An evaluation of computational methods for aggregate data meta-analyses of diagnostic test accuracy studies.

BACKGROUND: A Generalized Linear Mixed Model (GLMM) is recommended to meta-analyze diagnostic test accuracy studies (DTAs) based on aggregate or individual participant data. Since a GLMM does not have a closed-form likelihood function or parameter solutions, computational methods are conventionally used to approximate the likelihoods and obtain parameter estimates. The most commonly used computational methods are the Iteratively Reweighted Least Squares (IRLS), the Laplace approximation (LA), and the Adaptive Gauss-Hermite quadrature (AGHQ). Despite being widely used, it has not been clear how these computational methods compare and perform in the context of an aggregate data meta-analysis (ADMA) of DTAs. METHODS: We compared and evaluated the performance of three commonly used computational methods for GLMM - the IRLS, the LA, and the AGHQ, via a comprehensive simulation study and real-life data examples, in the context of an ADMA of DTAs. By varying several parameters in our simulations, we assessed the performance of the three methods in terms of bias, root mean squared error, confidence interval (CI) width, coverage of the 95% CI, convergence rate, and computational speed. RESULTS: For most of the scenarios, especially when the meta-analytic data were not sparse (i.e., there were no or negligible studies with perfect diagnosis), the three computational methods were comparable for the estimation of sensitivity and specificity. However, the LA had the largest bias and root mean squared error for pooled sensitivity and specificity when the meta-analytic data were sparse. Moreover, the AGHQ took a longer computational time to converge relative to the other two methods, although it had the best convergence rate. CONCLUSIONS: We recommend practitioners and researchers carefully choose an appropriate computational algorithm when fitting a GLMM to an ADMA of DTAs. We do not recommend the LA for sparse meta-analytic data sets. However, either the AGHQ or the IRLS can be used regardless of the characteristics of the meta-analytic data.

Efficient computation of high-dimensional penalized generalized linear mixed models by latent factor modeling of the random effects.

Modern biomedical datasets are increasingly high-dimensional and exhibit complex correlation structures. Generalized linear mixed models (GLMMs) have long been employed to account for such dependencies. However, proper specification of the fixed and random effects in GLMMs is increasingly difficult in high dimensions, and computational complexity grows with increasing dimension of the random effects. We present a novel reformulation of the GLMM using a factor model decomposition of the random effects, enabling scalable computation of GLMMs in high dimensions by reducing the latent space from a large number of random effects to a smaller set of latent factors. We also extend our prior work to estimate model parameters using a modified Monte Carlo Expectation Conditional Minimization algorithm, allowing us to perform variable selection on both the fixed and random effects simultaneously. We show through simulation that through this factor model decomposition, our method can fit high-dimensional penalized GLMMs faster than comparable methods and more easily scale to larger dimensions not previously seen in existing approaches.

Multivariate probit linear mixed models for multivariate longitudinal binary data.

When analyzing multivariate longitudinal binary data, we estimate the effects on the responses of the covariates while accounting for three types of complex correlations present in the data. These include the correlations within separate responses over time, cross-correlations between different responses at different times, and correlations between different responses at each time point. The number of parameters thus increases quadratically with the dimension of the correlation matrix, making parameter estimation difficult; the estimated correlation matrix must also meet the positive definiteness constraint. The correlation matrix may additionally be heteroscedastic; however, the matrix structure is commonly considered to be homoscedastic and constrained, such as exchangeable or autoregressive with order one. These assumptions are overly strong, resulting in skewed estimates of the covariate effects on the responses. Hence, we propose probit linear mixed models for multivariate longitudinal binary data, where the correlation matrix is estimated using hypersphere decomposition instead of the strong assumptions noted above. Simulations and real examples are used to demonstrate the proposed methods. An open source R package, BayesMGLM, is made available on GitHub at https://github.com/kuojunglee/BayesMGLM/ with full documentation to produce the results.

Multilevel modeling in single-case studies with zero-inflated and overdispersed count data.

Count outcomes are frequently encountered in single-case experimental designs (SCEDs). Generalized linear mixed models (GLMMs) have shown promise in handling overdispersed count data. However, the presence of excessive zeros in the baseline phase of SCEDs introduces a more complex issue known as zero-inflation, often overlooked by researchers. This study aimed to deal with zero-inflated and overdispersed count data within a multiple-baseline design (MBD) in single-case studies. It examined the performance of various GLMMs (Poisson, negative binomial [NB], zero-inflated Poisson [ZIP], and zero-inflated negative binomial [ZINB] models) in estimating treatment effects and generating inferential statistics. Additionally, a real example was used to demonstrate the analysis of zero-inflated and overdispersed count data. The simulation results indicated that the ZINB model provided accurate estimates for treatment effects, while the other three models yielded biased estimates. The inferential statistics obtained from the ZINB model were reliable when the baseline rate was low. However, when the data were overdispersed but not zero-inflated, both the ZINB and ZIP models exhibited poor performance in accurately estimating treatment effects. These findings contribute to our understanding of using GLMMs to handle zero-inflated and overdispersed count data in SCEDs. The implications, limitations, and future research directions are also discussed.

Safety signal detection with control of latent factors.

Postmarket drug safety database like vaccine adverse event reporting system (VAERS) collect thousands of spontaneous reports annually, with each report recording occurrences of any adverse events (AEs) and use of vaccines. We hope to identify signal vaccine-AE pairs, for which certain vaccines are statistically associated with certain adverse events (AE), using such data. Thus, the outcomes of interest are multiple AEs, which are binary outcomes and could be correlated because they might share certain latent factors; and the primary covariates are vaccines. Appropriately accounting for the complex correlation among AEs could improve the sensitivity and specificity of identifying signal vaccine-AE pairs. We propose a two-step approach in which we first estimate the shared latent factors among AEs using a working multivariate logistic regression model, and then use univariate logistic regression model to examine the vaccine-AE associations after controlling for the latent factors. Our simulation studies show that this approach outperforms current approaches in terms of sensitivity and specificity. We apply our approach in analyzing VAERS data and report our findings.

Differentiating between point and non-point source nutrient loadings of wastewater in an agriculturally impacted area using a hybrid statistical model.

Nutrient contamination from point and non-point sources can lead to harmful consequences, such as algal blooms. Point and non-point nutrient loading estimation is determined using modeling approaches and often require an abundance of variables and observations for calibration. Small rural streams that lack water use designations often lack available data to utilize current modeling strategies. This study proposes the use of a 3-phase hybrid stepwise statistical modeling approach using generalized linear mixed models (GLMM) and a reference stream. Two streams in Central Texas were sampled for 13 months between February 2020 and February 2021, one being impacted by a wastewater treatment plant (WWTP). Dissolved phosphorus (PO4-P), ammonia (NH3-N), nitrite/nitrate (NO2 + NO3-N), total nitrogen (TN), and total phosphorus (TP) were sampled in both streams for each month. Non-point sources of contamination, such as land use/land cover and geomorphology composition, were quantified for both sub-basin drainage areas. Phase I models predicted nutrient concentrations in the reference stream using non-point source variables along with discharge and temporal variables. Best fit models were carried forward to phase II and leveraged a point-source variable, which is a naïve estimate of effluent nutrient concentration in the absence of assimilation. Phase II model coefficients highlight the significance of point-source contamination in predicting nutrient concentration, but overall lacked the ability to make future predictions under new hydrologic regimes from WWTP intensification. Phase III models included deterministically calculating an uptake variable using the relationship between discharge and wetted widths, predicting background non-point concentrations by leveraging phase I models, and calculating future nutrient loadings from WWTP intensification. This approach predicted significant increases in nutrient concentrations under planned WWTP intensification scenarios and decreased uptake efficiencies under the new hydrologic regimes.

Mapping regional variability of exclusive breastfeeding and its determinants at different infant's age in Tanzania.

INTRODUCTION: Despite its numerous benefits, exclusive breastfeeding (EBF) remains an underutilized practice. Enhancing EBF uptake necessitates a focused approach targeting regions where its adoption is suboptimal. This study aimed to investigate regional disparities in EBF practices and identify determinants of EBF among infants aged 0-1, 2-3, and 4-5 months in Tanzania. METHODS: This cross-sectional study utilized data from the 2015/16 Tanzania Demographic and Health Survey. A total of 1,015 infants aged 0-5 met the inclusion criteria, comprising 378 aged 0-1 month, 334 at 2-3 months, and 303 at 4-5 months. EBF practices were assessed using a 24-hour recall method. A generalized linear mixed model, with fixed covariates encompassing infant and maternal attributes and clusters for enumeration areas (EAs) and regions, was employed to estimate EBF proportions. RESULTS: Regional disparities in EBF were evident among infants aged 0-1, 2-3, and 4-5 months, with decline in EBF proportions as an infant's age increases. This pattern was observed nationwide. Regional and EA factors influenced the EBF practices at 0-1 and 2-3 months, accounting for 17-40% of the variability at the regional level and 40-63% at the EA level. Literacy level among mothers had a significant impact on EBF practices at 2-3 months (e.g., women who could read whole sentences; AOR = 3.2, 95% CI 1.1,8.8). CONCLUSION: Regional disparities in EBF proportions exist in Tanzania, and further studies are needed to understand their underlying causes. Targeted interventions should prioritize regions with lower EBF proportions. This study highlights the clustering of EBF practices at 0-1 and 2-3 months on both regional and EA levels. Conducting studies in smaller geographical areas may enhance our understanding of the enablers and barriers to EBF and guide interventions to promote recommended EBF practices.

Bayesian multilevel modelling of the association between socio-economic status and stunting among under-five-year children in Tanzania.

BACKGROUND: Stunting is associated with socioeconomic status (SES) which is multidimensional. This study aimed to compare different SES indices in predicting stunting. METHODS: This was the secondary data analysis using Tanzania Demographics and Health Surveys (TDHS). The study used 7492, 6668, and 8790 under-five-year children from TDHS 2004/5, 2010, and 2015/16, respectively. The Household Wealth Index (HWI); Water and Sanitation, Assets, Maternal education and Income (WAMI); Wealth Assets, Education, and Occupation (WEO); and the Multidimensional Poverty Index (MPI) indices were compared. The summated scores, principal component analysis (PCA), and random forest (RF) approaches were used to construct indices. The Bayesian and maximum likelihood multilevel generalized linear mixed models (MGLMM) were constructed to determine the association between each SES index and stunting. RESULTS: The study revealed that 42.3%, 38.4%, and 32.4% of the studied under-five-year children were stunted in 2004/5, 2010, and 2015/16, respectively. Compared to other indicators of SES, the MPI had a better prediction of stunting for the TDHS 2004/5 and 2015/16, while the WAMI had a better prediction in 2010. For each score increase in WAMI, the odds of stunting were 64% [BPOR = 0.36; 95% CCI 0.3, 0.4] lower in 2010, while for each score increase in MPI there was 1 [BPOR = 1.1; 95% CCI 1.1, 1.2] times higher odds of stunting in 2015/16. CONCLUSION: The MPI and WAMI under PCA were the best measures of SES that predict stunting. Because MPI was the best predictor of stunting for two surveys (TDHS 2004/5 and 2015/16), studies dealing with stunting should use MPI as a proxy measure of SES. Use of BE-MGLMM in modelling stunting is encouraged. Strengthened availability of items forming MPI is inevitable for child growth potentials. Further studies should investigate the determinants of stunting using Bayesian spatial models to take into account spatial heterogeneity.

Trends of Exclusive Breastfeeding Practices and Its Determinants in Tanzania from 1999 to 2016.

Introduction: The benefits of exclusive breastfeeding (EBF) are widely reported. However, it is crucial to examine potential disparities in EBF practices across different regions of a country. Our study uses Tanzania demographic and health survey data to report on the trends of EBF across regions from 1999 to 2016, the patterns of the practice based on geographical location and socioeconomic status, and explores its determinants across the years. Methods: Descriptive statistics were used to establish the trends of EBF by geographical location and wealth quintile. A generalized linear mixed model was developed to incorporate both infant and maternal attributes as fixed covariates while considering enumeration areas and regions as clusters. The fitted model facilitated the estimation of EBF proportions at a regional level and identified key determinants influencing EBF practices across the survey periods. Moreover, we designed breastfeeding maps, visually depicting the performance of different regions throughout the surveys. Results: Across the various survey rounds, a notable regional variation in EBF practices was observed, with coastal regions generally exhibiting lower adherence to the practice. There was a linear trend between EBF and geographical residence (p < 0.05) and socioeconomic standing (p < 0.05) across the survey periods. Rural-dwelling women and those from the least affluent backgrounds consistently showcased a higher proportion of EBF. The prevalence of EBF declined as infants aged (p < 0.001), a trend consistent across all survey waves. The associations between maternal attributes and EBF practices displayed temporal variations. Furthermore, a correlation between exclusive breastfeeding and attributes linked to both regional disparities and enumeration areas was observed. The intra-cluster correlation ranged from 18% to 41.5% at the regional level and from 40% to 58.5% at the enumeration area level. Conclusions: While Tanzania's progress in EBF practices is laudable, regional disparities persist, demanding targeted interventions. Sustaining achievements while addressing wealth-based disparities and the decline in EBF with infant age is vital. The study highlights the need for broad national strategies and localized investigations to understand and enhance EBF practices across different regions and socioeconomic contexts.

A Description of the Statistical Methods for the Vaccine Impact on Diarrhea in Africa (VIDA) Study.

BACKGROUND: Diarrheal diseases remain a health threat to children in low- and middle-income countries. The Vaccine Impact on Diarrhea in Africa (VIDA) study was a 36-month, prospective, matched case-control study designed to estimate the etiology, incidence, and adverse clinical consequences of moderate-to-severe diarrhea (MSD) in children aged 0-59 months. VIDA was conducted following rotavirus vaccine introduction at 3 censused sites in sub-Saharan Africa that participated in the Global Enteric Multicenter Study (GEMS) ∼10 years earlier. We describe the study design and statistical methods of VIDA and where they differ from GEMS. METHODS: We aimed to enroll 8-9 MSD cases every 2 weeks from sentinel health centers in 3 age strata (0-11, 12-23, 24-59 months) and 1 to 3 controls matched by age, sex, date of case enrollment, and village. Clinical, epidemiological, and anthropometric data were collected at enrollment and ∼60 days later. A stool specimen collected at enrollment was analyzed by both conventional methods and quantitative PCR for enteric pathogens. For the matched case-control study, we estimated the population-based, pathogen-specific attributable fraction (AF) and attributable incidence adjusted for age, site, and other pathogens, and identified episodes attributable to a specific pathogen for additional analyses. A prospective cohort study nested within the original matched case-control study allowed assessment of (1) the association between potential risk factors and outcomes other than MSD status and (2) the impact of MSD on linear growth. CONCLUSIONS: GEMS and VIDA together comprise the largest and most comprehensive assessment of MSD conducted to date in sub-Saharan Africa populations at highest risk for morbidity and mortality from diarrhea. The statistical methods used in VIDA have endeavored to maximize the use of available data to produce more robust estimates of the pathogen-specific disease burden that might be prevented by effective interventions.

Bayesian generalized linear low rank regression models for the detection of vaccine-adverse event associations.

We propose a generalized linear low-rank mixed model (GLLRM) for the analysis of both high-dimensional and sparse responses and covariates where the responses may be binary, counts, or continuous. This development is motivated by the problem of identifying vaccine-adverse event associations in post-market drug safety databases, where an adverse event is any untoward medical occurrence or health problem that occurs during or following vaccination. The GLLRM is a generalization of a generalized linear mixed model in that it integrates a factor analysis model to describe the dependence among responses and a low-rank matrix to approximate the high-dimensional regression coefficient matrix. A sampling procedure combining the Gibbs sampler and Metropolis and Gamerman algorithms is employed to obtain posterior estimates of the regression coefficients and other model parameters. Testing of response-covariate pair associations is based on the posterior distribution of the corresponding regression coefficients. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures on binary and count outcomes. We further illustrate the GLLRM via a real data example based on the Vaccine Adverse Event Reporting System.

Beyond rankings: Learning (more) from algorithm validation.

Challenges have become the state-of-the-art approach to benchmark image analysis algorithms in a comparative manner. While the validation on identical data sets was a great step forward, results analysis is often restricted to pure ranking tables, leaving relevant questions unanswered. Specifically, little effort has been put into the systematic investigation on what characterizes images in which state-of-the-art algorithms fail. To address this gap in the literature, we (1) present a statistical framework for learning from challenges and (2) instantiate it for the specific task of instrument instance segmentation in laparoscopic videos. Our framework relies on the semantic meta data annotation of images, which serves as foundation for a General Linear Mixed Models (GLMM) analysis. Based on 51,542 meta data annotations performed on 2,728 images, we applied our approach to the results of the Robust Medical Instrument Segmentation Challenge (ROBUST-MIS) challenge 2019 and revealed underexposure, motion and occlusion of instruments as well as the presence of smoke or other objects in the background as major sources of algorithm failure. Our subsequent method development, tailored to the specific remaining issues, yielded a deep learning model with state-of-the-art overall performance and specific strengths in the processing of images in which previous methods tended to fail. Due to the objectivity and generic applicability of our approach, it could become a valuable tool for validation in the field of medical image analysis and beyond.

Bayesian hierarchical models and prior elicitation for fitting psychometric functions.

Our previous articles demonstrated how to analyze psychophysical data from a group of participants using generalized linear mixed models (GLMM) and two-level methods. The aim of this article is to revisit hierarchical models in a Bayesian framework. Bayesian models have been previously discussed for the analysis of psychometric functions although this approach is still seldom applied. The main advantage of using Bayesian models is that if the prior is informative, the uncertainty of the parameters is reduced through the combination of prior knowledge and the experimental data. Here, we evaluate uncertainties between and within participants through posterior distributions. To demonstrate the Bayesian approach, we re-analyzed data from two of our previous studies on the tactile discrimination of speed. We considered different methods to include a priori knowledge in the prior distribution, not only from the literature but also from previous experiments. A special type of Bayesian model, the power prior distribution, allowed us to modulate the weight of the prior, constructed from a first set of data, and use it to fit a second one. Bayesian models estimated the probability distributions of the parameters of interest that convey information about the effects of the experimental variables, their uncertainty, and the reliability of individual participants. We implemented these models using the software Just Another Gibbs Sampler (JAGS) that we interfaced with R with the package rjags. The Bayesian hierarchical model will provide a promising and powerful method for the analysis of psychometric functions in psychophysical experiments.

Sample size considerations for stepped wedge designs with subclusters.

The stepped wedge cluster randomized trial (SW-CRT) is an increasingly popular design for evaluating health service delivery or policy interventions. An essential consideration of this design is the need to account for both within-period and between-period correlations in sample size calculations. Especially when embedded in health care delivery systems, many SW-CRTs may have subclusters nested in clusters, within which outcomes are collected longitudinally. However, existing sample size methods that account for between-period correlations have not allowed for multiple levels of clustering. We present computationally efficient sample size procedures that properly differentiate within-period and between-period intracluster correlation coefficients in SW-CRTs in the presence of subclusters. We introduce an extended block exchangeable correlation matrix to characterize the complex dependencies of outcomes within clusters. For Gaussian outcomes, we derive a closed-form sample size expression that depends on the correlation structure only through two eigenvalues of the extended block exchangeable correlation structure. For non-Gaussian outcomes, we present a generic sample size algorithm based on linearization and elucidate simplifications under canonical link functions. For example, we show that the approximate sample size formula under a logistic linear mixed model depends on three eigenvalues of the extended block exchangeable correlation matrix. We provide an extension to accommodate unequal cluster sizes and validate the proposed methods via simulations. Finally, we illustrate our methods in two real SW-CRTs with subclusters.

Sampling Depth and Crop Growth Stage Affect Estimates of the Population Density of Lesion Nematodes (Pratylenchus spp.) in Corn Fields in Ohio.

The effects of sampling depth and crop growth stage on the population density of lesion nematodes were investigated in three commercial fields in Wayne and Fulton Counties, Ohio, during the 2016 and 2017 growing seasons. Soil samples were collected at five growth stages by removing 15 soil cores to a depth of 70 cm from each of 25 plots per field-year. Cores were divided into seven 10-cm sections, and nematodes were extracted from the soil and root fractions of each of them. Pratylenchus crenatus and P. thornei were detected in approximately 84 and 78% of the samples collected in Wayne and Fulton Counties, respectively. Depth significantly affected total population density of both species as well as densities in the soil and root factions in all field-years, but the effects of growth stage and its interaction with depth varied with field-year. In most cases, mean population densities were higher from 10 to 40 cm soil depth than at the reference 40 to 50 cm depth and lower from 50 to 70 cm. There were quadratic relationships between population density (on the log link scale) and depth, with the highest peaks in estimated predicted densities generally occurring between 20 and 40 cm, depending on crop growth stage and growing conditions. These findings suggest that the standard practice of sampling between growth stages V3 and V6 to a depth of 45 to 50 cm and using the entire core for extraction and enumeration could lead to underestimation of population densities of P. crenatus and P. thornei.

Assessing exposure-time treatment effect heterogeneity in stepped-wedge cluster randomized trials.

A stepped-wedge cluster randomized trial (CRT) is a unidirectional crossover study in which timings of treatment initiation for clusters are randomized. Because the timing of treatment initiation is different for each cluster, an emerging question is whether the treatment effect depends on the exposure time, namely, the time duration since the initiation of treatment. Existing approaches for assessing exposure-time treatment effect heterogeneity either assume a parametric functional form of exposure time or model the exposure time as a categorical variable, in which case the number of parameters increases with the number of exposure-time periods, leading to a potential loss in efficiency. In this article, we propose a new model formulation for assessing treatment effect heterogeneity over exposure time. Rather than a categorical term for each level of exposure time, the proposed model includes a random effect to represent varying treatment effects by exposure time. This allows for pooling information across exposure-time periods and may result in more precise average and exposure-time-specific treatment effect estimates. In addition, we develop an accompanying permutation test for the variance component of the heterogeneous treatment effect parameters. We conduct simulation studies to compare the proposed model and permutation test to alternative methods to elucidate their finite-sample operating characteristics, and to generate practical guidance on model choices for assessing exposure-time treatment effect heterogeneity in stepped-wedge CRTs.

A copula-based set-variant association test for bivariate continuous, binary or mixed phenotypes.

In genome wide association studies (GWAS), researchers are often dealing with dichotomous and non-normally distributed traits, or a mixture of discrete-continuous traits. However, most of the current region-based methods rely on multivariate linear mixed models (mvLMMs) and assume a multivariate normal distribution for the phenotypes of interest. Hence, these methods are not applicable to disease or non-normally distributed traits. Therefore, there is a need to develop unified and flexible methods to study association between a set of (possibly rare) genetic variants and non-normal multivariate phenotypes. Copulas are multivariate distribution functions with uniform margins on the [0, 1] interval and they provide suitable models to deal with non-normality of errors in multivariate association studies. We propose a novel unified and flexible copula-based multivariate association test (CBMAT) for discovering association between a genetic region and a bivariate continuous, binary or mixed phenotype. We also derive a data-driven analytic p-value procedure of the proposed region-based score-type test. Through simulation studies, we demonstrate that CBMAT has well controlled type I error rates and higher power to detect associations compared with other existing methods, for discrete and non-normally distributed traits. At last, we apply CBMAT to detect the association between two genes located on chromosome 11 and several lipid levels measured on 1477 subjects from the ASLPAC study.

Large old trees increase growth under shifting climatic constraints: Aligning tree longevity and individual growth dynamics in primary mountain spruce forests.

In a world of accelerating changes in environmental conditions driving tree growth, tradeoffs between tree growth rate and longevity could curtail the abundance of large old trees (LOTs), with potentially dire consequences for biodiversity and carbon storage. However, the influence of tree-level tradeoffs on forest structure at landscape scales will also depend on disturbances, which shape tree size and age distribution, and on whether LOTs can benefit from improved growing conditions due to climate warming. We analyzed temporal and spatial variation in radial growth patterns from ~5000 Norway spruce (Picea abies [L.] H. Karst) live and dead trees from the Western Carpathian primary spruce forest stands. We applied mixed-linear modeling to quantify the importance of LOT growth histories and stand dynamics (i.e., competition and disturbance factors) on lifespan. Finally, we assessed regional synchronization in radial growth variability over the 20th century, and modeled the effects of stand dynamics and climate on LOTs recent growth trends. Tree age varied considerably among forest stands, implying an important role of disturbance as an age constraint. Slow juvenile growth and longer period of suppressed growth prolonged tree lifespan, while increasing disturbance severity and shorter time since last disturbance decreased it. The highest age was not achieved only by trees with continuous slow growth, but those with slow juvenile growth followed by subsequent growth releases. Growth trend analysis demonstrated an increase in absolute growth rates in response to climate warming, with late summer temperatures driving the recent growth trend. Contrary to our expectation that LOTs would eventually exhibit declining growth rates, the oldest LOTs (>400 years) continuously increase growth throughout their lives, indicating a high phenotypic plasticity of LOTs for increasing biomass, and a strong carbon sink role of primary spruce forests under rising temperatures, intensifying droughts, and increasing bark beetle outbreaks.

A Comparison of Mathematical and Statistical Modeling with Longitudinal Data: An Application to Ecological Momentary Assessment of Behavior Change in Individuals with Alcohol Use Disorder.

Ecological momentary assessment (EMA) has been broadly used to collect real-time longitudinal data in behavioral research. Several analytic methods have been applied to EMA data to understand the changes of motivation, behavior, and emotions on a daily or within-day basis. One challenge when utilizing those methods on intensive datasets in the behavioral field is to understand when and why the methods are appropriate to investigate particular research questions. In this manuscript, we compared two widely used methods (generalized estimating equations and generalized linear mixed models) in behavioral research with three other less frequently used methods (Markov models, generalized linear mixed-effects Markov models, and differential equations) in behavioral research but widely used in other fields. The purpose of this manuscript is to illustrate the application of five distinct analytic methods to one dataset of intensive longitudinal data on drinking behavior, highlighting the utility of each method.

Beyond ANOVA and MANOVA for repeated measures: Advantages of generalized estimated equations and generalized linear mixed models and its use in neuroscience research.

In neuroscience research, longitudinal data are often analysed using analysis of variance (ANOVA) and multivariate analysis of variance (MANOVA) for repeated measures (rmANOVA/rmMANOVA). However, these analyses have special requirements: The variances of the differences between all possible pairs of within-subject conditions (i.e., levels of the independent variable) must be equal. They are also limited to fixed repeated time intervals and are sensitive to missing data. In contrast, other models, such as the generalized estimating equations (GEE) and the generalized linear mixed models (GLMM), suggest another way to think about the data and the studied phenomenon. Instead of forcing the data into the ANOVAs assumptions, it is possible to design a flexible/personalized model according to the nature of the dependent variable. We discuss some advantages of GEE and GLMM as alternatives to rmANOVA and rmMANOVA in neuroscience research, including the possibility of using different distributions for the parameters of the dependent variable, a better approach for different time length points, and better adjustment to missing data. We illustrate these advantages by showing a comparison between rmANOVA and GEE in a real example and providing the data and a tutorial code to reproduce these analyses in R. We conclude that GEE and GLMM may provide more reliable results when compared to rmANOVA and rmMANOVA in neuroscience research, especially in small sample sizes with unbalanced longitudinal designs with or without missing data.