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BACKGROUND: The diagnosis of failure to progress, the most common indication for intrapartum cesarean delivery, is based on the assessment of cervical dilation and station over time. Labor curves serve as references for expected changes in dilation and fetal descent. The labor curves of Friedman, Zhang et al, and others are based on time alone and derived from mothers with spontaneous labor onset. However, labor induction is now common, and clinicians also consider other factors when assessing labor progress. Labor curves that consider the use of labor induction and other factors that influence labor progress have the potential to be more accurate and closer to clinical decision-making. OBJECTIVE: This study aimed to compare the prediction errors of labor curves based on a single factor (time) or multiple clinically relevant factors using two modeling methods: mixed-effects regression, a standard statistical method, and Gaussian processes, a machine learning method. STUDY DESIGN: This was a longitudinal cohort study of changes in dilation and station based on data from 8022 births in nulliparous women with a live, singleton, vertex-presenting fetus ≥35 weeks of gestation with a vaginal delivery. New labor curves of dilation and station were generated with 10-fold cross-validation. External validation was performed using a geographically independent group. Model variables included time from the first examination in the 20 hours before delivery; dilation, effacement, and station recorded at the previous examination; cumulative contraction counts; and use of epidural anesthesia and labor induction. To assess model accuracy, differences between each models predicted value and its corresponding observed value were calculated. These prediction errors were summarized using mean absolute error and root mean squared error statistics. RESULTS: Dilation curves based on multiple parameters were more accurate than those derived from time alone. The mean absolute error of the multifactor methods was better (lower) than those of the single-factor methods (0.826 cm [95% confidence interval, 0.820-0.832] for the multifactor machine learning and 0.893 cm [95% confidence interval, 0.885-0.901] for the multifactor mixed-effects method and 2.122 cm [95% confidence interval, 2.108-2.136] for the single-factor methods; P

IntroductionMethodsResultsConclusionThe world’s population is aging rapidly, leading to increased public health and economic burdens due to age-related cardiovascular and neurodegenerative diseases. Early risk detection is essential for prevention and to improve the quality of life in elderly individuals. Plus, health risks associated with aging are not directly tied to chronological age, but are also influenced by a combination of environmental exposures. Past research has introduced the concept of “Phenotypic Age,” which combines age with biomarkers to estimate an individual’s health risk.This study explores which factors contribute most to the gap between chronological and phenotypic ages. We combined ten machine learning regression techniques applied to the NHANES dataset, containing demographic, laboratory and socioeconomic data from 41,474 patients, to identify the most important features. We then used clustering analysis and a mixed-effects model to stratify by sex, ethnicity, and education.We identified 28 demographic, biological and environmental factors related to a significant gap between phenotypic and chronological ages. Stratifying for sex, education and ethnicity, we found statistically significant differences in the outcome distributions.By showing that health risk prevention should consider both biological and sociodemographic factors, we offer a new approach to predict aging rates and potentially improve targeted prevention strategies for age-related conditions. [ABSTRACT FROM AUTHOR]

The modal verbs of necessity and obligation, a testing ground of grammatical change, have been shown to exhibit change and variation in world Englishes. Previous studies have primarily concentrated on English as a native language (ENL) and English as a second language (ESL) varieties. The present study extends this line of research and explores variation in modal verbs of necessity and obligation in English use as a Lingua Franca (ELF). Descriptive statistics indicate that ELF resembles American English and also shares similarities with ESL varieties. In addition, ELF further exhibits divergence from both ENL and ESL varieties that arises in multilingual interactions. The multivariate analysis of this study employs mixed-effects logistic regression on the use of must and have to. Integrating social and linguistic factors, this analysis exploits metadata gathered from the VOICE corpus, which has thus far been underused. The results of the inferential statistics indicate that the same sociolinguistic factors that influence the variation in ENL and ESL varieties also shape ELF grammar. These findings not only bring ELF closer to other English varieties but also demonstrate the advantage of studying ELF from a variationist sociolinguistic perspective. [ABSTRACT FROM AUTHOR]

Human immunodeficiency virus (HIV) dynamics have been the focus of epidemiological and biostatistical research during the past decades to understand the progression of acquired immunodeficiency syndrome (AIDS) in the population. Although there are several approaches for modeling HIV dynamics, one of the most popular is based on Gaussian mixed‐effects models because of its simplicity from the implementation and interpretation viewpoints. However, in some situations, Gaussian mixed‐effects models cannot (a) capture serial correlation existing in longitudinal data, (b) deal with missing observations properly, and (c) accommodate skewness and heavy tails frequently presented in patients' profiles. For those cases, mixed‐effects state‐space models (MESSM) become a powerful tool for modeling correlated observations, including HIV dynamics, because of their flexibility in modeling the unobserved states and the observations in a simple way. Consequently, our proposal considers an MESSM where the observations' error distribution is a skew‐t. This new approach is more flexible and can accommodate data sets exhibiting skewness and heavy tails. Under the Bayesian paradigm, an efficient Markov chain Monte Carlo algorithm is implemented. To evaluate the properties of the proposed models, we carried out some exciting simulation studies, including missing data in the generated data sets. Finally, we illustrate our approach with an application in the AIDS Clinical Trial Group Study 315 (ACTG‐315) clinical trial data set. [ABSTRACT FROM AUTHOR]

There is no literature on outlier‐robust parametric mixed‐effects quantile regression models for continuous proportion data as an alternative to systematically identifying and eliminating outliers. To fill this gap, we formulate a robust method by extending the recently proposed fixed‐effects quantile regression model based on the heavy‐tailed Johnson‐t$$ t $$ distribution for continuous proportion data to the mixed‐effects modeling context, using a Bayesian approach. Our proposed method is motivated by and used to model the extreme quantiles of the vitality of cushion plants to provide insights into the ecology of the system in which the plants are dominant. We conducted a simulation study to assess the new method's performance and robustness to outliers. We show that the new model has good accuracy and confidence interval coverage properties and is remarkably robust to outliers. In contrast, our study demonstrates that the current approach in the literature for modeling hierarchically structured bounded data's quantiles is susceptible to outliers, especially when modeling the extreme quantiles. We conclude that the proposed model is an appropriate robust alternative to the current approach for modeling the quantiles of correlated continuous proportions when outliers are present in the data. [ABSTRACT FROM AUTHOR]

Increasingly, mixed-effect fishery stock assessment models are being developed where deviations about functional forms of different processes are modelled as random effects and the extent of variance is estimated internal to the model. Concurrently, sampling variance parameters associated with likelihoods for fitting composition data within fisheries assessments are more often being estimated internal to the model as well. We examine the performance of stock assessment models when multiple process variance and sampling variance terms are simultaneously estimated within assessment models. We specifically examine how assessment performance is affected by the choice of composition likelihood, the degree of overdispersion in composition data, overparameterization, and modelling variation on the wrong process. In doing so, we build a simulation containing overdispersion and correlations in composition data, directional variation in catchability and/or selectivity, and estimation models which include random effects and composition likelihoods with theoretically estimable variances. Results suggest that with standard data available in fisheries assessments, process variance parameters associated with some commonly employed methods and sampling variance parameters can be simultaneously estimated internal to an assessment, and performance greatly improves with increased composition data. Our results also suggest little downside to overparameterization of selectivity and catchability when the true process is not time-varying, which largely agrees with previous research. However, when a process is truly time-varying and the assessment models time-variation on a different process, namely when selectivity is time-varying and instead natural mortality is modelled as potentially time-varying, we find a risk of severe increases in bias and decreases in confidence interval coverage for assessed quantities. This bias and decrease in coverage could, however, be partially mitigated by also modelling time-variation on the correct process. [ABSTRACT FROM AUTHOR]

An individual's size in early stages of life may be an important source of individual variation in lifetime reproductive performance, as size effects on ontogenetic development can have cascading physiological and behavioral consequences throughout life. Here, we explored how size‐at‐young influences subsequent reproductive performance in gray seals (Halichoerus grypus) using repeated encounter and reproductive data on a marked sample of 363 females that were measured for length after weaning, at ~4 weeks of age, and eventually recruited to the Sable Island breeding colony. Two reproductive traits were considered: provisioning performance (mass of weaned offspring), modeled using linear mixed effects models; and reproductive frequency (rate at which a female returns to breed), modeled using mixed effects multistate mark–recapture models. Mothers with the longest weaning lengths produced pups 8 kg heavier and were 20% more likely to breed in a given year than mothers with the shortest lengths. Correlation in body lengths between weaning and adult life stages, however, is weak: Longer pups do not grow to be longer than average adults. Thus, covariation between weaning length and future reproductive performance appears to be a carry‐over effect, where the size advantages afforded in early juvenile stages may allow enhanced long‐term performance in adulthood. [ABSTRACT FROM AUTHOR]

In this study we compare seven mathematical models of tumour growth using nonlinear mixed-effects which allows for a simultaneous fitting of multiple data and an estimation of both mean behaviour and variability. This is performed for two large datasets, a patient-derived xenograft (PDX) dataset consisting of 220 PDXs spanning six different tumour types and a cell-line derived xenograft (CDX) dataset consisting of 25 cell lines spanning eight tumour types. Comparison of the models is performed by means of visual predictive checks (VPCs) as well as the Akaike Information Criterion (AIC). Additionally, we fit the models to 500 bootstrap samples drawn from the datasets to expand the comparison of the models under dataset perturbations and understand the growth kinetics that are best fitted by each model. Through qualitative and quantitative metrics the best models are identified the effectiveness and practicality of simpler models is highlighted

Aim of study: This paper introduces comparative evaluations of artificial neural network models and regression modeling techniques based on some fitting statistics and desirable characteristics for predicting dominant height. Area of study: The data of this study were obtained from Oriental spruce (Picea orientalis L.) felled trees in even-aged and mixed Oriental spruce and Scotch pine (Pinus sylvestris L.) stands in the northeast of Türkiye. Material and methods: A total of 873 height-age pairs were obtained from Oriental spruce trees in a mixed forest stand. Nonlinear mixed-effects models (NLMEs), autoregressive models (ARM), dummy variable method (DVM), and artificial neural networks (ANNs) were compared to predict dominant height growth. Main results: The best predictive model was NLME with a single random parameter (root mean square error, RMSE: 0.68 m). The results showed that NLMEs outperformed ARM (RMSE: 1.09 m), DVM in conjunction with ARM (RMSE: 1.09 m), and ANNs (RMSE: from 1.11 to 2.40 m) in the majority of the cases. Whereas considering variations among observations by random parameter(s) significantly improved predictions of dominant height, considering correlated error terms by autoregressive correlation parameter(s) enhanced slightly the predictions. ANNs generally underperformed compared to NLMEs, ARM, and DVM with ARM. Research highlights: All regression techniques fulfilled the desirable characteristics such as sigmoidal pattern, polymorphism, multiple asymptotes, base-age invariance, and inflection point. However, ANNs could not replicate most of these features, excluding the sigmoidal pattern. Accordingly, ANNs seem insufficient to assure biological growth assumptions regarding dominant height growth.

In this study we compare seven mathematical models of tumour growth using nonlinear mixed-effects which allows for a simultaneous fitting of multiple data and an estimation of both mean behaviour and variability. This is performed for two large datasets, a patient-derived xenograft (PDX) dataset consisting of 220 PDXs spanning six different tumour types and a cell-line derived xenograft (CDX) dataset consisting of 25 cell lines spanning eight tumour types. Comparison of the models is performed by means of visual predictive checks (VPCs) as well as the Akaike Information Criterion (AIC). Additionally, we fit the models to 500 bootstrap samples drawn from the datasets to expand the comparison of the models under dataset perturbations and understand the growth kinetics that are best fitted by each model. Through qualitative and quantitative metrics the best models are identified the effectiveness and practicality of simpler models is highlighted [ABSTRACT FROM AUTHOR]

Abstract Background Longitudinal data analysis can improve our understanding of the influences on health trajectories across the life-course. There are a variety of statistical models which can be used, and their fitting and interpretation can be complex, particularly where there is a nonlinear trajectory. Our aim was to provide an accessible guide along with applied examples to using four sophisticated modelling procedures for describing nonlinear growth trajectories. Methods This expository paper provides an illustrative guide to summarising nonlinear growth trajectories for repeatedly measured continuous outcomes using (i) linear spline and (ii) natural cubic spline linear mixed-effects (LME) models, (iii) Super Imposition by Translation and Rotation (SITAR) nonlinear mixed effects models, and (iv) latent trajectory models. The underlying model for each approach, their similarities and differences, and their advantages and disadvantages are described. Their application and correct interpretation of their results is illustrated by analysing repeated bone mass measures to characterise bone growth patterns and their sex differences in three cohort studies from the UK, USA, and Canada comprising 8500 individuals and 37,000 measurements from ages 5–40 years. Recommendations for choosing a modelling approach are provided along with a discussion and signposting on further modelling extensions for analysing trajectory exposures and outcomes, and multiple cohorts. Results Linear and natural cubic spline LME models and SITAR provided similar summary of the mean bone growth trajectory and growth velocity, and the sex differences in growth patterns. Growth velocity (in grams/year) peaked during adolescence, and peaked earlier in females than males e.g., mean age at peak bone mineral content accrual from multicohort SITAR models was 12.2 years in females and 13.9 years in males. Latent trajectory models (with trajectory shapes estimated using a natural cubic spline) identified up to four subgroups of individuals with distinct trajectories throughout adolescence. Conclusions LME models with linear and natural cubic splines, SITAR, and latent trajectory models are useful for describing nonlinear growth trajectories, and these methods can be adapted for other complex traits. Choice of method depends on the research aims, complexity of the trajectory, and available data. Scripts and synthetic datasets are provided for readers to replicate trajectory modelling and visualisation using the R statistical computing software.

Abstract Background Wearable devices enable monitoring and measurement of physiological parameters over a 24-h period, and some of which exhibit circadian rhythm characteristics. However, the currently available R package cosinor could only analyze daily cross-sectional data and compare the parameters between groups with two levels. To evaluate longitudinal changes in the circadian patterns, we need to extend the model to a mixed-effect model framework, allowing for random effects and interaction between COSINOR parameters and time-varying covariates. Results We developed the cosinoRmixedeffects R package for modelling longitudinal periodic data using mixed-effects cosinor models. The model allows for covariates and interactions with the non-linear parameters MESOR, amplitude, and acrophase. To facilitate ease of use, the package utilizes the syntax and functions of the widely used emmeans package to obtain estimated marginal means and contrasts. Estimation and hypothesis testing involving the non-linear circadian parameters are carried out using bootstrapping. We illustrate the package functionality by modelling daily measurements of heart rate variability (HRV) collected among health care workers over several months. Differences in circadian patterns of HRV between genders, BMI, and during infection with SARS-CoV2 are evaluated to illustrate how to perform hypothesis testing. Conclusion cosinoRmixedeffects package provides the model fitting, estimation and hypothesis testing for the mixed-effects COSINOR model, for the linear and non-linear circadian parameters MESOR, amplitude and acrophase. The model accommodates factors with any number of categories, as well as complex interactions with circadian parameters and categorical factors.

Forest site (FS) and meteorological conditions are recognized as the main factors affecting tree growth and whole-stand sustainability. This study aims to detect the combined effects of FS and meteorological conditions on tree ring formation of Scots pine (Pinus sylvestris L.), the most common tree species in Lithuania and hemi-boreal forests of northeastern Europe. We used data on stand structure and productivity from the Lithuanian National Forest Inventory (NFI) and stem radial increment series of dominating trees during the period 1993-2012 collected since 2013. Pine stem basal area increment (BAI) was chosen as the response variable, while temperature in March (°C) and precipitation in June (mm) were used as predictor variables, as they best express the effect of climate change on Lithuanian forests. We simulated the effects on dominating pine annual increment of deciduous tree species, mainly Betula sp. and the level of soil moisture and fertility, accounting in addition for the random effects of NFI network tract, plot direction, and tree number. A nonlinear mixed-effects model explained up to 68% of the variation in the BAI of pine trees. The annual pine trees BAI increased with the increase in the proportion of deciduous trees in pine stands. Increases in temperature and precipitation in considered months reinforced this positive effect on pine BAI, especially in mature pine stands in temporarily waterlogged meso-eutrophic FSs on mineral soils. A negative effect of deciduous trees on pine stem increment was observed only in nutrient-rich eutrophic and drained peatland FSs. Forestry treatments directed towards the increase in deciduous tree proportion in the most common normal or temporarily waterlogged meso-eutrophic and oligotrophic pine stands might increase the biodiversity and productivity of pine stands, and their sustainability in future climate change scenarios.

Trial‐based cost‐effectiveness analyses (CEAs) are an important source of evidence in the assessment of health interventions. In these studies, cost and effectiveness outcomes are commonly measured at multiple time points, but some observations may be missing. Restricting the analysis to the participants with complete data can lead to biased and inefficient estimates. Methods, such as multiple imputation, have been recommended as they make better use of the data available and are valid under less restrictive Missing At Random (MAR) assumption. Linear mixed effects models (LMMs) offer a simple alternative to handle missing data under MAR without requiring imputations, and have not been very well explored in the CEA context. In this manuscript, we aim to familiarize readers with LMMs and demonstrate their implementation in CEA. We illustrate the approach on a randomized trial of antidepressants, and provide the implementation code in R and Stata. We hope that the more familiar statistical framework associated with LMMs, compared to other missing data approaches, will encourage their implementation and move practitioners away from inadequate methods. [ABSTRACT FROM AUTHOR]

Modelling tree height-diameter relationships in complex tropical rain forest ecosystems remains a challenge because of characteristics of multi-species, multi-layers, and indeterminate age composition. Effective modelling of such complex systems required innovative techniques to improve prediction of tree heights for use for aboveground biomass estimations. Therefore, in this study, deep learning algorithm (DLA) models based on artificial intelligence were trained for predicting tree heights in a tropical rain forest of Nigeria. The data consisted of 1736 individual trees representing 116 species, and measured from 52 0.25 ha sample plots. A K-means clustering was used to classify the species into three groups based on height-diameter ratios. The DLA models were trained for each species-group in which diameter at beast height, quadratic mean diameter and number of trees per ha were used as input variables. Predictions by the DLA models were compared with those developed by nonlinear least squares (NLS) and nonlinear mixed-effects (NLME) using different evaluation statistics and equivalence test. In addition, the predicted heights by the models were used to estimate aboveground biomass. The results showed that the DLA models with 100 neurons in 6 hidden layers, 100 neurons in 9 hidden layers and 100 neurons in 7 hidden layers for groups 1, 2, and 3, respectively, outperformed the NLS and NLME models. The root mean square error for the DLA models ranged from 1.939 to 3.887 m. The results also showed that using height predicted by the DLA models for aboveground biomass estimation brought about more than 30% reduction in error relative to NLS and NLME. Consequently, minimal errors were created in aboveground biomass estimation compared to those of the classical methods. [ABSTRACT FROM AUTHOR]

Correlation coefficients are often compared to investigate data across multiple research fields, as they allow investigators to determine different degrees of correlation to independent variables. Even with adequate sample size, such differences may be minor but still scientifically relevant. To date, although much effort has gone into developing methods for estimating differences across correlation coefficients, adequate tools for variable sample sizes and correlational strengths have yet to be tested. The present study evaluated four different methods for detecting the difference between two correlations and tested the adequacy of each method using simulations with multiple data structures. The methods tested were Cohen's q, Fisher's method, linear mixed-effects models (LMEM), and an ad hoc developed procedure that integrates bootstrap and effect size estimation. Correlation strengths and sample size was varied across a wide range of simulations to test the power of the methods to reject the null hypothesis (i.e., the two correlations are equal). Results showed that Fisher's method and the LMEM failed to reject the null hypothesis even in the presence of relevant differences between correlations and that Cohen's method was not sensitive to the data structure. Bootstrap followed by effect size estimation resulted in a fair, unbiased compromise for estimating quantitative differences between statistical associations and producing outputs that could be easily compared across studies. This unbiased method is easily implementable in MatLab through the bootes function, which was made available online by the author at MathWorks. [ABSTRACT FROM AUTHOR]

Unprecedented socioeconomic conditions during the COVID-19 pandemic impacted shipping. We combined ferry CO 2 emissions in Europe (from the EU-MRV) with port call data and vessel parameters, and analysed them using mixed-effects linear models with interactions. We found a generalized reduction in unitary emissions in 2020, confirming its causal relation with COVID-19. Furthermore, for larger ferries, additional and COVID-19-related reductions between 14% and 31% occurred, with the larger reductions for those built before 1999. Ferries operating in the Baltic and Mediterranean Seas experienced comparable reductions in their unitary emissions, but in the North Sea per-ship emissions decreased by an additional 18%. Per-ship emissions at berth, while showing increases or decreases depending on ferry type, did not significantly change at the fleet level. We believe that our methodology may help assess the progress of shipping toward decarbonisation in the presence of external shocks. [ABSTRACT FROM AUTHOR]

Abstract Background Norovirus has a higher level of under-reporting in England compared to other intestinal infectious agents such as Campylobacter or Salmonella, despite being recognised as the most common cause of gastroenteritis globally. In England, this under-reporting is a consequence of the frequently mild/self-limiting nature of the disease, combined with the passive surveillance system for infectious diseases reporting. We investigated heterogeneity in passive surveillance system in order to improve understanding of differences in reporting and laboratory testing practices of norovirus in England. Methods The reporting patterns of norovirus relating to age and geographical region of England were investigated using a multivariate negative binomial model. Multiple model formulations were compared, and the best performing model was determined by proper scoring rules based on one-week-ahead predictions. The reporting patterns are represented by epidemic and endemic random intercepts; values close to one and less than one imply a lower number of reports than expected in the given region and age-group. Results The best performing model highlighted atypically large and small amounts of reporting by comparison with the average in England. Endemic random intercept varied from the lowest in East Midlands in those in the under 5 year age-group (0.36, CI 0.18–0.72) to the highest in the same age group in South West (3.00, CI 1.68–5.35) and Yorkshire & the Humber (2.93, CI 1.74–4.94). Reporting by age groups showed the highest variability in young children. Conclusion We identified substantial variability in reporting patterns of norovirus by age and by region of England. Our findings highlight the importance of considering uncertainty in the design of forecasting tools for norovirus, and to inform the development of more targeted risk management approaches for norovirus disease.

Correlation coefficients are often compared to investigate data across multiple research fields, as they allow investigators to determine different degrees of correlation to independent variables. Even with adequate sample size, such differences may be minor but still scientifically relevant. To date, although much effort has gone into developing methods for estimating differences across correlation coefficients, adequate tools for variable sample sizes and correlational strengths have yet to be tested. The present study evaluated four different methods for detecting the difference between two correlations and tested the adequacy of each method using simulations with multiple data structures. The methods tested were Cohen’s q, Fisher’s method, linear mixed-effects models (LMEM), and an ad hoc developed procedure that integrates bootstrap and effect size estimation. Correlation strengths and sample size was varied across a wide range of simulations to test the power of the methods to reject the null hypothesis (i.e., the two correlations are equal). Results showed that Fisher’s method and the LMEM failed to reject the null hypothesis even in the presence of relevant differences between correlations and that Cohen’s method was not sensitive to the data structure. Bootstrap followed by effect size estimation resulted in a fair, unbiased compromise for estimating quantitative differences between statistical associations and producing outputs that could be easily compared across studies. This unbiased method is easily implementable in MatLab through the bootes function, which was made available online by the author at MathWorks.

Research on the mechanisms of desistance from substance abuse have delineated between subjective and structural mechanisms. Similarly, research on religiosity has distinguished two separate domains, behavioral and attitudinal. The present study bridges these concepts and examines the impact of spirituality and religious participation on binge drinking behavior. This paper uses a secondary data source for a sample of 1354 adolescents adjudicated for serious offenses followed over a 7-year period. The analysis employs multilevel mixed-effects logistic regression models to separate within, between, and person-context effects of subjective measure spirituality and structural measure religious participation on binge drinking. Analyses reveal that the subjective factor, spirituality, has significant within effects on the likelihood to engage in binge drinking, while religious participation was not significant at either level. Furthermore, the interaction effect was found to be significant in that increased religious participation in combination with increased spirituality can increase the likelihood of abstinence from binge drinking. Results of this study hold implications for the desistance mechanism debate within the context of religiosity and substance use. Finding suggest the subjective factor of spirituality is more influential in the desistance process of binge drinking than the structural factor of religious participation. • The concept of religiosity should be studied with at least two separate domains: behavioral and attitudinal • Findings indicate that spirituality may be more important than religious participation in desistance from binge drinking • Increases in religious participation and spirituality interact to descrease the likelihood of binge drinking • Quantitative desistance research should model interactions between subjective and structural variables [ABSTRACT FROM AUTHOR]

Background: Longitudinal data analysis can improve our understanding of the influences on health trajectories across the life-course. There are a variety of statistical models which can be used, and their fitting and interpretation can be complex, particularly where there is a nonlinear trajectory. Our aim was to provide an accessible guide along with applied examples to using four sophisticated modelling procedures for describing nonlinear growth trajectories.Methods: This expository paper provides an illustrative guide to summarising nonlinear growth trajectories for repeatedly measured continuous outcomes using (i) linear spline and (ii) natural cubic spline linear mixed-effects (LME) models, (iii) Super Imposition by Translation and Rotation (SITAR) nonlinear mixed effects models, and (iv) latent trajectory models. The underlying model for each approach, their similarities and differences, and their advantages and disadvantages are described. Their application and correct interpretation of their results is illustrated by analysing repeated bone mass measures to characterise bone growth patterns and their sex differences in three cohort studies from the UK, USA, and Canada comprising 8500 individuals and 37,000 measurements from ages 5-40 years. Recommendations for choosing a modelling approach are provided along with a discussion and signposting on further modelling extensions for analysing trajectory exposures and outcomes, and multiple cohorts.Results: Linear and natural cubic spline LME models and SITAR provided similar summary of the mean bone growth trajectory and growth velocity, and the sex differences in growth patterns. Growth velocity (in grams/year) peaked during adolescence, and peaked earlier in females than males e.g., mean age at peak bone mineral content accrual from multicohort SITAR models was 12.2 years in females and 13.9 years in males. Latent trajectory models (with trajectory shapes estimated using a natural cubic spline) identified up to four subgroups of individuals with distinct trajectories throughout adolescence.Conclusions: LME models with linear and natural cubic splines, SITAR, and latent trajectory models are useful for describing nonlinear growth trajectories, and these methods can be adapted for other complex traits. Choice of method depends on the research aims, complexity of the trajectory, and available data. Scripts and synthetic datasets are provided for readers to replicate trajectory modelling and visualisation using the R statistical computing software. [ABSTRACT FROM AUTHOR]

Background: Wearable devices enable monitoring and measurement of physiological parameters over a 24-h period, and some of which exhibit circadian rhythm characteristics. However, the currently available R package cosinor could only analyze daily cross-sectional data and compare the parameters between groups with two levels. To evaluate longitudinal changes in the circadian patterns, we need to extend the model to a mixed-effect model framework, allowing for random effects and interaction between COSINOR parameters and time-varying covariates. Results: We developed the cosinoRmixedeffects R package for modelling longitudinal periodic data using mixed-effects cosinor models. The model allows for covariates and interactions with the non-linear parameters MESOR, amplitude, and acrophase. To facilitate ease of use, the package utilizes the syntax and functions of the widely used emmeans package to obtain estimated marginal means and contrasts. Estimation and hypothesis testing involving the non-linear circadian parameters are carried out using bootstrapping. We illustrate the package functionality by modelling daily measurements of heart rate variability (HRV) collected among health care workers over several months. Differences in circadian patterns of HRV between genders, BMI, and during infection with SARS-CoV2 are evaluated to illustrate how to perform hypothesis testing. Conclusion: cosinoRmixedeffects package provides the model fitting, estimation and hypothesis testing for the mixed-effects COSINOR model, for the linear and non-linear circadian parameters MESOR, amplitude and acrophase. The model accommodates factors with any number of categories, as well as complex interactions with circadian parameters and categorical factors. [ABSTRACT FROM AUTHOR]

Relational reasoning is a complex form of human cognition involving the evaluation of relations between mental representations of information. Prior studies have modified stimulus properties of relational reasoning problems and examined differences in difficulty between different problem types. While subsets of these stimulus properties have been addressed in separate studies, there has not been a comprehensive study, to our knowledge, which investigates all of these properties in the same set of stimuli. This investigative gap has resulted in different findings across studies which vary in task design, making it challenging to determine what stimulus properties make relational reasoning—and the putative formation of mental models underlying reasoning—difficult. In this article, we present the Multidimensional Relational Reasoning Task (MRRT), a task which systematically varied an array of stimulus properties within a single set of relational reasoning problems. Using a mixed-effects framework, we demonstrate that reasoning problems containing a greater number of the premises as well as multidimensional relations led to greater task difficulty. The MRRT has been made publicly available for use in future research, along with normative data regarding the relative difficulty of each problem.

Background: Norovirus has a higher level of under-reporting in England compared to other intestinal infectious agents such as Campylobacter or Salmonella, despite being recognised as the most common cause of gastroenteritis globally. In England, this under-reporting is a consequence of the frequently mild/self-limiting nature of the disease, combined with the passive surveillance system for infectious diseases reporting. We investigated heterogeneity in passive surveillance system in order to improve understanding of differences in reporting and laboratory testing practices of norovirus in England.Methods: The reporting patterns of norovirus relating to age and geographical region of England were investigated using a multivariate negative binomial model. Multiple model formulations were compared, and the best performing model was determined by proper scoring rules based on one-week-ahead predictions. The reporting patterns are represented by epidemic and endemic random intercepts; values close to one and less than one imply a lower number of reports than expected in the given region and age-group.Results: The best performing model highlighted atypically large and small amounts of reporting by comparison with the average in England. Endemic random intercept varied from the lowest in East Midlands in those in the under 5 year age-group (0.36, CI 0.18-0.72) to the highest in the same age group in South West (3.00, CI 1.68-5.35) and Yorkshire & the Humber (2.93, CI 1.74-4.94). Reporting by age groups showed the highest variability in young children.Conclusion: We identified substantial variability in reporting patterns of norovirus by age and by region of England. Our findings highlight the importance of considering uncertainty in the design of forecasting tools for norovirus, and to inform the development of more targeted risk management approaches for norovirus disease. [ABSTRACT FROM AUTHOR]

Relational reasoning is a complex form of human cognition involving the evaluation of relations between mental representations of information. Prior studies have modified stimulus properties of relational reasoning problems and examined differences in difficulty between different problem types. While subsets of these stimulus properties have been addressed in separate studies, there has not been a comprehensive study, to our knowledge, which investigates all of these properties in the same set of stimuli. This investigative gap has resulted in different findings across studies which vary in task design, making it challenging to determine what stimulus properties make relational reasoning—and the putative formation of mental models underlying reasoning—difficult. In this article, we present the Multidimensional Relational Reasoning Task (MRRT), a task which systematically varied an array of stimulus properties within a single set of relational reasoning problems. Using a mixed-effects framework, we demonstrate that reasoning problems containing a greater number of the premises as well as multidimensional relations led to greater task difficulty. The MRRT has been made publicly available for use in future research, along with normative data regarding the relative difficulty of each problem. [ABSTRACT FROM AUTHOR]

India's sex ratio at birth (SRB) has become increasingly masculine, coinciding with a declining total fertility rate. Couples often resort to sex-selective abortion or even infanticide to ensure the birth of a son. We use household-level data from all four waves of India's National Family Health Survey (NFHS) to investigate the effect of India's demographic transition on the SRB. Mixed-effects logit regression analysis demonstrates that since the early 1990s, the probability of a third-order birth being male is decreasing in the number of sons previously born, while for second-order births, this effect does not become apparent until the 2000s. Accounting for geographic heterogeneity in the fertility transition, we find additional heterogeneity in son preference and sex selection at the village/neighborhood level. This heterogeneity has strengthened over time at both second- and third-order births and in more and less gender skewed regions of the country, suggesting potential convergence in sex ratios across India. By incorporating the most recent 2015–16 round of the NFHS, we demonstrate that previously documented trends in sex selection continue, and additionally that sex selection is increasingly occurring at lower parities as the desire for a smaller family combines with the traditional preference for sons. [ABSTRACT FROM AUTHOR]

In this article, mixed-effects state space models (MESSM, [Liu D, Lu T, Niu X-F, et al. Mixed-effects state-space models for analysis of longitudinal dynamic systems. Biometrics. 2011;67(2):476–485.]) are revisited. MESSM can be considered as an alternative to study the HIV dynamic in a longitudinal data environment, defining the mixed-effects component into state-space models setup. As in Liu et al.[Liu D, Lu T, Niu X-F, et al. Mixed-effects state-space models for analysis of longitudinal dynamic systems. Biometrics. 2011;67(2):476–485.], we consider a hierarchical structure to capture possible differences between the immune systems for different patients. We extend MESSM, allowing observational errors to follow a more flexible distribution to take account for heavy tails. Using the Bayesian paradigm, an efficient Markov Chain Monte Carlo (MCMC) algorithm based on McCausland et al. [McCausland WJ, Miller S, Pelletier D. Simulation smoothing for state.space models: A computational efficiency analysis. Comput Stat Data Anal. 2011;55(1):199–212.] is introduced for parameter and latent variables estimation. Moreover, the mixing variables obtained as a by-product of the scale mixture representation can be used to identify outliers. The methodology is illustrated using artificial and real datasets in order to investigate the properties and performance of the proposed model. [ABSTRACT FROM AUTHOR]

Multilevel Rasch models are increasingly used to estimate the relationships between test scores and student and school factors. Response data were generated to follow one-, two-, and three-parameter logistic (1PL, 2PL, 3PL) models, but the Rasch model was used to estimate the latent regression parameters. When the response functions followed 2PL or 3PL models, the proportion of variance explained in test scores by the simulated student or school predictors was estimated accurately with a Rasch model. Proportion of variance within and between schools was also estimated accurately. The regression coefficients were misestimated unless they were rescaled out of logit units. However, item-level parameters, such as DIF effects, were biased when the Rasch model was violated, similar to single-level models. [ABSTRACT FROM AUTHOR]

Height-diameter relationships are key component in tree and stand volume estimation and stand description and also management tool for forest managers. In this study, height-diameter models were developed for black pine (Pinus nigra Arnold.) plantations in Western Mediterranean Region of Turkey using the Gompertz model. Three alternative methods were evaluated: (1) fixed-effects model, (2) adjusted fixed-effects, and (3) mixed-effects model using two-fold evaluation procedure. Parameters of the adjusted fixed-effects and mixed-effects models were then calibrated using a subset of height measurements, ranging from 1 to 10 sample trees per plot. Evaluation statistics show that the mixed-effects model vastly improved height predictions compared to other models. Model performance improved with increasing sample size to calibration. However, a sample of two trees per plot seemed to be a good compromise between sampling cost and prediction accuracy and precision for Black pine plantations in Mediterranean Region of Turkey. [ABSTRACT FROM AUTHOR]

When bilinguals name pictures while in 'monolingual mode', we expect that under conditions of language-constraint and no cognate facilitation, factors influencing lexical retrieval in monolinguals ought to exert similar effects on bilinguals. To this end, we carried out a L1-only naming task on early Hindi–English bilinguals. Results of linear mixed effects analysis reveal AoA, Familiarity, Image Agreement and Codability (availability of alternate names) to be the most significant predictors of lexical retrieval speed for early bilinguals, confirming our expectations. However, we report, for the first time, a by-subject variation in Codability for bilinguals. Implications of the results are discussed in the context of current theories of bilingual lexical access and competition. In preparation for this study, Hindi norms from bilinguals for items in the Snodgrass and Vanderwart set have been established, which will be of use for stimuli selection in experimental studies involving bilinguals. [ABSTRACT FROM AUTHOR]

The mortality of trees across diameter class model is a useful tool for predicting changes in stand structure. Mortality data commonly contain a large fraction of zeros and general discrete models thus show more errors. Based on the traditional Poisson model and the negative binomial model, different forms of zero-inflated and hurdle models were applied to spruce-fir mixed forests data to simulate the number of dead trees. By comparing the residuals and Vuong test statistics, the zero-inflated negative binomial model performed best. A random effect was added to improve the model accuracy; however, the mixed-effects zero-inflated model did not show increased advantages. According to the model principle, the zero-inflated negative binomial model was the most suitable, indicating that the "0" events in this study, mainly from the sample "0", i.e., the zero mortality data, are largely due to the limitations of the experimental design and sample selection. These results also show that the number of dead trees in the diameter class is positively correlated with the number of trees in that class and the mean stand diameter, and inversely related to class size, and slope and aspect of the site. [ABSTRACT FROM AUTHOR]

• Many stock assessments use tuning algorithms when estimating recruitment. • Recruitment variance, bias-correction, and weight for composition data are often tuned. • Each tuning algorithm can be replaced by mixed-effect parameter estimation. • Using mixed effects would improve reproducibility, time-efficiency, and estimating uncertainty. • I therefore recommend improvements in stock assessment software to use mixed-effects models. Stock assessments are important to sustainable ocean management, but developing assessments remains time-consuming despite increased computation power and access to shared software. Improved efficiency in developing stock assessments could allow an increased rate of new assessments, increased attention to biological mechanisms in existing assessments, or accelerated testing of existing methods. I argue that the efficiency of the stock-assessment enterprise is hindered by a reliance upon ad hoc "tuning algorithms" that are conducted independently of standard parameter estimation. I present three examples where tuning algorithms are widely used: (1) determining the variance of recruitment, (2) bias-correcting recruitment deviations, and (3) determining the effective sample size for compositional data, and summarize why each tuning algorithm was originally developed. I then review recent research showing that each task can be replaced with parameter estimation involving random effects. Finally, I explain how model development, peer-review, and model testing would each be improved if tuning algorithms were replaced by parameter estimation, and outline the steps required to transition existing stock assessments to modern parameter estimation involving mixed effects. [ABSTRACT FROM AUTHOR]

In this paper, we investigate Bayesian generalized nonlinear mixed‐effects (NLME) regression models for zero‐inflated longitudinal count data. The methodology is motivated by and applied to colony forming unit (CFU) counts in extended bactericidal activity tuberculosis (TB) trials. Furthermore, for model comparisons, we present a generalized method for calculating the marginal likelihoods required to determine Bayes factors. A simulation study shows that the proposed zero‐inflated negative binomial regression model has good accuracy, precision, and credibility interval coverage. In contrast, conventional normal NLME regression models applied to log‐transformed count data, which handle zero counts as left censored values, may yield credibility intervals that undercover the true bactericidal activity of anti‐TB drugs. We therefore recommend that zero‐inflated NLME regression models should be fitted to CFU count on the original scale, as an alternative to conventional normal NLME regression models on the logarithmic scale. [ABSTRACT FROM AUTHOR]

Aiming to avoid the sensitivity in the parameters estimation due to atypical observations or skewness, we develop asymmetric nonlinear regression models with mixed-effects, which provide alternatives to the use of normal distribution and other symmetric distributions. Nonlinear models with mixed-effects are explored in several areas of knowledge, especially when data are correlated, such as longitudinal data, repeated measures and multilevel data, in particular, for their flexibility in dealing with measures of areas such as economics and pharmacokinetics. The random components of the present model are assumed to follow distributions that belong to scale mixtures of skew-normal (SMSN) distribution family, that encompasses distributions with light and heavy tails, such as skew-normal, skew-Student-t, skew-contaminated normal and skew-slash, as well as symmetrical versions of these distributions. For the parameters estimation we obtain a numerical solution via the EM algorithm and its extensions, and the Newton-Raphson algorithm. An application with pharmacokinetic data shows the superiority of the proposed models, for which the skew-contaminated normal distribution has shown to be the most adequate distribution. A brief simulation study points to good properties of the parameter vector estimators obtained by the maximum likelihood method. [ABSTRACT FROM AUTHOR]

• Critical forest management decisions are strongly supported by diameter predictions. • Modern modeling techniques were used for diameter predictions along the tree bole. • Levenberg-Marquardt algorithm was investigated for ANN models construction. • Diameter at 60% of the total height was identified as the best position for calibration. • Using the Levenberg-Marquardt ANN models results in accurate diameter predictions. Critical forest management decisions are strongly supported by the knowledge of forest ecosystems and their features. There is a growing trend towards using models to predict the most accurate yield projections for forest management. In this research area, features of standing trees, such as diameters along the tree bole, are of much interest. This paper is focused on the construction and evaluation of potential modeling approaches for Scots pine stem diameter prediction in north-eastern Turkey, including (1) fixed-effects, (2) mixed-effects, (3) three and five quantile regression, and (4) an artificial neural network modeling techniques. Nonlinear fixed-effects, mixed-effects, and both quantile regression models were based on a variable exponent taper equation, while the Levenberg-Marquardt algorithm was investigated for the artificial neural network (LMANN) models construction. Parameters of the tested models were calibrated by the use of several stem diameter measurements obtained at relative height positions, with models' superior performances in diameter predictions when the information of the additional diameter measured at 60% of total height, was included. Evaluation statistics show that both quantile regression and mixed-effects models improved results as compared to fixed-effects model. Overall, LMANN models achieved the best performance with higher accuracy for the Scots pine stem diameter prediction for the whole tree as well as for sections within the tree based on the ten relative height classes. Similarly to previous findings, the results of this study support that the use of mixed-effects modeling increases flexibility and efficiency of taper equations for stem diameter prediction. Moreover, the LMANN modeling approach was evaluated as superior according to its adequacy in predicting diameters along the tree stem. Therefore, the usage of the LMANNs for the tree stem diameter prediction can be a very useful tool in forest management practice and thus worth consideration. [ABSTRACT FROM AUTHOR]

Stochastic differential equations (SDEs) are increasingly used in longitudinal data analysis, compartmental models, growth modelling, and other applications in a number of disciplines. Parameter estimation, however, currently requires specialized software packages that can be difficult to use and understand. This work develops and demonstrates an approach for estimating reducible SDEs using standard nonlinear least squares or mixed-effects software. Reducible SDEs are obtained through a change of variables in linear SDEs, and are sufficiently flexible for modelling many situations. The approach is based on extending a known technique that converts maximum likelihood estimation for a Gaussian model with a nonlinear transformation of the dependent variable into an equivalent least-squares problem. A similar idea can be used for Bayesian maximum a posteriori estimation. It is shown how to obtain parameter estimates for reducible SDEs containing both process and observation noise, including hierarchical models with either fixed or random group parameters. Code and examples in R are given. Univariate SDEs are discussed in detail, with extensions to the multivariate case outlined more briefly. The use of well tested and familiar standard software should make SDE modelling more transparent and accessible. [ABSTRACT FROM AUTHOR]

Background: Advances in statistical methods and computing power have led to a renewed interest in addressing the statistical analysis challenges posed by Small-N Designs (SND). Linear mixed-effects modeling (LMEM) is a multiple regression technique that is flexible and suitable for SND and can provide standardized effect sizes and measures of statistical significance. Aims: Our primary goals are to: 1) explain LMEM at the conceptual level, situating it in the context of treatment studies, and 2) provide practical guidance for implementing LMEM in repeated measures SND. Methods & procedures: We illustrate an LMEM analysis, presenting data from a longitudinal training study of five individuals with acquired dysgraphia, analyzing both binomial (accuracy) and continuous (reaction time) repeated measurements. Outcomes & results: The LMEM analysis reveals that both spelling accuracy and reaction time improved and, for accuracy, improved significantly more quickly under a training schedule with distributed, compared to clustered, practice. We present guidance on obtaining and interpreting various effect sizes and measures of statistical significance from LMEM, and include a simulation study comparing two p-value methods for generalized LMEM. Conclusion: We provide a strong case for the application of LMEM to the analysis of training studies as a preferable alternative to visual analysis or other statistical techniques. When applied to a treatment dataset, the evidence supports that the approach holds up under the extreme conditions of small numbers of individuals, with repeated measures training data for both continuous (reaction time) and binomially distributed (accuracy) dependent measures. The approach provides standardized measures of effect sizes that are obtained through readily available and well-supported statistical packages, and provides statistically rigorous estimates of the expected average effect size of training effects, taking into account variability across both items and individuals. [ABSTRACT FROM AUTHOR]

Degradation is a primary cause of failures for many materials and products. Although stochastic processes have been widely applied to degradation data, there is a lack of efficient and accurate methods for interval estimation of model parameters and reliability characteristics given limited degradation data. Using the method of generalized pivotal quantities, this study develops interval estimation procedures for fixed-effects and mixed-effects Wiener degradation processes based on accelerated degradation test data. The fixed-effects processes are common for mature products and the mixed-effects model is capable of capturing heterogeneities in an immature product. The constructed confidence intervals are shown to have exact, or asymptotically exact, frequentist coverage probabilities. Extensive simulations are conducted to compare the proposed procedures to other competing methods, including the large sample normal approximation, and the bootstrap. The simulation results reveal that the proposed intervals have satisfactory performance in terms of the coverage probability and the average interval length. The proposed interval estimation procedures are successfully applied to accelerated degradation data from commercial white LEDs. [ABSTRACT FROM AUTHOR]

Many demographic processes vary by age and over time, but are also hypothesized to exhibit cohort-specific patterns in variation; accounting for this variation within fisheries management remains a key challenge for contemporary stock assessments. Although there is evidence for time, age, and cohort-specific patterns in the variation of various components within stock assessment (e.g., selectivity, growth), methods are sparsely documented or are lacking to simultaneously estimate autocorrelation over time, among ages, and by cohort while also quantifying residual variation. We demonstrate an approach that facilitates the simultaneous estimation of autocorrelation for time, age, and cohort correlations, and provide two options to estimate the pointwise variance of this process (termed conditional and marginal variance). Using eastern Bering Sea walleye pollock (Gadus chalcogrammus) as a case-study, we develop factorial model formulations to demonstrate differences in predicted weight-at-age values from models that estimate different combinations of correlation parameters along three axes (age, year, cohort). We show that traditional model selection tools can be used to identify the relative evidence for, and magnitude of, age, time, and cohort correlations, and demonstrate that this method can be easily integrated as a routine option within next-generation stock assessments. Code to replicate our analysis is provided in a GitHub repository (https://github.com/chengmatt/GMRF%5fWAA), and includes a Template Model Builder function for assembling the precision matrix to facilitate easy adoption in other software packages. • Demographic and fishery processes vary across ages, years, and cohorts. • We propose an approach to estimate partial correlations across ages, years, and cohorts with residual variation. • We use eastern Bering Sea walleye pollock as a case-study to illustrate the use of our method. • Assessment components suited to this approach include survival, maturity, growth, and fishing mortality (and selectivity). • Our method facilities the estimation of correlated processes in next-generation assessments [ABSTRACT FROM AUTHOR]

Leaf area influences dry matter production of trees, as well as the growth of trees and forest stands. The accurate estimation of leaf area plays an important role in analyzing the growth of trees and forest stands. Based on data of 76 Larix olgensis trees in a plantation of Heilongjiang Province, predicting models of branch leaf area ( BLA) and crown leaf area (CLA) were constructed, respectively. The results showed that a form of lnBLA = β1 +(β2 + b2) lnBD + (β3+b3) lnRDINC +β4lnDBH+ β5lnHT/DBH+(β6+b6)lnCR was selected as the optimal BLA mixed-effect model with the consideration of tree-level random effects, composed of three random-effect on lnBD, lnRDINC and lnCR (βi represented model fixed parameters, bi represented model random-effect parameters, BD was branch diameter, RDINC was the relative depth into crown from tree apex, DBH was tree diameter at breast height, HT/DBH represented the ratio of tree height to DBH, and CR represented the ratio of crown length to tree height). The adjusted coefficient of determination (Ra°), residual mean squares error (RMSE), mean error (ME), mean absolute error (MAE) and precision estimation (P) of the optimal BLA mixed model were 0.90, 0.5477, -0.03, 0.24 and 91%, respectively, indicating the model had a good performance in predicting. The CLA was calculated by predicted values of all branches based on developed BLA model and the final form of CLA model was as follows: lnCLA = γ0 + γ1, lnDBH+γ2 CR (γi, model parameters). Results of likelihood ratio test ( P >0.05) showed that plot-level random effect had no influence on the model performance, which can be ignored. The CLA model got a good-fitting effect with R² and RMSE being 0.87 and 0.3847, respectively. The CLA predicting model developed in this study could provide a good prediction of CLA for L. olgensis trees and provided a theoretical basis for the research on distribution of leaf area and photosynthesis. [ABSTRACT FROM AUTHOR]

Abstract: Existing studies have generally measured collective efficacy by combining survey respondents’ ratings of their local area into an overall summary for each neighborhood. Naturally, this approach results in a substantive focus on the variation in average levels of collective efficacy between neighborhoods. In this article, we focus on the variation in consensus of collective efficacy judgments. To account for differential consensus among neighborhoods, we use a mixed‐effects location‐scale model, with variability in the consensus of judgments treated as an additional neighborhood‐level random effect. Our results show that neighborhoods in London differ, not just in their average levels of collective efficacy but also in the extent to which residents agree with one another in their assessments. In accord with findings for U.S. cities, our results show that consensus in collective efficacy assessments is affected by the ethnic composition of neighborhoods. Additionally, we show that heterogeneity in collective efficacy assessments is consequential, with higher levels of criminal victimization, worry about crime, and risk avoidance behavior in areas where collective efficacy consensus is low. [ABSTRACT FROM AUTHOR]

Summary: A unified statistical methodology of sample size determination is developed for hierarchical designs that are frequently used in many areas, particularly in medical and health research studies. The solid foundation of the proposed methodology opens a new horizon for power analysis in presence of various conditions. Important features such as joint significance testing, unequal allocations of clusters across intervention groups, and differential attrition rates over follow up time points are integrated to address some useful questions that investigators often encounter while conducting such studies. Proposed methodology is shown to perform well in terms of maintaining type I error rates and achieving the target power under various conditions. Proposed method is also shown to be robust with respect to violation of distributional assumptions of random‐effects. [ABSTRACT FROM AUTHOR]