in breeding phenology is often a response to environmental forcing, but less is known of the mechanism underlying such changes and their fitness consequences. Here, we report on changes in the breeding phenology from a 27‐year longitudinal study (1991–2017) of individually marked, known‐aged grey seals (Halichoerus grypus) on Sable Island, Nova Scotia, Canada. We used generalized linear mixed models and a 3‐step process to develop a model that includes interactions between intrinsic and extrinsic covariates and to test hypotheses about the influence of fixed factors (maternal age, parity, previous reproductive success, pup sex, colony density, Atlantic Multidecal Oscillation (AMO), North Atlantic Oscillation (NAO), and Sea Surface Temperature) and a random factor (female identity) on parturition dates. We also examined the consequences of the shift in birthdates on maternal energy allocation in offspring as measured by pup weaning mass. Birthdates were known for 2,768 pups of 660 known‐age females. For 494 females with ≥2 parturition dates, repeatability as measured by the intraclass correlation was high (mean = 0.66). 87% of the variation in birthdates was explained by a mixed‐effects model that included intrinsic and extrinsic fixed effects. Most of the explained variation was associated with the random effect of female identity. Parity was the most important intrinsic fixed effect, with inexperienced mothers giving birth later in the season than multiparous females. Over almost 3 decades, mean birthdates advanced by 15 days. The mixed model with intrinsic effects and population size, the detrended AMO from the previous year and mean NAO in the previous 3 years explained 80% of the variation with 21% of variation from the fixed effects. Both primiparous and multiparous individuals responded to the climate forcing, and there was strong evidence for heterogeneity in the response. Nevertheless, the shift in birthdates did not impact pup weaning mass., Here, we studied how breeding phenology responds to maternal traits and demographic and environmental conditions over almost three decades and the resulting fitness consequences of those changes in a well‐studied population of grey seals. Mean birthdates advanced by 15 days. Longitudinal data on over 500 individual females showed that maternal birthdates were highly repeatable but despite that repeatability females responded to environmental forcing. Both primiparous and multiparous individuals responded to forcing by AMO, but there was strong evidence for heterogeneity in the response. Despite changing birthdates offspring weaning mass was not affected showing that climate driven changes in breeding phenology may not always have measurable consequences.

Epidemiological research often involves meta-analyses of proportions. Conventional two-step methods first transform each study’s proportion and subsequently perform a meta-analysis on the transformed scale. They suffer from several important limitations: the log and logit transformations impractically treat within-study variances as fixed, known values and require ad hoc corrections for zero counts; the results from arcsine-based transformations may lack interpretability. Generalized linear mixed models (GLMMs) have been advocated in meta-analyses as a one-step approach to fully accounting for within-study uncertainties. However, they are seldom used in current practice to synthesize proportions. This article summarizes various methods for meta-analyses of proportions, illustrates their implementations, and explores their performance using real and simulated datasets. In general, GLMMs led to smaller biases and mean squared errors, and higher coverage probabilities than two-step methods. Many software programs are readily available to implement these methods.

Policy decisions regarding allocation of resources to subgroups in a population, called small areas, are based on reliable predictors of their underlying parameters. However, the information is collected at a different scale than these subgroups. Hence, we need to predict characteristics of the subgroups based on the coarser scale data. In view of this, there is a growing demand for reliable small area predictors by borrowing information from other related sources. For this purpose, mixed models have been commonly used in small area estimation assuming independent small areas. There are many situations, however, that the small area parameters are related to their locations. For instance, it is an interest of policy makers (and public) to know the spatial pattern of a chronic disease (e.g., asthma) to identify small areas with high risk of disease for possible preventions. In this paper, we propose small area models in the class of spatial linear mixed models to be able to predict small area parameters and also to obtain corresponding mean squared prediction error (MSPE). We also provide unbiased estimators of MSPE of small area predictors using Taylor series expansion and parametric bootstrap methods. In our simulations, we show that our MSPE estimators using Taylor expansion and parametric bootstrap perform very well in terms of precision of small area predictors. Performance of our proposed approach is also evaluated through a real application of physician visits for Total Respiratory Morbidity conditions in Manitoba, Canada.

Summary Information criteria are commonly used for joint fixed and random effects selection in mixed models. While information criteria are straightforward to implement, a major difficulty in applying them is that they are typically based on maximum likelihood estimates, but calculating such estimates for one candidate mixed model, let alone multiple models, presents a major computational challenge. To overcome this hurdle, we study penalized quasilikelihood estimation and use it as the basis for performing fast joint selection. Under a general framework, we show that penalized quasilikelihood estimation produces consistent estimates of the true parameters. We then propose a new penalized quasilikelihood information criterion whose distinguishing feature is the way it accounts for model complexity in the random effects, since penalized quasilikelihood estimation effectively treats the random effects as fixed. We demonstrate that the criterion asymptotically identifies the true set of important fixed and random effects. Simulations show that the quasilikelihood information criterion performs competitively with and sometimes better than common maximum likelihood information criteria for joint selection, while offering substantial reductions in computation time.

Deep-sea corals and sponges (DSCS) inhabit the world’s oceans and are often associated with high fish abundance. However, the precise nature and extent of any association is difficult to quantify and remains poorly understood. We investigated associations between DSCS and demersal fish using data from the Northwest Fisheries Science Center’s bottom trawl survey (2003-2015). General linear mixed models showed that average species density of groundfish was slightly higher and groundfish biomass slightly lower in tows with DSCS. Multivariate analyses were used to examine relationships among fish community structure, DSCS biomass, and environmental parameters (depth, latitude, bottom temperature). No strong correlations occurred between the community structure of groundfish and DSCS biomass; instead, bottom temperature and depth were the primary drivers of community composition. However, indicator species analysis also showed various species-specific associations with DSCS. Specifically, some flatfish species exhibited relationships with coral and sea pen biomass, whereas some rockfishes were associated with high sponge biomass. Our results provide information on the broad-scale associations among DSCS and demersal fishes that may be useful for developing studies focused on the functional value of DSCS as essential fish habitat and the role they play in groundfish life history and ecology.

Urban Norway rats (Rattus norvegicus) carry several pathogens transmissible to people. However, pathogen prevalence can vary across fine spatial scales (i.e., by city block). Using a population genomics approach, we sought to describe rat movement patterns across an urban landscape and to evaluate whether these patterns align with pathogen distributions. We genotyped 605 rats from a single neighborhood in Vancouver, Canada, and used 1,495 genome‐wide single nucleotide polymorphisms to identify parent–offspring and sibling relationships using pedigree analysis. We resolved 1,246 pairs of relatives, of which only 1% of pairs were captured in different city blocks. Relatives were primarily caught within 33 meters of each other leading to a highly leptokurtic distribution of dispersal distances. Using binomial generalized linear mixed models, we evaluated whether family relationships influenced rat pathogen status with the bacterial pathogens Leptospira interrogans, Bartonella tribocorum, and Clostridium difficile, and found that an individual's pathogen status was not predicted any better by including disease status of related rats. The spatial clustering of related rats and their pathogens lends support to the hypothesis that spatially restricted movement promotes the heterogeneous patterns of pathogen prevalence evidenced in this population. Our findings also highlight the utility of evolutionary tools to understand movement and rat‐associated health risks in urban landscapes.

Sarcopenia is a geriatric syndrome characterized by significant loss of muscle mass. Based on a commonly used definition of the condition that involves three measurements, different subclinical and clinical states of sarcopenia are formed. These states constitute a partially ordered set (poset). This article focuses on the analysis of longitudinal poset in the context of sarcopenia. We propose an extension of the generalized linear mixed model and a recoding scheme for poset analysis such that two submodels-one for ordered categories and one for nominal categories-that include common random effects can be jointly estimated. The new poset model postulates random effects conceptualized as latent variables that represent an underlying construct of interest, that is, susceptibility to sarcopenia over time. We demonstrate how information can be gleaned from nominal sarcopenic states for strengthening statistical inference on a person's susceptibility to sarcopenia.

In cultivar testing, linear mixed models have been used routinely to analyze multienvironment trials. A single‐stage analysis is considered as the gold standard, whereas two‐stage analysis produces similar results when a fully efficient weighting method is used, namely when the full variance–covariance matrix of the estimated means from Stage 1 is forwarded to Stage 2. However, in practice, this may be hard to do and a diagonal approximation is often used. We conducted a cross‐validation with data from Swedish cultivar trials on winter wheat (Triticum aestivum L.) and spring barley (Hordeum vulgare L.) to assess the performance of single‐stage and two‐stage analyses. The fully efficient method and two diagonal approximation methods were used for weighting in the two‐stage analyses. In Sweden, cultivar recommendation is delineated by zones (regions), not individual locations. We demonstrate the use of best linear unbiased prediction (BLUP) for cultivar effects per zone, which exploits correlations between zones and thus allows information to be borrowed across zones. Complex variance–covariance structures were applied to allow for heterogeneity of cultivar × zone variance. The single‐stage analysis and the three weighted two‐stage analyses all performed similarly. Loss of information caused by a diagonal approximation of the variance–covariance matrix of adjusted means from Stage 1 was negligible. As expected, BLUP outperformed best linear unbiased estimation. Complex variance–covariance structures were dispensable. To our knowledge, this study is the first to use cross‐validation for comparing single‐stage analyses with stagewise analyses.

Data collected in various scientific fields are count data. One way to analyze such data is to compare the individual levels of the factor treatment using multiple comparisons. However, the measured individuals are often clustered - e.g. according to litter or rearing. This must be considered when estimating the parameters by a repeated measurement model. In addition, ignoring the overdispersion to which count data is prone leads to an increase of the type one error rate. We carry out simulation studies using several different data settings and compare different multiple contrast tests with parameter estimates from generalized estimation equations and generalized linear mixed models in order to observe coverage and rejection probabilities. We generate overdispersed, clustered count data in small samples as can be observed in many biological settings. We have found that the generalized estimation equations outperform generalized linear mixed models if the variance-sandwich estimator is correctly specified. Furthermore, generalized linear mixed models show problems with the convergence rate under certain data settings, but there are model implementations with lower implications exists. Finally, we use an example of genetic data to demonstrate the application of the multiple contrast test and the problems of ignoring strong overdispersion.

–In the pharmaceutical industry, all analytical methods must be shown to deliver unbiased and precise results. In an assay qualification or validation study, the trueness, accuracy, and int...

Stepped wedge cluster trials are an increasingly popular alternative to traditional parallel cluster randomized trials. Such trials often utilize a small number of clusters and numerous time intervals, and these components must be considered when choosing an analysis method. A generalized linear mixed model containing a random intercept and fixed time and intervention covariates is the most common analysis approach. However, the sole use of a random intercept applies a constant intraclass correlation coefficient structure, which is an assumption that is likely to be violated given stepped wedge trials (SWTs) have multiple time intervals. Alternatively, generalized estimating equations (GEE) are robust to the misspecification of the working correlation structure, although it has been shown that small-sample adjustments to standard error estimates and the use of appropriate degrees of freedom are required to maintain the validity of inference when the number of clusters is small. In this article, we show, using an extensive simulation study based on a motivating example and a more general design, the use of GEE can maintain the validity of inference in small-sample SWTs with binary outcomes. Furthermore, we show which combinations of bias corrections to standard error estimates and degrees of freedom work best in terms of attaining nominal type I error rates.

Environmental characteristics of an invaded environment can predict the invasion success of a species, depending on its habits and life strategies. Cichla kelberi is a visual and voracious predator introduced in the Upper Parana River floodplain, an area that suffers with several upstream dams that caused many environmental changes over the years (e.g. increased water transparency). As this species is a pre-adapted species to environments that presents high water transparency, our main goal was to test the hypothesis that variables related to the underwater visibility would be important drivers of the successful invasion of C. kelberi in the Upper Parana River floodplain. We predict that turbidity (proxy of water transparency) is one of the major limnological determinants of occurrence and abundance of C. kelberi. Individuals of the invasive species and seven limnological variables were sampled quarterly between February 2000 and November 2018. This long-term data is part of the sixth site of the Brazilian Long Term Ecological Program (PELD). We fitted two regression models to all occurrence and abundance data (response variables) against the limnological variables (explanatory variables). For occurrence data, we fitted a Generalized Linear Mixed Model and for abundance data, we fitted a Linear Mixed Effects Model. The occurrence data of C. kelberi showed that turbidity and dissolved oxygen were the variables that most influenced the presence of this species, negatively and positively, respectively. The abundance data showed that dissolved oxygen and concentration of chlorophyll-a were the ones that most influenced the abundance of this species, negatively and positively, respectively. Our findings showed that besides turbidity, other limnological variables were also determinants for the occurrence and abundance of C. kelberi . Therefore, our results provided important information about the main environmental drivers of the establishment process of C. kelberi in the Upper Parana River floodplain.

Two-part mixed effects models are often used for analyzing longitudinal data with many zeros. Typically, these models are formulated with binary and continuous components separately with random effects that are correlated between the two components. Researchers have developed maximum-likelihood and Bayesian approaches for fitting these models that often require using particular software packages or very specialized software. We propose an imputation approach that will allow practitioners to separately use standard linear and generalized linear mixed models to estimate the fixed effects for two-part mixed effects models with complex random effects structures. An approximation to the conditional distribution of positive measurements given an individual’s pattern of non-zero measurements is proposed that can be easily estimated and then imputed from. We show that for a wide range of parameter values, the imputation approach results in nearly unbiased estimation and can be implemented with standard software. We illustrate the proposed imputation approach for the analysis of longitudinal clinical trial data with many zeros.

For the special case of balanced one-way random effects ANOVA, it has been established that the generalized likelihood ratio test (LRT) and Wald’s test are largely equivalent in testing the variance component. We extend these results to explore the relationships between Wald’s F test, and the LRT for a much broader class of linear mixed models; the generalized split-plot models. In particular, we explore when the two tests are equivalent and prove that when they are not equivalent, Wald’s F test is more powerful, thus making the LRT test inadmissible. We show that inadmissibility arises in realistic situations with common number of degrees of freedom. Further, we derive the statistical distribution of the LRT under both the null and alternative hypotheses $$H_0$$ and $$H_1$$ where $$H_0$$ is the hypothesis that the between variance component is zero. Providing an exact distribution of the test statistic for the LRT in these models will help in calculating a more accurate p-value than the traditionally used p-value derived from the large sample chi-square mixture approximations.

Low birth weight (LBW) is a major determinant of morbidity, mortality and disability in infancy and childhood and has a long-term impact on health outcomes in adult life. This study was aimed to model LBW using marginal and generalized linear mixed models as well as identify the potential risk factors of LBW in Ethiopia. Data was taken from the 2011 Ethiopian demographic and health survey, which is a nationally representative survey of children in the 0–59 month age groups. Two model families, generalized estimating equation and alternating logistic regression models from marginal model family, and generalized linear mixed model from cluster specific model family were used for the analysis. The result showed that 34.8% of children were born with LBW. Alternating logistic regression model was best fits the data for population-averaged effects of the given factors on birth weight than generalized estimating equation model. Generalized linear mixed model with two random intercepts was the best model to evaluate within and between regional heterogeneity of birth weight. Both the best-fitted models gave the same conclusion that sex, wealth status, age, antenatal care, marital status, vaccination, anemia and mother education level were the determinant factors of LBW. This study contributes to the understanding of the individual and collective effect of maternal, socio-economic and child related factors influencing infant birth weight in Ethiopia.

Misspecification of the covariance structure in a linear mixed model (LMM) can lead to biased population parameters' estimates under MAR drop-out. In our motivating example of modeling CD4 cell counts during untreated HIV infection, random intercept and slope LMMs are frequently used. In this article, we evaluate the performance of LMMs with specific covariance structures, in terms of bias in the fixed effects estimates, under specific MAR drop-out mechanisms, and adopt a Bayesian model comparison criterion to discriminate between the examined approaches in real-data applications. We analytically show that using a random intercept and slope structure when the true one is more complex can lead to seriously biased estimates, with the degree of bias depending on the magnitude of the MAR drop-out. Under misspecified covariance structure, we compare in terms of induced bias the approach of adding a fractional Brownian motion (BM) process on top of random intercepts and slopes with the approach of using splines for the random effects. In general, the performance of both approaches was satisfactory, with the BM model leading to smaller bias in most cases. A simulation study is carried out to evaluate the performance of the proposed Bayesian criterion in identifying the model with the correct covariance structure. Overall, the proposed method performs better than the AIC and BIC criteria under our specific simulation setting. The models under consideration are applied to real data from the CASCADE study; the most plausible model is identified by all examined criteria.

Multivariate longitudinal data usually exhibit complex features such as the presence of censored responses due to detection limits of the assay and unavoidable missing values arising when participants make irregular visits that lead to intermittently recorded characteristics. A generalization of the multivariate linear mixed model constructed by taking into account impacts of censored and intermittent missing responses simultaneously, which is named as the MLMM-CM, has been recently proposed for more precisely analyzing such kinds of data. This paper aims at presenting a fully Bayesian sampling-based approach to the MLMM-CM for addressing the uncertainties of censored and missing responses as well as unknown parameters. Two widely accepted Bayesian computational techniques based on the Markov chain Monte Carlo and the inverse Bayes formulas coupled with the Gibbs (IBF-Gibbs) schemes are developed for carrying out posterior inference of the model. The proposed methodology is illustrated through a simulation study and a real-data example from the Adult AIDS Clinical Trials Group 388 study. Numerical results show empirically that the proposed Bayesian methodology performs satisfactorily and offers reliable posterior inference.

Species distribution models (SDMs) are used to test ecological theory and to direct targeted surveys for species of conservation concern. Several studies have tested for an influence of species traits on the predictive accuracy of SDMs. However, most used the same set of environmental predictors for all species and/or did not use truly independent data to test SDM accuracy. We built eight SDMs for each of 24 plant species of conservation concern, varying the environmental predictors included in each SDM version. We then measured the accuracy of each SDM using independent presence and absence data to calculate area under the receiver operating characteristic curve (AUC) and true positive rate (TPR). We used generalized linear mixed models to test for a relationship between species traits and SDM accuracy, while accounting for variation in SDM performance that might be introduced by different predictor sets. All traits affected one or both SDM accuracy measures. Species with lighter seeds, animal‐dispersed seeds, and a higher density of occurrences had higher AUC and TPR than other species, all else being equal. Long‐lived woody species had higher AUC than herbaceous species, but lower TPR. These results support the hypothesis that the strength of species–environment correlations is affected by characteristics of species or their geographic distributions. However, because each species has multiple traits, and because AUC and TPR can be affected differently, there is no straightforward way to determine a priori which species will yield useful SDMs based on their traits. Most species yielded at least one useful SDM. Therefore, it is worthwhile to build and test SDMs for the purpose of finding new populations of plant species of conservation concern, regardless of these species’ traits., We used independent field survey data to assess the accuracy of species distribution models (SDMs) built for 24 plant species of conservation concern. We tested whether traits of species (e.g., dispersal mechanism) or characteristics of their distribution (e.g., mean latitude) influenced model accuracy. Traits do influence species–environment relationships and therefore SDM accuracy, nevertheless a useful SDM could be built for most species.

In random-effects meta-analysis the between-study variance (τ 2) has a key role in assessing heterogeneity of study-level estimates and combining them to estimate an overall effect. For odds ratios the most common methods suffer from bias in estimating τ 2 and the overall effect and produce confidence intervals with below-nominal coverage. An improved approximation to the moments of Cochran's Q statistic, suggested by Kulinskaya and Dollinger (KD), yields new point and interval estimators of τ 2 and of the overall log-odds-ratio. Another, simpler approach (SSW) uses weights based only on study-level sample sizes to estimate the overall effect. In extensive simulations we compare our proposed estimators with established point and interval estimators for τ 2 and point and interval estimators for the overall log-odds-ratio (including the Hartung-Knapp-Sidik-Jonkman interval). Additional simulations included three estimators based on generalized linear mixed models and the Mantel-Haenszel fixed-effect estimator. Results of our simulations show that no single point estimator of τ 2 can be recommended exclusively, but Mandel-Paule and KD provide better choices for small and large numbers of studies, respectively. The KD estimator provides reliable coverage of τ 2. Inverse-variance-weighted estimators of the overall effect are substantially biased, as are the Mantel-Haenszel odds ratio and the estimators from the generalized linear mixed models. The SSW estimator of the overall effect and a related confidence interval provide reliable point and interval estimation of the overall log-odds-ratio.

In nephrology, a great deal of information is measured repeatedly in patients over time, often alongside data on events of clinical interest. In this introductory article we discuss how these two types of data can be simultaneously analysed using the joint model (JM) framework, illustrated by clinical examples from nephrology. As classical survival analysis and linear mixed models form the two main components of the JM framework, we will also briefly revisit these techniques.

Statistics matter greatly in biology, whether we like it or not. As a discipline with an empirical inclination, we are faced with data every day and we rely on inferential statistical models to make sense of it and to provide us with novel insights. Much of the time, the growing level of complexity and sophistication of the models we put to use in ecology and evolution have led to more appropriate analyses of our data. However, this is not always the case. Here, I draw attention to a classic flaw in inferential statistics that has resurfaced in a new flavor as a result of increased reliance on complex linear mixed models - the multifaceted and disturbingly persistent problem of pseudoreplication.

Introduction: A method for identifying significant predictors of roadway accident counts has been presented. This process is applied to real-world accident data collected from roadways in Hamilton County, TN. Methods: In preprocessing, an aggregation procedure based on segmenting roadways into fixed lengths has been introduced, and then accident counts within each segment have been observed according to predefined weather conditions. Based on the physical roadway characteristics associated with each individual accident record, a collection of roadway features is assigned to each segment. A mixed-effects Negative Binomial regression form is assumed to approximate the relationship between accident counts and several explanatory variables including roadway characteristics, weather conditions, and several interactions between them. Standard diagnostics and a validation procedure show that our model form is properly specified and suitably fits the data. Results: Interpreting interaction terms leads to the follow findings: 1) rural roads with cloudy conditions are associated with relative increases in accident frequency; 2) lower/moderate AADT and rainy weather are associated with relative decreases in accident frequency, while high AADT and rain are associated with relative increases in accident frequency; 3) higher AADT and wider pavements are associated with relative increases in accident frequency; and 4) higher speed limits in residential areas are associated with relative increases in accident frequency. Conclusion: Results illustrate the complicated relationship between accident frequency and both roadway features and weather. Therefore, it is not sufficient to observe the effects of weather and roadway features independently as these variables interact with one another.

Invasive alien species are a major threat to biodiversity and human activities, providing a strong incentive to understand the processes by which alien invasion occurs. While it is important to understand the determinants of success at each of several invasion stages—transport, introduction, establishment, and spread—few studies have explored the first of these stages. Here, we quantify and analyze variation in the success of individual animals in surviving the transport stage, based on shipping records of European passerines destined for New Zealand. We mined the original documents of Acclimatisation Societies, established in New Zealand for the purpose of introducing supposedly beneficial alien species, in combination with recently digitized newspaper archives, to produce a unique dataset of 122 ships that carried passerines from Europe to New Zealand between 1850 and 1885. For 37 of these shipments, data on the survival of individual species were available. Using generalized linear mixed models, we explored how survival was related to characteristics of the shipments and the species. We show that species differed greatly in their survival, but none of the tested traits accounted for these differences. Yet, survival increased over time, which mirrors the switch from early haphazard shipments to larger organized shipments. Our results imply that it was the quality of care received by the birds that most affected success at this stage of the invasion process., While it is important to understand the determinants of success at each of several invasion stages—transport, introduction, establishment, and spread—few studies have explored the first of these stages. Here, we quantify and analyse variation in the success of individual animals in surviving the transport stage, based on shipping records of European passerines destined for New Zealand. Our results imply that it was the quality of care received by the birds that most affected success at this stage of the invasion process.

Many studies have reported associations between respiratory symptoms and resident proximity to traffic. However, only a few have documented information about the relationship between traffic volume and air quality in local areas. This study investigates the impact of traffic volume on air quality at different geographical locations in the state of South Carolina using multilevel linear mixed models and Grey Systems. Historical traffic volume and air quality data between 2006 and 2016 are obtained from the South Carolina Department of Transportation (SCDOT) and the United States Environmental Protection Agency (EPA) monitoring stations. The data are used to develop prediction models that relate Air Quality Index (AQI) to traffic volume for selected counties and schools. For the counties, two models are developed, one with Ozone ( O 3 ) and one with PM 2.5 as the dependent variable. For the schools, only one model is developed, with O 3 as the dependent variable. The number of counties and schools studied are limited by the availability of air monitoring stations dedicated to measuring O 3 and PM 2.5 . Several types of models were investigated. They include linear regression model (LM), linear mixed-effect regression model (LMER), Grey Systems (GM), error corrected GM (EGM), Grey Verhulst (GV), error corrected GV (EGV), and LMER + EGM. The LM model produced the least accurate estimate while the LMER + EGM model produced the most accurate estimate (average RMSE is less than 5%). The models’ estimates suggest that air quality in South Carolina will continue to get worse in the coming years due to increasing AADT. An interesting finding of this study is that some counties and schools will have higher levels of O 3 or PM 2.5 when AADT decreases. This finding suggests that there are other factors, other than AADT, that influence the air quality in these counties and schools.

Bacterial black node (BBN) due to Pseudomonas syringae pv. syringae (PSS) is the most serious bacterial disease of barley in Japan. Here we identified the risk factors that affect barley at harvest using statistical models and graphic models updating the chance of BBN incidence after each event occurred. Three models, based on separate data from Okayama and Kagawa Prefectures or combined data from both prefectures from 2002 through 2018, were developed using a generalized linear mixed model (GLMM). The Okayama model included the number of days that the minimum temperature in January was − 4 °C or below (AIC value = 39.7), and the Kagawa model included that parameter and the number of days that the mean temperature in January was ≥ 5 °C, and the number of rainy days (≥ 5 mm/day) in March (AIC value = 230.4). The combined data model included the number of days in January ≤ − 4 °C and number of rainy days in March (AIC value = 330.2). Thus, three predictive models were obtained by GLMM. In results of risk analyses constructed by Bayesian inference, when risk factors occurred, disease incidence was 2.1 to 2.5 times higher than when risk factors were not present. This is the first report to demonstrate risk factors for BBN incidence using GLMM and to assess the contribution of each risk factor to increased BBN based on 17 years of historical data.

Data augmentation (DA) turns seemingly intractable computational problems into simple ones by augmenting latent missing data. In addition to computational simplicity, it is now well-established that DA equipped with a deterministic transformation can improve the convergence speed of iterative algorithms such as an EM algorithm or Gibbs sampler. In this article, we outline a framework for the transformation-based DA, which we call data transforming augmentation (DTA), allowing augmented data to be a deterministic function of latent and observed data, and unknown parameters. Under this framework, we investigate a novel DTA scheme that turns heteroscedastic models into homoscedastic ones to take advantage of simpler computations typically available in homoscedastic cases. Applying this DTA scheme to fitting linear mixed models, we demonstrate simpler computations and faster convergence rates of resulting iterative algorithms, compared with those under a non-transformation-based DA scheme. We also fit a Beta-Binomial model using the proposed DTA scheme, which enables sampling approximate marginal posterior distributions that are available only under homoscedasticity. An R package, Rdta, is publicly available at CRAN.