Random Effect and Latent Variable Model Selection

Pharmacokinetic-Pharmacodynamic Modeling and Simulation

In the previous chapters, we discussed autoregressive linear mixed effects models. In this section, we discuss the relationships between the autoregressive linear mixed effects models and nonlinear mixed effects models, growth curves, and differential equations. The autoregressive model shows a profile approaching an asymptote, where the change is proportional to the distance remaining to the asymptote. Autoregressive models in discrete time correspond to monomolecular curves in continuous time. Autoregressive linear mixed effects models correspond to monomolecular curves with random effects in the baseline and asymptote, and special error terms. The autoregressive coefficient is a nonlinear parameter, but all random effects parameters in the model are linear. Therefore, autoregressive linear mixed effects models are nonlinear mixed effects models without nonlinear random effects and have a closed form of likelihood. When there are time-dependent covariates, autoregressive linear mixed effects models are represented by a differential equation and random effects. The monomolecular curve is one of the popular growth curves. We introduce other growth curves, such as the logistic curves and von Bertalanffy curves, and generalizations of growth curves. Re-parameterization is often performed in nonlinear models, and various representations of re-parameterization in monomolecular and other curves are provided herein.

A central point of disagreement, in certain long-standing discussions about a particular whaling dataset in the Scientific Committee of the International Whaling Commission, has directly involved model selection issues for linear mixed effect models. The biological question under discussion is associated with a clearly defined parameter of primary interest, a focus parameter, which makes model selection with the Focused Information Criterion (FIC) more appropriate than other selection methods. Since the existing FIC methodology has not covered the case of linear mixed effects models, this article sets up the required framework and develops the necessary formulae for the relevant FIC. Our new criterion requires the asymptotic distribution of estimators derived for a given candidate linear mixed model but with behaviour examined under a wider linear mixed model. These results, needed here to build our FIC, also have independent interest.

In this paper, we discuss two different data transformation techniques for dealing with censored data: Kaplan-Meier weights and the k-nearest neighbor imputation method. The main objective of this paper is to find penalized spline estimates for the components of a linear mixed effect model with right-censored data. In the context of a mixed model setting, the estimation procedure is performed based on the modified or transformed dataset obtained via these transformation techniques. In order to compare the outcomes from a linear mixed model using these two approaches, a Monte Carlo simulation and two real data examples are presented. According to our results, the k-nearest neighbor imputation is very successful in dealing with censored observations.

Linear mixed effects (LME) models are important statistical tools for analysis of clustered and correlated data. High breakdown estimators are currently the robust methods of choice for multivariate linear regression, but extensions of such estimators have been developed only for completely balanced LME models. In this work, we propose a generalized S-estimator for a general unbalanced LME model. Our GS-estimator reduces to the classic high breakdown S-estimator when the LME model reduces to a multivariate normal location and scale model or mul- tivariate regression model. The asymptotic properties are established, and we show that the estimator may be viewed as a redescending M-estimator. A small simu- lation study is conducted to compare performance of the GS-estimates, monotone M-estimates, and restricted maximum likelihood (REML) estimates under various contamination patterns. The proposed estimator is used for analysis of age-related changes in hemoglobin levels of sickle cell disease patients.

Previous chapters discussed linear mixed effects models and autoregressive linear mixed effects models for analysis of longitudinal data. This chapter discusses multivariate extensions of these models. In longitudinal clinical studies, multivariate responses are often collected at each measurement time point from each subject. When two response variables, such as an efficacy measurement and a safety measurement are obviously correlated, there are advantages in analyzing the bivariate responses jointly. Parathyroid hormone (PTH) and serum calcium (Ca) measurements in the treatment of secondary hyperparathyroidism in chronic hemodialysis patients provide an example in which joint bivariate responses are of interest. We introduce multivariate longitudinal data and explain bivariate autoregressive linear mixed effects models in which the current responses are regressed on the previous responses of both variables, fixed effects, and random effects. The dependent bivariate responses approach equilibria, and the equilibria are modeled using fixed and random effects. These type of profiles are observed in long-term clinical studies. We also explain bivariate linear mixed effects models.

Bipolar disorder is a psychopathy characterized by manic and major depressive episodes. It is important todetermine the degree of depression when treating patients with bipolar disorder because 8 ˘ 10% of bipolarpatients commit suicide during the periods in which they experience major depressive episodes. The Hamil-ton depression rating scale is most commonly used to estimate the degree of depression in a patient. Thispaper proposes using the Hamilton depression rating scale to estimate the effectiveness of patient treatmentbased on the linear mixed effects model and the transition model. Study subjects were recruited from theSeoul National University Bundang Hospital who scored 8 points or above in the Hamilton depression ratingscale on their first medical examination. The linear mixed effects model and the transition model were fittedusing the Hamilton depression rating scales measured at the baseline, six month, and twelve month follow-ups. Then, Hamilton depression rating scale at the twenty-four month follow-up was predicted using thesemodels. The prediction models were then evaluated by comparing the observed and predicted Hamiltondepression rating scales on the twenty-four month follow-up.Keywords: Prediction model, linear mixed effects model, transition model, bipolar disorder, Hamilton de-pression rating scale.

본 논문은 불균형 자료에서 선형혼합모형에 적용되는 Akaike Information Criterion(AIC)의 효율에 대한 연구이다. Vaida와 Balanchard (2005)에 의해 제안된 cAIC(conditional AIC)는 mAIC(marginal AIC)가 임의효과의 예측에 대한 불확실성을 모형선택에서 반영하지 못하는 단점을 극복할 수 있는 방법이다. cAIC에 대한 이론적인 성질과 확장은 Liang 등 (2008)과 Greven과 Kneib (2010)에 의하여 연구되었다. cAIC의 형태는 자료의 구조에 영향을 받지는 않지만 선형혼합모형에서 모수의 추정 효율은 자료의 불균형의 정도에 따라 많은 영향을 받는 것이 알려져 있다. 기존의 연구에서 실시한 모든 모의실험이 자료가 균형인 경우에만 실행되어 자료의 불균형이 AIC에 근거한 혼합모형 선택 방법의 효율에 어떤 영향을 미치는지 알려져 있지 않다. 본 논문은 자료의 불균형이 모형선택 방법의 효율에 미치는 영향을 모의실험을 통하여 알아보았다. 자료의 불균형이 심해짐에 따라 AIC에 근거한 모형선택방법은 복잡한 모형을 선택하는 경향이 낮아짐을 보였다. This article consider a performance model selection based on AIC under unbalanced deign in linear mixed effect models. Vaida and Balanchard (2005) proposed conditional AIC for model selection in linear mixed effect models when the prediction of random effects is of primary interest. Theoretical properties of cAIC and related criteria have been investigated by Liang et al. (2008) and Greven and Kneib (2010). However, all of the simulation studies were performed under a balanced design. Even though functional form of AIC remain same even under the unbalanced deign, it is worthwhile to investigate performance of AIC based model selection criteria under the unbalanced design. The simulation study in this article shows how unbalancedness affects model selection in linear mixed effect models.

339 Relationships of Jugular Bulb Parameters Used as Indicators of Cerebral Perfusion and Metabolism With Cerebral Perfusion and Metabolism After Resuscitation from Cardiac Arrest: A Post-hoc Analysis of Experimental Studies Using a Minipig Model

Summary Recent advances in computing make it practical to use complex hierarchical models. However, the complexity makes it difficult to see how features of the data determine the fitted model. This paper describes an approach to diagnostics for hierarchical models, specifically linear hierarchical models with additive normal or t-errors. The key is to express hierarchical models in the form of ordinary linear models by adding artificial ‘cases' to the data set corresponding to the higher levels of the hierarchy. The error term of this linear model is not homoscedastic, but its covariance structure is much simpler than that usually used in variance component or random effects models. The re-expression has several advantages. First, it is extremely general, covering dynamic linear models, random effect and mixed effect models, and pairwise difference models, among others. Second, it makes more explicit the geometry of hierarchical models, by analogy with the geometry of linear models. Third, the analogy with linear models provides a rich source of ideas for diagnostics for all the parts of hierarchical models. This paper gives diagnostics to examine candidate added variables, transformations, collinearity, case influence and residuals.

Linear mixed effects models are highly flexible in handling a broad range of data types and are therefore widely used in applications. A key part in the analysis of data is model selection, which often aims to choose a parsimonious model with other desirable properties from a possibly very large set of candidate statistical models. Over the last 5–10 years the literature on model selection in linear mixed models has grown extremely rapidly. The problem is much more complicated than in linear regression because selection on the covariance structure is not straightforward due to computational issues and boundary problems arising from positive semidefinite constraints on covariance matrices. To obtain a better understanding of the available methods, their properties and the relationships between them, we review a large body of literature on linear mixed model selection. We arrange, implement, discuss and compare model selection methods based on four major approaches: information criteria such as AIC or BIC, shrinkage methods based on penalized loss functions such as LASSO, the Fence procedure and Bayesian techniques.

Diagnostic tests are of vital importance in a number of veterinary fields and are essential for decision-making by veterinary practioners, researchers and the veterinary authorities. The development and evaluation of laboratory diagnostic tests as well as the interpretation of test results engage a number of different veterinary disciplines including virologists, parasitologists, bacteriologists, laboratory experts, clinicians as well as epidemiologists and biostatisticians. This thesis was devised shortly after the section of epidemiology came into existence at the Vetsuisse Faculty end of 2009. The aim is to interrelate veterinary epidemiology - being closely linked to virology, parasitology, bacteriology and clinical medicine - with biostatistics. Thus allowing innovative concepts and recent software developments to provide solutions and answers in our veterinary field. After a brief introduction into diagnostic tests, the thesis is structured into three main parts. First, from a laboratory perspective, aspects of analytical sensitivity and specificity are illustrated by three peer-reviewed papers presenting practical applications of veterinary diagnostic tests for feline calicivirus and porcine parvovirus. Second, in the context of assessing agreement and method comparison studies, categorical test results are compared by Cohen’s k and continuous measurements by linear mixed effects models extending the classical use of Bland-Altman plots with limits of agreement. The former is illustrated in a publication on the diagnostic test Interferon-Gamma to classify bovines being infected with Mycobacterium bovis when analysing samples from the same animals in five different laboratories and from different anatomical locations. Two peer-reviewed papers aim to assess the agreement of serumspecific lipase, as a diagnostic test for feline pancreatitis with a commercial test kit and ultrasonographic findings. In the context of comparing continuous measurements, i.e. cardiac output and blood pressure measured directly and indirectly, two peer-reviewed paper illustrate the application of linear mixed effects models to simultaneously assess bias, precision and covariate information. Typical pitfalls arising in method comparison studies are summarised in a review paper. Building upon the previous parts, the third part adds to the existing knowledge by presenting novel and innovative approaches when assessing the performance of diagnostic tests in the absence of a perfect gold standard. So-called no gold standard models (NGS) are applied to assess the diagnostic test accuracies in the context of zoonotic diseases such as bovine tuberculosis, porcine toxoplasmosis as well as canine and vulpine echinococcosis. Additionally, these models are applied to assess diagnostic test accuracies to diagnose Brachyspira hyodysenteriae, an economically important disease in pigs. Furthermore, they are also utilised to assess diagnostic accuracies of diagnostic tools for subclinical mastitis in dairy cattle. In this part, Bayesian approaches are presented, together with technical aspects including conditional dependencies, Markov Chain Monte Carlo simulations and aspects of model selection. The innovative aspects and main novelty of the work presented in this thesis pertain to the incorporation of covariate information and random effects. Whereas covariate information in the form of risk factors has been included in statistical analyses since decades, considering random effects to account for clustering of animals at herd level just became possible with increased computational power. Nowadays dealing appropriately with the hierarchical structure of animal data is considered as good statistical practice and warranted in epidemiological studies to avoid biased results. However, diagnostic test studies including covariate information and random effects are scarce. The aim of this thesis is to fill this gap by showcasing a number of Bayesian latent class analyses for various infectious diseases in animals.

Data quality control in longitudinal epidemiologic studies: conditional studentized residuals from linear mixed effects models for outlier detection in the setting of pediatric chronic kidney disease

Objective: To analyze the short-term effect of individual atmospheric PM2.5 exposure on the diversity, enterotype, and community structure of gut microbiome in healthy elderly people in Jinan, Shandong province. Methods: The present panel study recruited 76 healthy elderly people aged 60-69 years old in Dianliu Street, Lixia District, Jinan, Shandong Province, and followed them up five times from September 2018 to January 2019. The relevant information was collected by questionnaire, physical examination, precise monitoring of individual PM2.5 exposure, fecal sample collection and gut microbiome 16S rDNA sequencing. The Dirichlet multinomial mixtures (DMM) model was used to analyze the enterotype. Linear mixed effect model and generalized linear mixed effect model were used to analyze the effect of PM2.5 exposure on gut microbiome α diversity indices (Shannon, Simpson, Chao1, and ACE indices), enterotype and abundance of core species. Results: Each of the 76 subjects participated in at least two follow-up visits, resulting in a total of 352 person-visits. The age of 76 subjects was (65.0±2.8) years old with BMI (25.0±2.4) kg/m2. There were 38 males accounting for 50% of the subjects. People with an educational level of primary school or below accounted for 10.5% of the 76 subjects, and those with secondary school and junior college or above accounting for 71.1% and 18.4%. The individual PM2.5 exposure concentration of 76 subjects during the study period was (58.7±53.7) μg/m3. DMM model showed that the subjects could be divided into four enterotypes, which were mainly driven by Bacteroides, Faecalibacterium, Lachnospiraceae, Prevotellaceae, and Ruminococcaceae. Linear mixed effects model showed that different lag periods of PM2.5 exposure were significantly associated with a lower gut α diversity index (FDR<0.05 after correction). Further analysis showed that PM2.5 exposure was significantly associated with changes in the abundances of Firmicutes (Megamonas, Blautia, Streptococcus, etc.) and Bacteroidetes (Alistipes) (FDR<0.05 after correction). Conclusion: Short-term PM2.5 exposure is significantly associated with a decrease in gut microbiome diversity and changes in the abundance of several species of Firmicutes and Bacteroidetes in the elderly. It is necessary to further explore the underlying mechanisms between PM2.5 exposure and the gut microbiome, so as to provide a scientific basis for promoting the intestinal health of the elderly.

This chapter expands on linear models through the introduction of random effects, where the independent variables in the model include those variables that are fixed and those that vary across subjects. The general linear mixed effects model (LMEM) is introduced as methods for parameter estimation – maximum likelihood and restricted maximum likelihood. Model selection and goodness of fit in the context of LMEMs are discussed. The concept of empirical Bayes estimates and how shrinkage affects these estimates are also discussed. Building upon LMEMs, partial LMEMs are introduced, which use penalized spline regression to obtain a nonparametric-type smooth to the data, and how these might be used for covariate selection when knowing the exact nature of the effect of time is not needed. Three examples of LMEMs are provided: results from a food effect study, modeling tumor growth in a mouse xenograft model, and a detailed analysis of QT prolongation in clinical studies.