Accuracy of Laplace approximation for discrete response mixed models

A Note on Standard Errors for Multidimensional Two-Parameter Logistic Models Using Gaussian Variational Estimation

Accurate item parameters and standard errors (SEs) are crucial for many multidimensional item response theory (MIRT) applications. A recent study proposed the Gaussian Variational Expectation Maximization (GVEM) algorithm to improve computational efficiency and estimation accuracy (Cho et al., 2021). However, the SE estimation procedure has yet to be fully addressed. To tackle this issue, the present study proposed an updated supplemented expectation maximization (USEM) method and a bootstrap method for SE estimation. These two methods were compared in terms of SE recovery accuracy. The simulation results demonstrated that the GVEM algorithm with bootstrap and item priors (GVEM-BSP) outperformed the other methods, exhibiting less bias and relative bias for SE estimates under most conditions. Although the GVEM with USEM (GVEM-USEM) was the most computationally efficient method, it yielded an upward bias for SE estimates.

Variation in Reporting of Incidental Findings on Initial Lung Cancer Screening and Associations With Clinician Assessment

PURPOSE

The aim of this study was to quantify the distribution, frequency, and clinical significance of incidental findings (IFs) on initial lung cancer screening (LCS) and the association of report characteristics with subsequent assessment.

METHODS

Health records of patients undergoing initial LCS from 2015 to 2018 in the Minneapolis VA Health Care System were retrospectively reviewed for demographics, Lung CT Screening Reporting & Data System coding, IFs, and subsequent clinical assessment. IFs were considered potentially significant if they were likely to require any follow-up. High-risk significant IFs (SIFs) were potentially malignant. The primary outcome was the SIF being addressed. Outcomes were analyzed using a mixed-effects model.

RESULTS

Patients (n = 901) were primarily male (94.1%) smokers (62.1%) with a mean age of 65.2 years. IFs were extremely common (93.9%), with an average of 2.6 IFs per scan (n = 2,296). Seven hundred eighty-six IFs (34.2%) were deemed likely SIFs, of which 58 (7.4%) were high risk. Two hundred twenty-two (28.2%) were addressed by clinicians, of which 104 (13.2%) underwent testing. Reporting of SIFs varied among radiologists, with at least one SIF in the impression in 24% to 78% of low-dose CT studies with the S modifier, used to indicate the presence of a SIF, applied to 0% to 51% of reports. In the mutually adjusted model, radiologist recommendation (adjusted odds ratio [OR], 4.67; 95% confidence interval [CI], 2.23-9.76), high-risk finding (adjusted OR, 4.35; 95% CI, 1.81-10.45), and reporting in the impression (adjusted OR, 2.58; 95% CI, 1.28-5.18) were associated with increased odds of the SIF's being addressed.

CONCLUSIONS

Radiologists vary in their reporting of IFs on LCS. Further standardization of reporting of SIFs may improve this process, with the simultaneous goals of generating appropriate testing when needed and minimizing low-value care.

Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models

We present generalized additive latent and mixed models (GALAMMs) for analysis of clustered data with responses and latent variables depending smoothly on observed variables. A scalable maximum likelihood estimation algorithm is proposed, utilizing the Laplace approximation, sparse matrix computation, and automatic differentiation. Mixed response types, heteroscedasticity, and crossed random effects are naturally incorporated into the framework. The models developed were motivated by applications in cognitive neuroscience, and two case studies are presented. First, we show how GALAMMs can jointly model the complex lifespan trajectories of episodic memory, working memory, and speed/executive function, measured by the California Verbal Learning Test (CVLT), digit span tests, and Stroop tests, respectively. Next, we study the effect of socioeconomic status on brain structure, using data on education and income together with hippocampal volumes estimated by magnetic resonance imaging. By combining semiparametric estimation with latent variable modeling, GALAMMs allow a more realistic representation of how brain and cognition vary across the lifespan, while simultaneously estimating latent traits from measured items. Simulation experiments suggest that model estimates are accurate even with moderate sample sizes.

Evaluation of Pointing Ray Techniques for Distant Object Referencing in Model-Free Outdoor Collaborative Augmented Reality

Referencing objects of interest is a common requirement in many collaborative tasks. Nonetheless, accurate object referencing at a distance can be challenging due to the reduced visibility of the objects or the collaborator and limited communication medium. Augmented Reality (AR) may help address the issues by providing virtual pointing rays to the target of common interest. However, such pointing ray techniques can face critical limitations in large outdoor spaces, especially when the environment model is unavailable. In this work, we evaluated two pointing ray techniques for distant object referencing in model-free AR from the literature: the Double Ray technique enhancing visual matching between rays and targets, and the Parallel Bars technique providing artificial orientation cues. Our experiment in outdoor AR involving participants as pointers and observers partially replicated results from a previous study that only evaluated observers in simulated AR. We found that while the effectiveness of the Double Ray technique is reduced with the additional workload for the pointer and human pointing errors, it is still beneficial for distant object referencing.

Cryptosporidium parvum infection and management-based risk factors of dairy calves in Taiwan

Cryptosporidiosis is one of the major causes of diarrhea in calves. Cryptosporidium parvum is considered the most important calf diarrhea pathogen in the Cryptosporidium species. Not only could infected calves spread C. parvum, but infected adult cattle could also shed oocysts. The objectives of this study were (1) to investigate the prevalence of C. parvum in dairy herds in Taiwan, including calves, the dams in delivery enclosure, the floor, and the drinking water; (2) to clarify the relationship of diarrhea, management, and C. parvum infection. Twenty dairy herds in Taiwan were selected by random sampling, including 226 calves and 198 dams, and other environmental samples were collected. A questionnaire was filled out by the farm owners to collect information regarding the management of calves and the delivery enclosure. Hierarchical logistic regression was used to analyze the risk factors for C. parvum infection. The prevalence of C. parvum infection in calves was 26.5% (60/226), while in dams, it was 19.7% (39/198). The C. parvum infection in calves increased with environmental contamination of C. parvum and clinical signs of diarrhea, while it decreased with a yard provided in the delivery enclosure. In conclusion, the management of the delivery enclosure appears to be more important for preventing cryptosporidiosis in calves in Taiwan.

Dynamic latent variable models for the analysis of cognitive abilities in the elderly population

Cognitive functioning is a key indicator of overall individual health. Identifying factors related to cognitive status, especially in later life, is of major importance. We concentrate on the analysis of the temporal evolution of cognitive abilities in the elderly population. We propose to model the individual cognitive functioning as a multidimensional latent process that accounts also for the effects of individual-specific characteristics (gender, age, and years of education). The proposed model is specified within the generalized linear latent variable framework, and its efficient estimation is obtained using a recent approximation technique, called dimensionwise quadrature. It provides a fast and streamlined approximate inference for complex models, with better or no degradation in accuracy compared with standard techniques. The methodology is applied to the cognitive assessment data from the Health and Retirement Study combined with the Asset and Health Dynamic study in the years between 2006 and 2010. We evaluate the temporal relationship between two dimensions of cognitive functioning, that is, episodic memory and general mental status. We find a substantial influence of the former on the evolution of the latter, as well as evidence of severe consequences on both cognitive abilities among less-educated and older individuals.

Functional joint models for chronic kidney disease in kidney transplant recipients

This functional joint model paper is motivated by a chronic kidney disease study post kidney transplantation. The available kidney organ is a scarce resource because millions of end-stage renal patients are on the waiting list for kidney transplantation. The life of the transplanted kidney can be extended if the progression of the chronic kidney disease stage can be slowed, and so a major research question is how to extend the transplanted kidney life to maximize the usage of the scarce organ resource. The glomerular filtration rate is the best test to monitor the progression of the kidney function, and it is a continuous longitudinal outcome with repeated measures. The patient's survival status is characterized by time-to-event outcomes including kidney transplant failure, death with kidney function, and death without kidney function. Few studies have been carried out to simultaneously investigate these multiple clinical outcomes in chronic kidney disease stage patients based on a joint model. Therefore, this paper proposes a new functional joint model from this clinical chronic kidney disease study. The proposed joint models include a longitudinal sub-model with a flexible basis function for subject-level trajectories and a competing-risks sub-model for multiple time-to event outcomes. The different association structures can be accomplished through a time-dependent function of shared random effects from the longitudinal process or the whole longitudinal history in the competing-risks sub-model. The proposed joint model that utilizes basis function and competing-risks sub-model is an extension of the standard linear joint models. The application results from the proposed joint model can supply some useful clinical references for chronic kidney disease study post kidney transplantation.

A note on the accuracy of adaptive Gauss–Hermite quadrature

Numerical quadrature methods are needed for many models in order to approximate integrals in the likelihood function. In this note, we correct the error rate given by Liu & Pierce (1994) for integrals approximated with adaptive Gauss–Hermite quadrature and show that the approximation is less accurate than previously thought. We discuss the relationship between the error rates of adaptive Gauss–Hermite quadrature and Laplace approximation, and provide a theoretical explanation of simulation results obtained in previous studies regarding the accuracy of adaptive Gauss–Hermite quadrature.

Evaluation of quarter-based selective dry cow therapy using Petrifilm on-farm milk culture: A randomized controlled trial

The objective of this randomized controlled trial was to assess the efficacy of an on-farm culture system using Petrifilm (3M, London, ON, Canada) for targeted treatment decisions at the quarter level at dry-off and its effects on dry period intramammary infections (IMI) and udder health and milk production in the subsequent lactation. A total of 568 cows (2,247 quarters) from 9 dairy herds with bulk tank somatic cell count <250,000 cells/mL in Québec, Canada, were systematically enrolled and randomly allocated to 4 groups: 2 quarter-based selective (QSDCT) groups, using results of quarter-milk culture on Petrifilm, and 2 blanket dry cow therapy (BDCT) groups. The 2 QSDCT groups consisted of (1) antimicrobial to infected quarters and internal teat sealant (ITS) to healthy quarters (QSDCT/ITS); and (2) antimicrobial and ITS to infected quarters and ITS to healthy quarters (QSDCT+ITS/ITS). The 2 BDCT groups were (1) antimicrobial alone to all quarters (BDCT); and (2) antimicrobial and ITS to all quarters (BDCT+ITS). Quarter milk samples were collected at dry-off and after calving for routine bacteriological culture at the laboratory to monitor IMI; data on milk production, somatic cell count, and clinical mastitis recorded up to 120 d in milk were retrieved from health and DHI records. The probability of avoiding antimicrobial treatment in QSDCT groups was estimated at 48.3% (95% confidence interval: 35.7, 60.9). There was no significant difference between the 4 treatment groups regarding acquisition of new IMI (15.9, 13.2, 15.8, and 15.1% probability for BDCT, BDCT+ITS, QSDCT/ITS, and QSDCT+ITS/ITS, respectively) or persistence of existing IMI (3.2, 2.1, 3.4, and 2.7% probability, respectively) over the dry period. In the subsequent lactation, there was no difference between groups regarding incidence of clinical mastitis (2.4, 3.7, 2.9, and 1.7% respectively for BDCT, BDCT+ITS, QSDCT/ITS, and QSDCT+ITS/ITS), mean milk somatic cell score (1.7, 2.0, 2.0, and 2.0 respectively), or mean daily milk production (43.8, 44.2, 43.2, and 42.6 kg/d, respectively) during the first 120 d in milk. In conclusion, QSDCT using the Petrifilm on-farm culture system to detect infected quarters at dry-off is an interesting option to decrease antibiotic use without any negative effects on udder health or milk production in the first 120 d of the subsequent lactation compared with BDCT.

Poisson Multilevel Models with Small Samples

Recent methodological studies have investigated the properties of multilevel models with small samples. Previous work has primarily focused on continuous outcomes and little attention has been paid to count outcomes. The estimation of count outcome models can be difficult because the likelihood has no closed-form solution, meaning that approximation methods are required. Although adaptive Gaussian quadrature (AGQ) is generally seen as the gold standard, its comparative performance has been investigated with larger samples. AGQ approximates the full likelihood, a function that is known to produce biased estimates with small samples with continuous outcomes. Conversely, penalized quasi-likelihood (PQL) is considered to be a less desirable approximation; however, it can approximate the restricted likelihood function, a function that is known to perform well with smaller samples with continuous outcomes. The goal of this paper is to compare the small sample bias of full likelihood methods to the linearization bias of PQL with restricted likelihood. Simulation results indicate that the linearization bias of PQL is preferable to the finite sample bias of AGQ with smaller samples.

Efficient estimation of generalized linear latent variable models

Generalized linear latent variable models (GLLVM) are popular tools for modeling multivariate, correlated responses. Such data are often encountered, for instance, in ecological studies, where presence-absences, counts, or biomass of interacting species are collected from a set of sites. Until very recently, the main challenge in fitting GLLVMs has been the lack of computationally efficient estimation methods. For likelihood based estimation, several closed form approximations for the marginal likelihood of GLLVMs have been proposed, but their efficient implementations have been lacking in the literature. To fill this gap, we show in this paper how to obtain computationally convenient estimation algorithms based on a combination of either the Laplace approximation method or variational approximation method, and automatic optimization techniques implemented in R software. An extensive set of simulation studies is used to assess the performances of different methods, from which it is shown that the variational approximation method used in conjunction with automatic optimization offers a powerful tool for estimation.

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.

Geostatistical Methods for Disease Mapping and Visualisation Using Data from Spatio-temporally Referenced Prevalence Surveys

In this paper, we set out general principles and develop geostatistical methods for the analysis of data from spatio-temporally referenced prevalence surveys. Our objective is to provide a tutorial guide that can be used in order to identify parsimonious geostatistical models for prevalence mapping. A general variogram-based Monte Carlo procedure is proposed to check the validity of the modelling assumptions. We describe and contrast likelihood-based and Bayesian methods of inference, showing how to account for parameter uncertainty under each of the two paradigms. We also describe extensions of the standard model for disease prevalence that can be used when stationarity of the spatio-temporal covariance function is not supported by the data. We discuss how to define predictive targets and argue that exceedance probabilities provide one of the most effective ways to convey uncertainty in prevalence estimates. We describe statistical software for the visualisation of spatio-temporal predictive summaries of prevalence through interactive animations. Finally, we illustrate an application to historical malaria prevalence data from 1 334 surveys conducted in Senegal between 1905 and 2014.

Correlated Poisson models for age-period-cohort analysis

Age-period-cohort (APC) models are widely used to analyze population-level rates, particularly cancer incidence and mortality. These models are used for descriptive epidemiology, comparative risk analysis, and extrapolating future disease burden. Traditional APC models have 2 major limitations: (1) they lack parsimony because they require estimation of deviations from linear trends for each level of age, period, and cohort; and (2) rates observed at similar ages, periods, and cohorts are treated as independent, ignoring any correlations between them that may lead to biased parameter estimates and inefficient standard errors. We propose a novel approach to estimation of APC models using a spatially correlated Poisson model that accounts for over-dispersion and correlations in age, period, and cohort, simultaneously. We treat the outcome of interest as event rates occurring over a grid defined by values of age, period, and cohort. Rates defined in this manner lend themselves to well-established approaches from spatial statistics in which correlation among proximate observations may be modeled using a spatial random effect. Through simulations, we show that in the presence of spatial dependence and over-dispersion: (1) the correlated Poisson model attains lower AIC; (2) the traditional APC model produces biased trend parameter estimates; and (3) the correlated Poisson model corrects most of this bias. We illustrate our approach using brain and breast cancer incidence rates from the Surveillance Epidemiology and End Results Program of the United States. Our approach can be easily extended to accommodate comparative risk analyses and interpolation of cells in the Lexis with sparse data.

Probability of atrial fibrillation after ablation: Using a parametric nonlinear temporal decomposition mixed effects model

Atrial fibrillation is an arrhythmic disorder where the electrical signals of the heart become irregular. The probability of atrial fibrillation (binary response) is often time varying in a structured fashion, as is the influence of associated risk factors. A generalized nonlinear mixed effects model is presented to estimate the time-related probability of atrial fibrillation using a temporal decomposition approach to reveal the pattern of the probability of atrial fibrillation and their determinants. This methodology generalizes to patient-specific analysis of longitudinal binary data with possibly time-varying effects of covariates and with different patient-specific random effects influencing different temporal phases. The motivation and application of this model is illustrated using longitudinally measured atrial fibrillation data obtained through weekly trans-telephonic monitoring from an NIH sponsored clinical trial being conducted by the Cardiothoracic Surgery Clinical Trials Network.

A mechanistic nonlinear model for censored and mismeasured covariates in longitudinal models, with application in AIDS studies

When modeling longitudinal data, the true values of time-varying covariates may be unknown because of detection-limit censoring or measurement error. A common approach in the literature is to empirically model the covariate process based on observed data and then predict the censored values or mismeasured values based on this empirical model. Such an empirical model can be misleading, especially for censored values since the (unobserved) censored values may behave very differently than observed values due to the underlying data-generation mechanisms or disease status. In this paper, we propose a mechanistic nonlinear covariate model based on the underlying data-generation mechanisms to address censored values and mismeasured values. Such a mechanistic model is based on solid scientific or biological arguments, so the predicted censored or mismeasured values are more reasonable. We use a Monte Carlo EM algorithm for likelihood inference and apply the methods to an AIDS dataset, where viral load is censored by a lower detection limit. Simulation results confirm that the proposed models and methods offer substantial advantages over existing empirical covariate models for censored and mismeasured covariates.

Evaluating Testing, Profile Likelihood Confidence Interval Estimation, and Model Comparisons for Item Covariate Effects in Linear Logistic Test Models

The linear logistic test model (LLTM) has been widely applied to investigate the effects of item covariates on item difficulty. The LLTM was extended with random item residuals to account for item differences not explained by the item covariates. This extended LLTM is called the LLTM-R. In this article, statistical inference methods are investigated for these two models. Type I error rates and power are compared via Monte Carlo studies. Based on the simulation results, the use of the likelihood ratio test (LRT) is recommended over the paired-sample t test based on sum scores, the Wald z test, and information criteria, and the LRT is recommended over the profile likelihood confidence interval because of the simplicity of the LRT. In addition, it is concluded that the LLTM-R is the better general model approach. Inferences based on the LLTM while the LLTM-R is the true model appear to be largely biased in the liberal way, while inferences based on the LLTM-R while the LLTM is the true model are only biased in a very minor and conservative way. Furthermore, in the absence of residual variance, Type I error rate and power were acceptable except for power when the number of items is small (10 items) and also the number of persons is small (200 persons). In the presence of residual variance, however, the number of items needs to be large (80 items) to avoid an inflated Type I error and to reach a power level of .90 for a moderate effect.

A unified approach for assessing heterogeneity in age-period-cohort model parameters using random effects

Age-period-cohort models are a popular tool for studying population-level rates; for example, trends in cancer incidence and mortality. Age-period-cohort models decompose observed trends into age effects that correlate with natural history, period effects that reveal factors impacting all ages simultaneously (e.g. innovations in screening), and birth cohort effects that reflect differential risk exposures that vary across birth years. Methodology for the analysis of multiple population strata (e.g. ethnicity, cancer registry) within the age-period-cohort framework has not been thoroughly investigated. Here, we outline a general model for characterizing differences in age-period-cohort model parameters for a potentially large number of strata. Our model incorporates stratum-specific random effects for the intercept, the longitudinal age trend, and the model-based estimate of annual percent change (net drift), thereby enabling a comprehensive analysis of heterogeneity. We also extend the standard model to include quadratic terms for age, period, and cohort, along with the corresponding random effects, which quantify possible stratum-specific departures from global curvature. We illustrate the utility of our model with an application to metastatic prostate cancer incidence (2004-2013) in non-Hispanic white and black men, using 17 population-based cancer registries in the Surveillance, Epidemiology, and End Results Program.

A Variational Maximization-Maximization Algorithm for Generalized Linear Mixed Models with Crossed Random Effects

We present a variational maximization-maximization algorithm for approximate maximum likelihood estimation of generalized linear mixed models with crossed random effects (e.g., item response models with random items, random raters, or random occasion-specific effects). The method is based on a factorized variational approximation of the latent variable distribution given observed variables, which creates a lower bound of the log marginal likelihood. The lower bound is maximized with respect to the factorized distributions as well as model parameters. With the proposed algorithm, a high-dimensional intractable integration is translated into a two-dimensional integration problem. We incorporate an adaptive Gauss-Hermite quadrature method in conjunction with the variational method in order to increase computational efficiency. Numerical studies show that under the small sample size conditions that are considered the proposed algorithm outperforms the Laplace approximation.

New Insights into Tree Height Distribution Based on Mixed Effects Univariate Diffusion Processes

The aim of this paper is twofold: to introduce the mathematics of stochastic differential equations (SDEs) for forest dynamics modeling and to describe how such a model can be applied to aid our understanding of tree height distribution corresponding to a given diameter using the large dataset provided by the Lithuanian National Forest Inventory (LNFI). Tree height-diameter dynamics was examined with Ornstein-Uhlenbeck family mixed effects SDEs. Dynamics of a tree height, volume and their coefficients of variation, quantile regression curves of the tree height, and height-diameter ratio were demonstrated using newly developed tree height distributions for a given diameter. The parameters were estimated by considering a discrete sample of the diameter and height and by using an approximated maximum likelihood procedure. All models were evaluated using a validation dataset. The dataset provided by the LNFI (2006-2010) of Scots pine trees is used in this study to estimate parameters and validate our modeling technique. The verification indicated that the newly developed models are able to accurately capture the behavior of tree height distribution corresponding to a given diameter. All of the results were implemented in a MAPLE symbolic algebra system.

Estimation Methods for Mixed Logistic Models with Few Clusters

For mixed models generally, it is well known that modeling data with few clusters will result in biased estimates, particularly of the variance components and fixed effect standard errors. In linear mixed models, small sample bias is typically addressed through restricted maximum likelihood estimation (REML) and a Kenward-Roger correction. Yet with binary outcomes, there is no direct analog of either procedure. With a larger number of clusters, estimation methods for binary outcomes that approximate the likelihood to circumvent the lack of a closed form solution such as adaptive Gaussian quadrature and the Laplace approximation have been shown to yield less-biased estimates than linearization estimation methods that instead linearly approximate the model. However, adaptive Gaussian quadrature and the Laplace approximation are approximating the full likelihood rather than the restricted likelihood; the full likelihood is known to yield biased estimates with few clusters. On the other hand, linearization methods linearly approximate the model, which allows for restricted maximum likelihood and the Kenward-Roger correction to be applied. Thus, the following question arises: Which is preferable, a better approximation of a biased function or a worse approximation of an unbiased function? We address this question with a simulation and an illustrative empirical analysis.

A multiphase non-linear mixed effects model: An application to spirometry after lung transplantation

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time-varying coefficients.

Bayesian regression analysis of data with random effects covariates from nonlinear longitudinal measurements

Joint models for a wide class of response variables and longitudinal measurements consist on a mixed-effects model to fit longitudinal trajectories whose random effects enter as covariates in a generalized linear model for the primary response. They provide a useful way to assess association between these two kinds of data, which in clinical studies are often collected jointly on a series of individuals and may help understanding, for instance, the mechanisms of recovery of a certain disease or the efficacy of a given therapy. When a nonlinear mixed-effects model is used to fit the longitudinal trajectories, the existing estimation strategies based on likelihood approximations have been shown to exhibit some computational efficiency problems (De la Cruz et al., 2011). In this article we consider a Bayesian estimation procedure for the joint model with a nonlinear mixed-effects model for the longitudinal data and a generalized linear model for the primary response. The proposed prior structure allows for the implementation of an MCMC sampler. Moreover, we consider that the errors in the longitudinal model may be correlated. We apply our method to the analysis of hormone levels measured at the early stages of pregnancy that can be used to predict normal versus abnormal pregnancy outcomes. We also conduct a simulation study to assess the importance of modelling correlated errors and quantify the consequences of model misspecification.

A mixed effect model for bivariate meta-analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution

Diagnostic test accuracy studies typically report the number of true positives, false positives, true negatives and false negatives. There usually exists a negative association between the number of true positives and true negatives, because studies that adopt less stringent criterion for declaring a test positive invoke higher sensitivities and lower specificities. A generalized linear mixed model (GLMM) is currently recommended to synthesize diagnostic test accuracy studies. We propose a copula mixed model for bivariate meta-analysis of diagnostic test accuracy studies. Our general model includes the GLMM as a special case and can also operate on the original scale of sensitivity and specificity. Summary receiver operating characteristic curves are deduced for the proposed model through quantile regression techniques and different characterizations of the bivariate random effects distribution. Our general methodology is demonstrated with an extensive simulation study and illustrated by re-analysing the data of two published meta-analyses. Our study suggests that there can be an improvement on GLMM in fit to data and makes the argument for moving to copula random effects models. Our modelling framework is implemented in the package CopulaREMADA within the open source statistical environment R.

Incidence of carbapenem-resistant gram negatives in Italian transplant recipients: a nationwide surveillance study

BACKGROUND

Bacterial infections remain a challenge to solid organ transplantation. Due to the alarming spread of carbapenem-resistant gram negative bacteria, these organisms have been frequently recognized as cause of severe infections in solid organ transplant recipients.

METHODS AND FINDINGS

Between 15 May and 30 September 2012 we enrolled 887 solid organ transplant recipients in Italy with the aim to describe the epidemiology of gram negative bacteria spreading, to explore potential risk factors and to assess the effect of early isolation of gram negative bacteria on recipients' mortality during the first 90 days after transplantation. During the study period 185 clinical isolates of gram negative bacteria were reported, for an incidence of 2.39 per 1000 recipient-days. Positive cultures for gram negative bacteria occurred early after transplantation (median time 26 days; incidence rate 4.33, 1.67 and 1.14 per 1,000 recipient-days in the first, second and third month after SOT, respectively). Forty-nine of these clinical isolates were due to carbapenem-resistant gram negative bacteria (26.5%; incidence 0.63 per 1000 recipient-days). Carbapenems resistance was particularly frequent among Klebsiella spp. isolates (49.1%). Recipients with longer hospital stay and those who received either heart or lung graft were at the highest risk of testing positive for any gram negative bacteria. Moreover recipients with longer hospital stay, lung recipients and those admitted to hospital for more than 48h before transplantation had the highest probability to have culture(s) positive for carbapenem-resistant gram negative bacteria. Forty-four organ recipients died (0.57 per 1000 recipient-days) during the study period. Recipients with at least one positive culture for carbapenem-resistant gram negative bacteria had a 10.23-fold higher mortality rate than those who did not.

CONCLUSION

The isolation of gram-negative bacteria is most frequent among recipient with hospital stays >48 hours prior to transplant and in those receiving either heart or lung transplants. Carbapenem-resistant gram negative isolates are associated with significant mortality.

Survival analysis of clinical mastitis data using a nested frailty Cox model fit as a mixed-effects Poisson model

Mastitis is a complex disease affecting dairy cows and is considered to be the most costly disease of dairy herds. The hazard of mastitis is a function of many factors, both managerial and environmental, making its control a difficult issue to milk producers. Observational studies of clinical mastitis (CM) often generate datasets with a number of characteristics which influence the analysis of those data: the outcome of interest may be the time to occurrence of a case of mastitis, predictors may change over time (time-dependent predictors), the effects of factors may change over time (time-dependent effects), there are usually multiple hierarchical levels, and datasets may be very large. Analysis of such data often requires expansion of the data into the counting-process format - leading to larger datasets - thus complicating the analysis and requiring excessive computing time. In this study, a nested frailty Cox model with time-dependent predictors and effects was applied to Canadian Bovine Mastitis Research Network data in which 10,831 lactations of 8035 cows from 69 herds were followed through lactation until the first occurrence of CM. The model was fit to the data as a Poisson model with nested normally distributed random effects at the cow and herd levels. Risk factors associated with the hazard of CM during the lactation were identified, such as parity, calving season, herd somatic cell score, pasture access, fore-stripping, and proportion of treated cases of CM in a herd. The analysis showed that most of the predictors had a strong effect early in lactation and also demonstrated substantial variation in the baseline hazard among cows and between herds. A small simulation study for a setting similar to the real data was conducted to evaluate the Poisson maximum likelihood estimation approach with both Gaussian quadrature method and Laplace approximation. Further, the performance of the two methods was compared with the performance of a widely used estimation approach for frailty Cox models based on the penalized partial likelihood. The simulation study showed good performance for the Poisson maximum likelihood approach with Gaussian quadrature and biased variance component estimates for both the Poisson maximum likelihood with Laplace approximation and penalized partial likelihood approaches.

Additive multilevel item structure models with random residuals: item modeling for explanation and item generation

An additive multilevel item structure (AMIS) model with random residuals is proposed. The model includes multilevel latent regressions of item discrimination and item difficulty parameters on covariates at both item and item category levels with random residuals at both levels. The AMIS model is useful for explanation purposes and also for prediction purposes as in an item generation context. The parameters can be estimated with an alternating imputation posterior algorithm that makes use of adaptive quadrature, and the performance of this algorithm is evaluated in a simulation study.

Logistic Regression with Multiple Random Effects: A Simulation Study of Estimation Methods and Statistical Packages

Several statistical packages are capable of estimating generalized linear mixed models and these packages provide one or more of three estimation methods: penalized quasi-likelihood, Laplace, and Gauss-Hermite. Many studies have investigated these methods' performance for the mixed-effects logistic regression model. However, the authors focused on models with one or two random effects and assumed a simple covariance structure between them, which may not be realistic. When there are multiple correlated random effects in a model, the computation becomes intensive, and often an algorithm fails to converge. Moreover, in our analysis of smoking status and exposure to anti-tobacco advertisements, we have observed that when a model included multiple random effects, parameter estimates varied considerably from one statistical package to another even when using the same estimation method. This article presents a comprehensive review of the advantages and disadvantages of each estimation method. In addition, we compare the performances of the three methods across statistical packages via simulation, which involves two- and three-level logistic regression models with at least three correlated random effects. We apply our findings to a real dataset. Our results suggest that two packages-SAS GLIMMIX Laplace and SuperMix Gaussian quadrature-perform well in terms of accuracy, precision, convergence rates, and computing speed. We also discuss the strengths and weaknesses of the two packages in regard to sample sizes.

An assessment of estimation methods for generalized linear mixed models with binary outcomes

Two main classes of methodology have been developed for addressing the analytical intractability of generalized linear mixed models: likelihood-based methods and Bayesian methods. Likelihood-based methods such as the penalized quasi-likelihood approach have been shown to produce biased estimates especially for binary clustered data with small clusters sizes. More recent methods using adaptive Gaussian quadrature perform well but can be overwhelmed by problems with large numbers of random effects, and efficient algorithms to better handle these situations have not yet been integrated in standard statistical packages. Bayesian methods, although they have good frequentist properties when the model is correct, are known to be computationally intensive and also require specialized code, limiting their use in practice. In this article, we introduce a modification of the hybrid approach of Capanu and Begg, 2011, Biometrics 67, 371-380, as a bridge between the likelihood-based and Bayesian approaches by employing Bayesian estimation for the variance components followed by Laplacian estimation for the regression coefficients. We investigate its performance as well as that of several likelihood-based methods in the setting of generalized linear mixed models with binary outcomes. We apply the methods to three datasets and conduct simulations to illustrate their properties. Simulation results indicate that for moderate to large numbers of observations per random effect, adaptive Gaussian quadrature and the Laplacian approximation are very accurate, with adaptive Gaussian quadrature preferable as the number of observations per random effect increases. The hybrid approach is overall similar to the Laplace method, and it can be superior for data with very sparse random effects.

Internal validation of risk models in clustered data: a comparison of bootstrap schemes

Internal validity of a risk model can be studied efficiently with bootstrapping to assess possible optimism in model performance. Assumptions of the regular bootstrap are violated when the development data are clustered. We compared alternative resampling schemes in clustered data for the estimation of optimism in model performance. A simulation study was conducted to compare regular resampling on only the patient level with resampling on only the cluster level and with resampling sequentially on both the cluster and patient levels (2-step approach). Optimism for the concordance index and calibration slope was estimated. Resampling of only patients or only clusters showed accurate estimates of optimism in model performance. The 2-step approach overestimated the optimism in model performance. If the number of centers or intraclass correlation coefficient was high, resampling of clusters showed more accurate estimates than resampling of patients. The 3 bootstrap schemes also were applied to empirical data that were clustered. The results presented in this paper support the use of resampling on only the clusters for estimation of optimism in model performance when data are clustered.

Parameter estimation of multiple item response profile model

Multiple item response profile (MIRP) models are models with crossed fixed and random effects. At least one between-person factor is crossed with at least one within-person factor, and the persons nested within the levels of the between-person factor are crossed with the items within levels of the within-person factor. Maximum likelihood estimation (MLE) of models for binary data with crossed random effects is challenging. This is because the marginal likelihood does not have a closed form, so that MLE requires numerical or Monte Carlo integration. In addition, the multidimensional structure of MIRPs makes the estimation complex. In this paper, three different estimation methods to meet these challenges are described: the Laplace approximation to the integrand; hierarchical Bayesian analysis, a simulation-based method; and an alternating imputation posterior with adaptive quadrature as the approximation to the integral. In addition, this paper discusses the advantages and disadvantages of these three estimation methods for MIRPs. The three algorithms are compared in a real data application and a simulation study was also done to compare their behaviour.