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Typical joint modeling of longitudinal measurements and time to event data assumes that two models share a common set of random effects with a normal distribution assumption. But, sometimes the underlying population that the sample is extracted from is a heterogeneous population and detecting homogeneous subsamples of it is an important scientific question. In this paper, a finite mixture of normal distributions for the shared random effects is proposed for considering the heterogeneity in the population. For detecting whether the unobserved heterogeneity exits or not, we use a simple graphical exploratory diagnostic tool proposed by Verbeke and Molenberghs [34] to assess whether the traditional normality assumption for the random effects in the mixed model is adequate. In the joint modeling setting, in the case of evidence against normality (homogeneity), a finite mixture of normals is used for the shared random-effects distribution. A Bayesian MCMC procedure is developed for parameter estimation and inference. The methodology is illustrated using some simulation studies. Also, the proposed approach is used for analyzing a real HIV data set, using the heterogeneous joint model for this data set, the individuals are classified into two groups: a group with high risk and a group with moderate risk. [ABSTRACT FROM PUBLISHER]

Since the seminal paper by Cook and Weisberg [9], local influence, next to case deletion, has gained popularity as a tool to detect influential subjects and measurements for a variety of statistical models. For the linear mixed model the approach leads to easily interpretable and computationally convenient expressions, not only highlighting influential subjects, but also which aspect of their profile leads to undue influence on the model's fit [17]. Ouwenset al.[24] applied the method to the Poisson-normal generalized linear mixed model (GLMM). Given the model's nonlinear structure, these authors did not derive interpretable components but rather focused on a graphical depiction of influence. In this paper, we consider GLMMs for binary, count, and time-to-event data, with the additional feature of accommodating overdispersion whenever necessary. For each situation, three approaches are considered, based on: (1) purely numerical derivations; (2) using a closed-form expression of the marginal likelihood function; and (3) using an integral representation of this likelihood. Unlike when case deletion is used, this leads to interpretable components, allowing not only to identify influential subjects, but also to study the cause thereof. The methodology is illustrated in case studies that range over the three data types mentioned. [ABSTRACT FROM AUTHOR]

In this paper, we investigate estimation methods to deal with situations where random intercepts are associated to time-varying covariates in the context of linear mixed models. First, a review of previous ways to deal with this so-called endogeneity issue is presented, then a new method based on shared random effects is proposed. Simulation studies and an empirical example are utilized to assess the performance of our proposed method. It is shown that our new approach is more efficient than most competitors and is robust to the misspecification of the random-effects distributions. [ABSTRACT FROM PUBLISHER]

Count data are most commonly modeled using the Poisson model, or by one of its many extensions. Such extensions are needed for a variety of reasons: (1) a hierarchical structure in the data, e.g., due to clustering, the collection of repeated measurements of the outcome, etc.; (2) the occurrence of overdispersion (or underdispersion), meaning that the variability encountered in the data is not equal to the mean, as prescribed by the Poisson distribution; and (3) the occurrence of extra zeros beyond what a Poisson model allows. The first issue is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. Overdispersion is often dealt with through a model developed for this purpose, such as, for example, the negative-binomial model for count data. This can be conceived through a random Poisson parameter. Excess zeros are regularly accounted for using so-called zero-inflated models, which combine either a Poisson or negative-binomial model with an atom at zero. The novelty of this article is that it combines all these features. The work builds upon the modelling framework defined by Molenberghs et al. (2010) in which clustering and overdispersion are accommodated for through two separate sets of random effects in a generalized linear model. [ABSTRACT FROM PUBLISHER]

Multilevel growth curve models for repeated measures data have become increasingly popular and stand as a flexible tool for investigating longitudinal change in students' outcome variables. In addition, these models allow the estimation of school effects on students' outcomes though making strong assumptions about the serial independence of level-1 residuals. This paper introduces a method which takes into account the serial correlation of level-1 residuals and also introduces such serial correlation at level-2 in a complex double serial correlation (DSC) multilevel growth curve model. The results of this study from both real and simulated data show a great improvement in school effects estimates compared to those that have previously been found using multilevel growth curve models without correcting for DSC for both the students' status and growth criteria. [ABSTRACT FROM AUTHOR]

In this paper, we consider the analysis of unequally spaced longitudinal data using transition regression models with random effects. Diffusion as well as stabilization processes will be discussed, but our main focus will be on the latter. The initial conditions problem, which usually arises in transition models with random effects, is addressed. The usefulness of the proposed model is assessed on a large database of longitudinal haemoglobin values collected from blood donations by a Dutch private organization. [ABSTRACT FROM AUTHOR]

Abstract: Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson regression. Two of the main reasons for extending this family are (1) the occurrence of overdispersion, meaning that the variability in the data is not adequately described by the models, which often exhibit a prescribed mean-variance link, and (2) the accommodation of hierarchical structure in the data, stemming from clustering in the data which, in turn, may result from repeatedly measuring the outcome, for various members of the same family, etc. The first issue is dealt with through a variety of overdispersion models, such as, for example, the beta-binomial model for grouped binary data and the negative-binomial model for counts. Clustering is often accommodated through the inclusion of random subject-specific effects. Though not always, one conventionally assumes such random effects to be normally distributed. While both of these phenomena may occur simultaneously, models combining them are uncommon. This paper starts from the broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. We place particular emphasis on so-called conjugate random effects at the level of the mean for the first aspect and normal random effects embedded within the linear predictor for the second aspect, even though our family is more general. The binary and binomial cases are our focus. Apart from model formulation, we present an overview of estimation methods, and then settle for maximum likelihood estimation with analytic-numerical integration. The methodology is applied to two datasets of which the outcomes are binary and binomial, respectively. [Copyright &y& Elsevier]

Motivation: Phosphorylation by protein kinases is a central theme in biological systems. Aberrant protein kinase activity has been implicated in a variety of human diseases (e.g. cancer). Therefore, modulation of kinase activity represents an attractive therapeutic approach for the treatment of human illnesses. Thus, identification of signature peptides is crucial for protein kinase targeting and can be achieved by using PamChip® microarray technology. We propose a flexible semiparametric mixed model for analyzing PamChip® data. This approach enables the estimation of the phosphorylation rate (Velocity) as a function of time together with pointwise confidence intervals.Results: Using a publicly available dataset, we show that our model is capable of adequately fitting the kinase activity profiles and provides velocity estimates over time. Moreover, it allows to test for differences in the velocity of kinase inhibition between responding and non-responding cell lines. This can be done at individual time point as well as for the entire velocity profile.Contact: pushpike@med.kuleuven.beSupplementary information: Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

When data are incomplete, models are often catalogued according to one of the three modelling frameworks to which they belong: selection models (SeM), pattern-mixture models (PMM) and shared-parameter models (SPM). The missing data mechanism is conventionally classified as missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR). Under MCAR, measurement and missingness mechanism are independent, but that is not the case for MAR. The definition of MAR is in SeM terms. Molenberghs et al. (1998) provided a characterization for PMM. Here, MAR is characterized in the SPM framework, using an extended SPM class. A subfamily, satisfying the MAR condition, is studied in detail. Particular implications for non-monotone missingness as well as for longitudinal data subject to dropout are studied. It is indicated how SPM can be constrained such that dropout at a given point in time can depend on current and past, but not on future measurements. Although, a natural requirement, it is less easily imposed in the PMM and SPM frameworks than in the SeM case. Some of the models proposed are illustrated using a clinical trial in toenail dermatophyte onychomycosis. [ABSTRACT FROM AUTHOR]

Statistical models often extend beyond the data available. First, in coarse data, what is actually observed is less detailed than what might be, owing to incompleteness, censoring, grouping, or a combination thereof. Second, in augmented data, the observed data are hypothetically supplemented with random effects, latent variables/classes, or component membership in mixture distributions. The two settings together will be referred to as enriched data. Reasons for modelling enriched data encompass mathematical and computational convenience, advantages in interpretation, and substantive plausibility. Models for enriched data combine evidence coming from empirical data with unverifiable model components, resting entirely on assumptions.This has acute consequences for enriched data, but knowledge about this issue is somewhat scattered. We provide a unified framework for enriched data and show, generally and with focus on incomplete-data models and random-effects models on the other hand, that to any given model an entire class of models can be assigned, with all of its members producing the same fit to the observed data but arbitrary regarding the unobservable parts of the enriched data. The concepts developed are illustrated using a clinical trial in toenail dermatophyte onychomycosis and a developmental toxicity study conducted in mice. [ABSTRACT FROM AUTHOR]

The majority of the statistical literature for the joint modeling of longitudinal and time-to-event data has focused on the development of models that aim at capturing specific aspects of the motivating case studies. However, little attention has been given to the development of diagnostic and model-assessment tools. The main difficulty in using standard model diagnostics in joint models is the nonrandom dropout in the longitudinal outcome caused by the occurrence of events. In particular, the reference distribution of statistics, such as the residuals, in missing data settings is not directly available and complex calculations are required to derive it. In this article, we propose a multiple-imputation-based approach for creating multiple versions of the completed data set under the assumed joint model. Residuals and diagnostic plots for the complete data model can then be calculated based on these imputed data sets. Our proposals are exemplified using two real data sets. [ABSTRACT FROM AUTHOR]

Correlated data frequently arise in contexts such as, for example, repeated measures and meta-analysis. The amount of information in such data depends not only on the sample size, but also on the structure and strength of the correlations among observations from the same independent block. A general concept is discussed, the effective sample size, as a way of quantifying the amount of information in such data. It is defined as the sample size one would need in an independent sample to equal the amount of information in the actual correlated sample. This concept is widely applicable, for Gaussian data and beyond, and provides important insight. For example, it helps explain why fixed-effects and random-effects inferences of meta-analytic data can be so radically divergent. Further, we show that in some cases the amount of information is bounded, even when the number of measures per independent block approaches infinity. We use the method to devise a new denominator degreesof-freedom method for fixed-effects testing. It is compared to the classical Satterthwaite and Kenward-Roger methods for performance and, more importantly, to enhance insight. A key feature of the proposed degrees-of-freedom method is that it, unlike the others, can be used for non-Gaussian data, too. [ABSTRACT FROM AUTHOR]

Whereas marginal models, random-effects models, and conditional models are routinely considered to be the three main modeling families for continuous and discrete repeated measures with linear and generalized linear mean structures, respectively, it is less common to consider nonlinear models, let alone frame them within the above taxonomy. In the latter situation, indeed, when considered at all, the focus is often exclusively on random-effects models. In this article, we consider all three families, exemplify their great flexibility and relative ease of use, and apply them to a simple but illustrative set of data on tree circumference growth of orange trees. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

In this study, we propose a calibration method for preprocessing spiked-in microarray experiments based on nonlinear mixed-effects models. This method uses a spike-in calibration curve to estimate normalized absolute expression values. Moreover, using the asymptotic properties of the calibration estimate, 100(1-α)% confidence intervals for the estimated expression values can be constructed. Simulations are used to show that the approximations on which the construction of the confidence intervals are based are sufficiently accurate to reach the desired coverage probabilities. We illustrate applicability of our method, by estimating the normalized absolute expression values together with the corresponding confidence intervals for two publicly available cDNA microarray experiments (Hilson et al., 2004; Smets et al., 2008). This method can easily be adapted to preprocess one-color oligonucleotide microarray data with a slight adjustment to the mixed model. [ABSTRACT FROM AUTHOR]

Model selection and assessment with incomplete data pose challenges in addition to the ones encountered with complete data. There are two main reasons for this. First, many models describe characteristics of the complete data, in spite of the fact that only an incomplete subset is observed. Direct comparison between model and data is then less than straightforward. Second, many commonly used models are more sensitive to assumptions than in the complete-data situation and some of their properties vanish when they are fitted to incomplete, unbalanced data. These and other issues are brought forward using two key examples, one of a continuous and one of a categorical nature. We argue that model assessment ought to consist of two parts: (i) assessment of a model's fit to the observed data and (ii) assessment of the sensitivity of inferences to unverifiable assumptions, that is, to how a model described the unobserved data given the observed ones. [ABSTRACT FROM AUTHOR]

The analysis of continuous hierarchical data such as repeated measures or data from meta-analyses can be carried out by means of the linear mixed-effects model. However, in some situations this model, in its standard form, does pose computational problems. For example, when dealing with crossed random-effects models, the estimation of the variance components becomes a non-trivial task if only one observation is available for each cross-classified level. Pseudolikelihood ideas have been used in the context of binary data with standard generalized linear multilevel models. However, even in this case the problem of the estimation of the variance remains non-trivial. In this paper, we first propose a method to fit a crossed random-effects model with two levels and continuous outcomes, borrowing ideas from conditional linear mixed-effects model theory. We also propose a crossed random-effects model for binary data combining ideas of conditional logistic regression with pseudolikelihood estimation. We apply this method to a case study with data coming from the field of psychometrics and study a series of items (responses) crossed with participants. A simulation study assesses the operational characteristics of the method. [ABSTRACT FROM AUTHOR]

We present a review of statistical inference in generalized linear mixed models (GLMMs). GLMMs are an extension of generalized linear models and are suitable for the analysis of non-normal data with a clustered structure. A GLMM contains parameters common to all clusters (fixed regression effects and variance components) and cluster-specific parameters. The latter parameters are assumed to be randomly drawn from a population distribution. The parameters of this population distribution (the variance components) have to be estimated together with the fixed effects. We focus on the case in which the cluster-specific parameters are normally distributed. The cluster-specific effects are integrated out of the likelihood so that the fixed effects and variance components can be estimated. Unfortunately, the integral over the cluster-specific effects is intractable for most GLMMs with a normal mixing distribution. Within a classical statistical framework, we distinguish between two broad classes of methods to handle this intractable integral: methods that rely on a numerical approximation to the integral and methods that use an analytical approximation to the integrand. Finally, we present an overview of available methods for testing hypotheses about the parameters of GLMMs. [ABSTRACT FROM AUTHOR]

A mixed model is a flexible tool for joint modeling purposes, especially when the gathered data are unbalanced. However, computational problems due to the dimension of the joint covariance matrix of the random effects arise as soon as the number of outcomes and/or the number of used random effects per outcome increases. We propose a pairwise approach in which all possible bivariate models are fitted, and where inference follows from pseudo-likelihood arguments. The approach is applicable for linear, generalized linear, and nonlinear mixed models, or for combinations of these. The methodology will be illustrated for linear mixed models in the analysis of 22-dimensional, highly unbalanced, longitudinal profiles of hearing thresholds. [ABSTRACT FROM AUTHOR]

Incomplete series of data is a common feature in quality-of-life studies, in particular in chronic diseases where attrition of patients is high. Two alternative approaches to modeling longitudinal data with incomplete measurements have frequently been proposed in the literature, selection models and pattern-mixture models. In this paper we focus on, by way of sensitivity analysis, extrapolating incomplete patterns using identifying restrictions. Perhaps the best known ones are so-called complete case missing value restrictions (CCMV), where for a given pattern, the conditional distribution of the missing data, given the observed data, is equated to its counterpart in the completers. Available case missing value (ACMV) restrictions equate this conditional density to the one calculated from the subgroup of all patterns for which all required components have been observed. Neighboring case missing value restrictions (NCMV) equate this conditional density to the one calculated from the pattern with one additional measurement obtained. In this paper, these three identifying restriction strategies are used to multiply impute missing data in a study in metastatic prostate cancer. Multiple imputation is employed to reduce the uncertainty of single imputation. It is shown how hypothesis testing and sensitivity analyses are carried out in this setting. [ABSTRACT FROM AUTHOR]

A response from the authors of the article "The analysis of multivariate longitudinal data: A review," that was published in a previous 2014 issue is presented.