Likelihood Ratio, Score, and Wald Tests in a Constrained Parameter Space

Modeling item-level heterogeneous treatment effects: A tutorial with the glmer function from the lme4 package in R

Recent advancements in education scholarship have introduced Item Response Theory (IRT) models to address treatment heterogeneity at the assessment item level. These models for item-level heterogeneous treatment effects (IL-HTE) enable detailed analyses of treatments that may have varying impacts on individual items within an assessment. This article offers a comprehensive tutorial for applied researchers interested in implementing IL-HTE analysis in R, utilizing the lme4 package. Using empirical data from a second-grade reading comprehension assessment as a running example, this tutorial emphasizes model-building strategies, interpretation techniques, visualization methods, and extensions. By following this tutorial, researchers will gain practical insights into utilizing IL-HTE analysis for enhanced understanding and interpretation of treatment effects at the item level.

Statistical Genetic Approaches to Investigate Genotype-by-Environment Interaction: Review and Novel Extension of Models

Statistical genetic models of genotype-by-environment (G×E) interaction can be divided into two general classes, one on G×E interaction in response to dichotomous environments (e.g., sex, disease-affection status, or presence/absence of an exposure) and the other in response to continuous environments (e.g., physical activity, nutritional measurements, or continuous socioeconomic measures). Here we develop a novel model to jointly account for dichotomous and continuous environments. We develop the model in terms of a joint genotype-by-sex (for the dichotomous environment) and genotype-by-social determinants of health (SDoH; for the continuous environment). Using this model, we show how a depression variable, as measured by the Beck Depression Inventory-II survey instrument, is not only underlain by genetic effects (as has been reported elsewhere) but is also significantly determined by joint G×Sex and G×SDoH interaction effects. This model has numerous applications leading to potentially transformative research on the genetic and environmental determinants underlying complex diseases.

Nonlinear Regression Modelling: A Primer with Applications and Caveats

Use of nonlinear statistical methods and models are ubiquitous in scientific research. However, these methods may not be fully understood, and as demonstrated here, commonly-reported parameter p-values and confidence intervals may be inaccurate. The gentle introduction to nonlinear regression modelling and comprehensive illustrations given here provides applied researchers with the needed overview and tools to appreciate the nuances and breadth of these important methods. Since these methods build upon topics covered in first and second courses in applied statistics and predictive modelling, the target audience includes practitioners and students alike. To guide practitioners, we summarize, illustrate, develop, and extend nonlinear modelling methods, and underscore caveats of Wald statistics using basic illustrations and give key reasons for preferring likelihood methods. Parameter profiling in multiparameter models and exact or near-exact versus approximate likelihood methods are discussed and curvature measures are connected with the failure of the Wald approximations regularly used in statistical software. The discussion in the main paper has been kept at an introductory level and it can be covered on a first reading; additional details given in the Appendices can be worked through upon further study. The associated online Supplementary Information also provides the data and R computer code which can be easily adapted to aid researchers to fit nonlinear models to their data.

Problems of Domain Factors with Small Factor Loadings in Bi-Factor Models

Many measurement designs produce domain factors with small variances and factor loadings. The current study investigates the cause, prevalence, and problematic consequences of such domain factors. We collected a meta-analytic sample of empirical applications, conducted a simulation study on statistical power and estimation precision, and provide a reanalysis of an empirical example. The meta-analysis shows that about a quarter of all standardized domain factor loadings is in the range of - .2 < λ < .2 and about a third of all domains is measured by five or fewer indicators, resulting in small factor variances. The simulation study examines the associated difficulties concerning statistical power, trait recovery, irregular estimates, and estimation precision for a range of such realistic cases. The empirical example illustrates the challenge to develop measures that produce clearly interpretable domain factors. Study planning and interpretation need to take the (expected) sum of squared factor loadings per domain factor into account. This is relevant even if influences of domain factors are desired to be small, and equally applies to different model variants. We propose several strategies for how researchers may better unlock the bifactor model's full potential and clarify its interpretation.

An investigation of non-informative priors for Bayesian dose-response modeling

Toxicology analyses are built around dose-response modeling, and increasingly these methodologies utilize Bayesian estimation techniques. Bayesian estimation is unique because it includes prior distributional information in the analysis, which may impact the dose-response estimate meaningfully. As such analyses are often used for human health risk assessment, the practitioner must understand the impact of adding prior information to the dose-response study. One proposal in the literature is the use of the flat uniform prior distribution, which places a uniform prior probability over the dose-response model's parameters for a chosen range of values. Though the motivation of such a prior distribution is laudable in that it is most like maximum likelihood estimation seeking unbiased estimates of the dose-response, one can show that such priors add information and may introduce unexpected biases into the analysis. This manuscript shows through numerous empirical examples why prior distributions that are non-informative across all endpoints of interest do not exist for dose-response models; that is, other quantities of interest will be informed by choosing one inferential quantity not informed.

Bivariate logistic regression model diagnostics applied to analysis of outlier cancer patients with comorbid diabetes and hypertension in Malawi

The joint occurrence of diabetes and hypertension conditions in a patient is common. The two diseases share a number of risk factors, and are hence usually modelled concurrently using bivariate logistic regression. However, the postestimation assessment for the model, such as analysis of outlier observations, is seldom carried out. In this article, we apply outlier detection methods for multivariate data models to study characteristics of cancer patients with joint outlying diabetes and hypertension outcomes observed from among 398 randomly selected cancer patients at Queen Elizabeth and Kamuzu Central Hospitals in Malawi. We used R software version 4.2.2 to perform the analyses and STATA version 12 for data cleaning. The results showed that one patient was an outlier to the bivariate diabetes and hypertension logit model. The patient had both diabetes and hypertension and was based in rural area of the study population, where it was observed that comorbidity of the two diseases was uncommon. We recommend thorough analysis of outlier patients to comorbid diabetes and hypertension before rolling out interventions for managing the two diseases in cancer patients to avoid misaligned interventions. Future research could perform the applied diagnostic assessments for the bivariate logit model on a wider and larger dataset of the two diseases.

scShapes: a statistical framework for identifying distribution shapes in single-cell RNA-sequencing data

BACKGROUND

Single-cell RNA sequencing (scRNA-seq) methods have been advantageous for quantifying cell-to-cell variation by profiling the transcriptomes of individual cells. For scRNA-seq data, variability in gene expression reflects the degree of variation in gene expression from one cell to another. Analyses that focus on cell-cell variability therefore are useful for going beyond changes based on average expression and, instead, identifying genes with homogeneous expression versus those that vary widely from cell to cell.

RESULTS

We present a novel statistical framework, scShapes, for identifying differential distributions in single-cell RNA-sequencing data using generalized linear models. Most approaches for differential gene expression detect shifts in the mean value. However, as single-cell data are driven by overdispersion and dropouts, moving beyond means and using distributions that can handle excess zeros is critical. scShapes quantifies gene-specific cell-to-cell variability by testing for differences in the expression distribution while flexibly adjusting for covariates if required. We demonstrate that scShapes identifies subtle variations that are independent of altered mean expression and detects biologically relevant genes that were not discovered through standard approaches.

CONCLUSIONS

This analysis also draws attention to genes that switch distribution shapes from a unimodal distribution to a zero-inflated distribution and raises open questions about the plausible biological mechanisms that may give rise to this, such as transcriptional bursting. Overall, the results from scShapes help to expand our understanding of the role that gene expression plays in the transcriptional regulation of a specific perturbation or cellular phenotype. Our framework scShapes is incorporated into a Bioconductor R package (https://www.bioconductor.org/packages/release/bioc/html/scShapes.html).

stepRNA: Identification of Dicer cleavage signatures and passenger strand lengths in small RNA sequences

The enzyme Dicer is a component of many small RNA (sRNA) pathways involved in RNA processing for post-transcriptional regulation, anti-viral response and control of transposable elements. Cleavage of double-stranded RNA by Dicer produces a signature overhanging sequence at the 3’ end of the sRNA sequence relative to a complementary passenger strand in a RNA duplex. There is a need for reliable tools to computationally search for Dicer cleavage signatures to help characterise families of sRNAs. This is increasingly important due to the rising popularity of sRNA sequencing, especially in non-model organisms. Here, we present stepRNA, a fast, local tool that identifies (i) overhang signatures strongly indicative of Dicer cleavage in RNA sequences, and (ii) the length of the passenger strand in sRNAs duplexes. We demonstrate the use of stepRNA with simulated and biological datasets to detect Dicer cleavage signatures in experimentally validated examples. Compared to currently available tools, stepRNA is more accurate, requires only sRNA sequence data rather than a reference genome, and provides information about other important features such as passenger strand length. stepRNA is freely available at https://github.com/Vicky-Hunt-Lab/stepRNA and is easily installable.

Generalized linear mixed-effects models for studies using different sets of stimuli across conditions

A non-repeated item (NRI) design refers to an experimental design in which items used in one level of experimental conditions are not repeatedly used at other levels. Recent literature has suggested the use of generalized linear mixed-effects models (GLMMs) for experimental data analysis, but the existing specification of GLMMs does not account for all possible dependencies among the outcomes in NRI designs. Therefore, the current study proposed a GLMM with a level-specific item random effect for NRI designs. The hypothesis testing performance of the newly proposed model was evaluated via a simulation study to detect the experimental condition effect. The model with a level-specific item random effect performed better than the existing model in terms of power when the variance of the item effect was heterogeneous. Based on these results, we suggest that experimental researchers using NRI designs consider setting a level-specific item random effect in the model.

Genomic prediction of hybrid performance: comparison of the efficiency of factorial and tester designs used as training sets in a multiparental connected reciprocal design for maize silage

Calibrating a genomic selection model on a sparse factorial design rather than on tester designs is advantageous for some traits, and equivalent for others. In maize breeding, the selection of the candidate inbred lines is based on topcross evaluations using a limited number of testers. Then, a subset of single-crosses between these selected lines is evaluated to identify the best hybrid combinations. Genomic selection enables the prediction of all possible single-crosses between candidate lines but raises the question of defining the best training set design. Previous simulation results have shown the potential of using a sparse factorial design instead of tester designs as the training set. To validate this result, a 363 hybrid factorial design was obtained by crossing 90 dent and flint inbred lines from six segregating families. Two tester designs were also obtained by crossing the same inbred lines to two testers of the opposite group. These designs were evaluated for silage in eight environments and used to predict independent performances of a 951 hybrid factorial design. At a same number of hybrids and lines, the factorial design was as efficient as the tester designs, and, for some traits, outperformed them. All available designs were used as both training and validation set to evaluate their efficiency. When the objective was to predict single-crosses between untested lines, we showed an advantage of increasing the number of lines involved in the training set, by (1) allocating each of them to a different tester for the tester design, or (2) reducing the number of hybrids per line for the factorial design. Our results confirm the potential of sparse factorial designs for genomic hybrid breeding.

Using a mixed-effect model with a parameter-space of heterogenous dimension to evaluate whether accountable care organizations are associated with greater uniformity across constituent practices

Accountable care organization (ACO) legislation was designed to improve patient outcomes by inducing greater coordination of care and adoption of best practices. Therefore, it is of interest to assess whether greater uniformity occurs among practices comprising an ACO post ACO formation. We develop a mixed-effect model with a difference-in-difference design to evaluate the effect of a patient receiving care from an ACO on patient outcomes and adapt this model to examine whether an ACO is associated with increased uniformity across its constituent practices. The task is complicated by the organizations within an ACO forming an additional layer in the multilevel model, due to medical practices and hospitals that form an ACOs being nested within the ACO, making the number of levels of the model variable and the dimension of the parameter space time-varying. We develop the model and a procedure for testing the hypothesis that ACO formation was associated with increased uniformity among its constituent practices. We apply our procedure to a cohort of medicare beneficiaries followed over 2009-2014. Although there is extensive heterogeneity of becoming an ACOs across practices, we find that the formation of an ACO appears to be associated with greater uniformity of patient outcomes among its constituent practices.

Risk difference tests for stratified binary data under Dallal's model

In medical studies, the binary data is often encountered when the paired organs or body parts receive treatment. However, the same treatment may lead to different therapeutic effects based on the stratified factors or confounding effects. Under Dallal's model, the paper proposes the homogeneity test of risk difference to determine the necessity of stratified treatment. When the stratification is not necessary, common test is introduced to investigate if the risk difference is equal to a fixed constant between two groups. Several statistical tests are derived to analyze homogeneity and common hypotheses, respectively. Monte Carlo simulations show that the score tests behave well in both of hypotheses. Wald-type and Rosner's statistics are always liberal but have higher empirical powers. Especially, the likelihood ratio statistic is better for the homogeneity test in the case of smaller data with larger strata. Two real examples are provided to illustrate the effectiveness of the proposed methods in ankle instability and otolaryngology studies.

Modification Indices for Diagnostic Classification Models

Diagnostic classification models (DCMs) are psychometric models for evaluating a student's mastery of the essential skills in a content domain based upon their responses to a set of test items. Currently, diagnostic model and/or Q-matrix misspecification is a known problem with limited avenues for remediation. To address this problem, this paper defines a one-sided score statistic that is a computationally efficient method for detecting under-specification at the item level of both the Q-matrix and the model parameters of the particular DCM chosen in an analysis. This method is analogous to the modification indices widely used in structural equation modeling. The results of a simulation study show the Type I error rate of modification indices for DCMs are acceptably close to the nominal significance level when the appropriate mixture χ2 reference distribution is used. The simulation results indicate that modification indices are very powerful in the detection of an under-specified Q-matrix and have ample power to detect the omission of model parameters in large samples or when the items are highly discriminating. An application of modification indices for DCMs to an analysis of response data from a large-scale administration of a diagnostic test demonstrates how they can be useful in diagnostic model refinement.

Two-level moderated mediation models with single-level data and new measures of effect sizes

This article proposes a two-level moderated mediation (2moME) model with single level data, and develops measures to quantify the moderated mediation (moME) effect sizes for both the conventional moME model and the 2moME model. A Bayesian approach is developed to estimate and test moME effects and the corresponding effect sizes (ES). Monte Carlo results indicate that (1) the 2moME model yields more accurate estimates of the parameters than the conventional moME model; (2) the 95% credibility interval following the 2moME model covers the moME effects and the ESs more accurately than that following the conventional moME model; and (3) statistical tests for the existence of the moME effects with the 2moME model are more reliable in controlling type I errors than those with the conventional moME model, especially under heteroscedasticity conditions. In addition, the developed measures of ES are more interpretable, and directly answer the questions regarding the extent to which a moderator can account for the change of the mediation effect between the predictor and the outcome variable through the mediator variable. An empirical example illustrates the application of the 2moME model and the ES measures.

An extension of the mixed-effects growth model that considers between-person differences in the within-subject variance and the autocorrelation

Experience sampling methods have led to a significant increase in the availability of intensive longitudinal data. Typically, this type of data is analyzed with a mixed-effects model that allows to examine hypotheses concerning between-person differences in the mean structure by including multiple random effects per individual (eg, random intercept and random slopes). Here, we describe an extension of this model that-in addition to the random effects for the mean structure-also includes a random effect for the within-subject variance and a random effect for the autocorrelation. After the description of the model, we show how its parameters can be efficiently estimated using a marginal maximum likelihood (ML) approach. We then illustrate the model using a real data example. We also present the results of a small simulation study in which we compare the ML approach with a Bayesian estimation approach.

An IBD-based mixed model approach for QTL mapping in multiparental populations

The identity-by-descent (IBD)-based mixed model approach introduced in this study can detect quantitative trait loci (QTLs) referring to the parental origin and simultaneously account for multilevel relatedness of individuals within and across families. This unified approach is proved to be a powerful approach for all kinds of multiparental population (MPP) designs. Multiparental populations (MPPs) have become popular for quantitative trait loci (QTL) detection. Tools for QTL mapping in MPPs are mostly developed for specific MPPs and do not generalize well to other MPPs. We present an IBD-based mixed model approach for QTL mapping in all kinds of MPP designs, e.g., diallel, Nested Association Mapping (NAM), and Multiparental Advanced Generation Intercross (MAGIC) designs. The first step is to compute identity-by-descent (IBD) probabilities using a general Hidden Markov model framework, called reconstructing ancestry blocks bit by bit (RABBIT). Next, functions of IBD information are used as design matrices, or genetic predictors, in a mixed model approach to estimate variance components for multiallelic genetic effects associated with parents. Family-specific residual genetic effects are added, and a polygenic effect is structured by kinship relations between individuals. Case studies of simulated diallel, NAM, and MAGIC designs proved that the advanced IBD-based multi-QTL mixed model approach incorporating both kinship relations and family-specific residual variances (IBD.MQMkin_F) is robust across a variety of MPP designs and allele segregation patterns in comparison to a widely used benchmark association mapping method, and in most cases, outperformed or behaved at least as well as other tools developed for specific MPP designs in terms of mapping power and resolution. Successful analyses of real data cases confirmed the wide applicability of our IBD-based mixed model methodology.

Effects of semantic reinforcement, semantic discrimination, and affix frequency on new word learning in skilled and less skilled readers in Grades 6 to 12

Two approaches to word learning were investigated in 1214 6th- to 12th-grade students. Definitions were provided, followed either by two sentences that were semantically correct exemplars, called semantic reinforcement learning, or by one correct sentence and a contrasting incorrect sentence (i.e., example followed by a structurally aligned non-example), called semantic discrimination learning. Type of learning was blocked, and examples and non-examples were explained. Effects of affix frequency were also assessed. Students were taught words, followed by assessments of abilities to recall the meanings of the words immediately after learning them, to choose the correct words among distractors to match given definitions after all words had been instructed, and to judge the semantic veracity of new sentences containing taught words 1-3 days later. Explanatory item response models were used to predict word learning using student and item characteristics along with their interactions. Few grade-related differences emerged. Higher-frequency affixes were generally beneficial for learning and retention across comprehension skill levels and measures. Immediate recall of word meanings was facilitated by semantic reinforcement learning. In contrast, performance after all the words had been instructed was facilitated by semantic discrimination learning, but only for more highly skilled comprehenders. The ability to learn the meanings of new words accounted for unique variance on one measure of reading comprehension, controlling for decoding, previously acquired vocabulary knowledge, and working memory. Results are discussed with reference to models of vocabulary learning and implications for vocabulary instruction for adolescents.

Testing inflated zeros in binomial regression models

Binomial regression models are commonly applied to proportion data such as those relating to the mortality and infection rates of diseases. However, it is often the case that the responses may exhibit excessive zeros; in such cases a zero-inflated binomial (ZIB) regression model can be applied instead. In practice, it is essential to test if there are excessive zeros in the outcome to help choose an appropriate model. The binomial models can yield biased inference if there are excessive zeros, while ZIB models may be unnecessarily complex and hard to interpret, and even face convergence issues, if there are no excessive zeros. In this paper, we develop a new test for testing zero inflation in binomial regression models by directly comparing the amount of observed zeros with what would be expected under the binomial regression model. A closed form of the test statistic, as well as the asymptotic properties of the test, is derived based on estimating equations. Our systematic simulation studies show that the new test performs very well in most cases, and outperforms the classical Wald, likelihood ratio, and score tests, especially in controlling type I errors. Two real data examples are also included for illustrative purpose.

Poisson–Tweedie mixed-effects model: A flexible approach for the analysis of longitudinal RNA-seq data

We present a new modelling approach for longitudinal overdispersed counts that is motivated by the increasing availability of longitudinal RNA-sequencing experiments. The distribution of RNA-seq counts typically exhibits overdispersion, zero-inflation and heavy tails; moreover, in longitudinal designs repeated measurements from the same subject are typically (positively) correlated. We propose a generalized linear mixed model based on the Poisson–Tweedie distribution that can flexibly handle each of the aforementioned features of longitudinal overdispersed counts. We develop a computational approach to accurately evaluate the likelihood of the proposed model and to perform maximum likelihood estimation. Our approach is implemented in the R package ptmixed, which can be freely downloaded from CRAN. We assess the performance of ptmixed on simulated data, and we present an application to a dataset with longitudinal RNA-sequencing measurements from healthy and dystrophic mice. The applicability of the Poisson–Tweedie mixed-effects model is not restricted to longitudinal RNA-seq data, but it extends to any scenario where non-independent measurements of a discrete overdispersed response variable are available.

Sample size calculations for the differential expression analysis of RNA-seq data using a negative binomial regression model

High throughput RNA sequencing (RNA-seq) technology is increasingly used in disease-related biomarker studies. A negative binomial distribution has become the popular choice for modeling read counts of genes in RNA-seq data due to over-dispersed read counts. In this study, we propose two explicit sample size calculation methods for RNA-seq data using a negative binomial regression model. To derive these new sample size formulas, the common dispersion parameter and the size factor as an offset via a natural logarithm link function are incorporated. A two-sided Wald test statistic derived from the coefficient parameter is used for testing a single gene at a nominal significance level 0.05 and multiple genes at a false discovery rate 0.05. The variance for the Wald test is computed from the variance-covariance matrix with the parameters estimated from the maximum likelihood estimates under the unrestricted and constrained scenarios. The performance and a side-by-side comparison of our new formulas with three existing methods with a Wald test, a likelihood ratio test or an exact test are evaluated via simulation studies. Since other methods are much computationally extensive, we recommend our M1 method for quick and direct estimation of sample sizes in an experimental design. Finally, we illustrate sample sizes estimation using an existing breast cancer RNA-seq data.

A statistical measure for the skewness of X chromosome inactivation based on case-control design

BACKGROUND

Skewed X chromosome inactivation (XCI), which is a non-random process, is frequently observed in both healthy and affected females. Furthermore, skewed XCI has been reported to be related to many X-linked diseases. However, no statistical method is available in the literature to measure the degree of the skewness of XCI for case-control design. Therefore, it is necessary to develop methods for such a task.

RESULTS

In this article, we first proposed a statistical measure for the degree of XCI skewing by using a case-control design, which is a ratio of two logistic regression coefficients after a simple reparameterization. Based on the point estimate of the ratio, we further developed three types of confidence intervals (the likelihood ratio, Fieller's and delta methods) to evaluate its variation. Simulation results demonstrated that the likelihood ratio method and the Fieller's method have more accurate coverage probability and more balanced tail errors than the delta method. We also applied these proposed methods to analyze the Graves' disease data for their practical use and found that rs3827440 probably undergoes a skewed XCI pattern with 68.7% of cells in heterozygous females having the risk allele T active, while the other 31.3% of cells keeping the normal allele C active.

CONCLUSIONS

For practical application, we suggest using the Fieller's method in large samples due to the non-iterative computation procedure and using the LR method otherwise for its robustness despite its slightly heavy computational burden.

A comprehensive overview of genomic imprinting in breast and its deregulation in cancer

Genomic imprinting plays an important role in growth and development. Loss of imprinting (LOI) has been found in cancer, yet systematic studies are impeded by data-analytical challenges. We developed a methodology to detect monoallelically expressed loci without requiring genotyping data, and applied it on The Cancer Genome Atlas (TCGA, discovery) and Genotype-Tissue expression project (GTEx, validation) breast tissue RNA-seq data. Here, we report the identification of 30 putatively imprinted genes in breast. In breast cancer (TCGA), HM13 is featured by LOI and expression upregulation, which is linked to DNA demethylation. Other imprinted genes typically demonstrate lower expression in cancer, often associated with copy number variation and aberrant DNA methylation. Downregulation in cancer frequently leads to higher relative expression of the (imperfectly) silenced allele, yet this is not considered canonical LOI given the lack of (absolute) re-expression. In summary, our novel methodology highlights the massive deregulation of imprinting in breast cancer.

Autoregressive Generalized Linear Mixed Effect Models with Crossed Random Effects: An Application to Intensive Binary Time Series Eye-Tracking Data

As a method to ascertain person and item effects in psycholinguistics, a generalized linear mixed effect model (GLMM) with crossed random effects has met limitations in handing serial dependence across persons and items. This paper presents an autoregressive GLMM with crossed random effects that accounts for variability in lag effects across persons and items. The model is shown to be applicable to intensive binary time series eye-tracking data when researchers are interested in detecting experimental condition effects while controlling for previous responses. In addition, a simulation study shows that ignoring lag effects can lead to biased estimates and underestimated standard errors for the experimental condition effects.

A new and intuitive test for zero modification

Abstract:

While there do exist several statistical tests for detecting zero modification in count data regression models, these rely on asymptotical results and do not transparently distinguish between zero inflation and zero deflation. In this manuscript, a novel non-asymptotic test is introduced which makes direct use of the fact that the distribution of the number of zeros under the null hypothesis of no zero modification can be described by a Poisson-binomial distribution. The computation of critical values from this distribution requires estimation of the mean parameter under the null hypothesis, for which a hybrid estimator involving a zero-truncated mean estimator is proposed. Power and nominal level attainment rates of the new test are studied, which turn out to be very competitive to those of the likelihood ratio test. Illustrative data examples are provided.

Evaluating the effects of rater and subject factors on measures of association

Large-scale agreement studies are becoming increasingly common in medical settings to gain better insight into discrepancies often observed between experts' classifications. Ordered categorical scales are routinely used to classify subjects' disease and health conditions. Summary measures such as Cohen's weighted kappa are popular approaches for reporting levels of association for pairs of raters' ordinal classifications. However, in large-scale studies with many raters, assessing levels of association can be challenging due to dependencies between many raters each grading the same sample of subjects' results and the ordinal nature of the ratings. Further complexities arise when the focus of a study is to examine the impact of rater and subject characteristics on levels of association. In this paper, we describe a flexible approach based upon the class of generalized linear mixed models to assess the influence of rater and subject factors on association between many raters' ordinal classifications. We propose novel model-based measures for large-scale studies to provide simple summaries of association similar to Cohen's weighted kappa while avoiding prevalence and marginal distribution issues that Cohen's weighted kappa is susceptible to. The proposed summary measures can be used to compare association between subgroups of subjects or raters. We demonstrate the use of hypothesis tests to formally determine if rater and subject factors have a significant influence on association, and describe approaches for evaluating the goodness-of-fit of the proposed model. The performance of the proposed approach is explored through extensive simulation studies and is applied to a recent large-scale cancer breast cancer screening study.

How Much Rugby is Too Much? A Seven-Season Prospective Cohort Study of Match Exposure and Injury Risk in Professional Rugby Union Players

INTRODUCTION

Numerous studies have documented the incidence and nature of injuries in professional rugby union, but few have identified specific risk factors for injury in this population using appropriate statistical methods. In particular, little is known about the role of previous short-term or longer-term match exposures in current injury risk in this setting.

OBJECTIVES

Our objective was to investigate the influence that match exposure has upon injury risk in rugby union.

METHOD

We conducted a seven-season (2006/7-2012/13) prospective cohort study of time-loss injuries in 1253 English premiership professional players. Players' 12-month match exposure (number of matches a player was involved in for ≥20 min in the preceding 12 months) and 1-month match exposure (number of full-game equivalent [FGE] matches in preceding 30 days) were assessed as risk factors for injury using a nested frailty model and magnitude-based inferences.

RESULTS

The 12-month match exposure was associated with injury risk in a non-linear fashion; players who had been involved in fewer than ≈15 or more than ≈35 matches over the preceding 12-month period were more susceptible to injury. Monthly match exposure was linearly associated with injury risk (hazard ratio [HR]: 1.14 per 2 standard deviation [3.2 FGE] increase, 90% confidence interval [CI] 1.08-1.20; likely harmful), although this effect was substantially attenuated for players in the upper quartile for 12-month match exposures (>28 matches).

CONCLUSION

A player's accumulated (12-month) and recent (1-month) match exposure substantially influences their current injury risk. Careful attention should be paid to planning the workloads and monitoring the responses of players involved in: (1) a high (>≈35) number of matches in the previous year, (2) a low (<≈15) number of matches in the previous year, and (3) a low-moderate number of matches in previous year but who have played intensively in the recent past. These findings make a major contribution to evidence-based policy decisions regarding match workload limits in professional rugby union.

Assessing the influence of rater and subject characteristics on measures of agreement for ordinal ratings

Widespread inconsistencies are commonly observed between physicians' ordinal classifications in screening tests results such as mammography. These discrepancies have motivated large-scale agreement studies where many raters contribute ratings. The primary goal of these studies is to identify factors related to physicians and patients' test results, which may lead to stronger consistency between raters' classifications. While ordered categorical scales are frequently used to classify screening test results, very few statistical approaches exist to model agreement between multiple raters. Here we develop a flexible and comprehensive approach to assess the influence of rater and subject characteristics on agreement between multiple raters' ordinal classifications in large-scale agreement studies. Our approach is based upon the class of generalized linear mixed models. Novel summary model-based measures are proposed to assess agreement between all, or a subgroup of raters, such as experienced physicians. Hypothesis tests are described to formally identify factors such as physicians' level of experience that play an important role in improving consistency of ratings between raters. We demonstrate how unique characteristics of individual raters can be assessed via conditional modes generated during the modeling process. Simulation studies are presented to demonstrate the performance of the proposed methods and summary measure of agreement. The methods are applied to a large-scale mammography agreement study to investigate the effects of rater and patient characteristics on the strength of agreement between radiologists. Copyright © 2017 John Wiley & Sons, Ltd.

Group testing regression models with dilution submodels

Group testing, where specimens are tested initially in pools, is widely used to screen individuals for sexually transmitted diseases. However, a common problem encountered in practice is that group testing can increase the number of false negative test results. This occurs primarily when positive individual specimens within a pool are diluted by negative ones, resulting in positive pools testing negatively. If the goal is to estimate a population-level regression model relating individual disease status to observed covariates, severe bias can result if an adjustment for dilution is not made. Recognizing this as a critical issue, recent binary regression approaches in group testing have utilized continuous biomarker information to acknowledge the effect of dilution. In this paper, we have the same overall goal but take a different approach. We augment existing group testing regression models (that assume no dilution) with a parametric dilution submodel for pool-level sensitivity and estimate all parameters using maximum likelihood. An advantage of our approach is that it does not rely on external biomarker test data, which may not be available in surveillance studies. Furthermore, unlike previous approaches, our framework allows one to formally test whether dilution is present based on the observed group testing data. We use simulation to illustrate the performance of our estimation and inference methods, and we apply these methods to 2 infectious disease data sets.

Modelling individual response time effects between and within experimental speed conditions: A GLMM approach for speeded tests

Completing test items under multiple speed conditions avoids the performance measure being confounded with individual differences in the speed-accuracy compromise, and offers insights into the response process, that is, how response time relates to the probability of a correct response. This relation is traditionally represented by two conceptually different functions: the speed-accuracy trade-off function (SATF) across conditions relating the condition average response time to the condition average of accuracy, and the conditional accuracy function (CAF) within a condition describing accuracy conditional on response time. Using a generalized linear mixed modelling approach, we propose an item response modelling framework that is suitable for item response and response time data from experimental speed conditions. The proposed SATF and CAF model accommodates response time effects between conditions (i.e., person and item SATF slope) and within conditions (i.e., residual CAF slopes), captures person and item differences in these effects, and is suitable for measures with a strong speed component. Moreover, for a single condition a CAF model is proposed distinguishing person, item and residual CAF. The properties of the models are illustrated with an empirical example.

Multidimensional heritability analysis of neuroanatomical shape

In the dawning era of large-scale biomedical data, multidimensional phenotype vectors will play an increasing role in examining the genetic underpinnings of brain features, behaviour and disease. For example, shape measurements derived from brain MRI scans are multidimensional geometric descriptions of brain structure and provide an alternate class of phenotypes that remains largely unexplored in genetic studies. Here we extend the concept of heritability to multidimensional traits, and present the first comprehensive analysis of the heritability of neuroanatomical shape measurements across an ensemble of brain structures based on genome-wide SNP and MRI data from 1,320 unrelated, young and healthy individuals. We replicate our findings in an extended twin sample from the Human Connectome Project (HCP). Our results demonstrate that neuroanatomical shape can be significantly heritable, above and beyond volume, and can serve as a complementary phenotype to study the genetic determinants and clinical relevance of brain structure.

Modeling Caries Experience: Advantages of the Use of the Hurdle Model

In dental epidemiology, the decayed (D), missing (M), and filled (F) teeth or surfaces index (DFM index) is a frequently used measure. The DMF index is characterized by a strongly positive skewed distribution with a large stack of zero counts for those individuals without caries experience. Therefore, standard generalized linear models often lead to a poor fit. The hurdle regression model is a highly suitable class to model a DMF index, but its use is subordinated. We aim to overcome the gap between the suitability of the hurdle model to fit DMF indices and the frequency of its use in caries research. A theoretical introduction to the hurdle model is provided, and an extensive comparison with the zero-inflated model is given. Using an illustrative data example, both types of models are compared, with a special focus on interpretation of their parameters. Accompanying R code and example data are provided as online supplementary material.

Morphometricity as a measure of the neuroanatomical signature of a trait

Complex physiological and behavioral traits, including neurological and psychiatric disorders, often associate with distributed anatomical variation. This paper introduces a global metric, called morphometricity, as a measure of the anatomical signature of different traits. Morphometricity is defined as the proportion of phenotypic variation that can be explained by macroscopic brain morphology. We estimate morphometricity via a linear mixed-effects model that uses an anatomical similarity matrix computed based on measurements derived from structural brain MRI scans. We examined over 3,800 unique MRI scans from nine large-scale studies to estimate the morphometricity of a range of phenotypes, including clinical diagnoses such as Alzheimer's disease, and nonclinical traits such as measures of cognition. Our results demonstrate that morphometricity can provide novel insights about the neuroanatomical correlates of a diverse set of traits, revealing associations that might not be detectable through traditional statistical techniques.