CiteULike: jyuh mixed-model

A Markov regression random-effects model for remission of functional disability in patients following a first stroke: a Bayesian approach.

SL Pan — 2008-07-22T12:06:33-00:00

Statistics in medicine, Vol. 26, No. 29. (20 December 2007), pp. 5335-5353.

Few attempts have been made to model the dynamics of stroke-related disability. It is possible though, using panel data and multi-state Markov regression models that incorporate measured covariates and latent variables (random effects). This study aimed to model a series of functional transitions (following a first stroke) using a three-state Markov model with or without considering random effects. Several proportional hazards parameterizations were considered. A Bayesian approach that utilizes the Markov Chain Monte Carlo (MCMC) and Gibbs sampling functionality of WinBUGS (a Windows-based Bayesian software package) was developed to generate the marginal posterior distributions of the various transition parameters (e.g. the transition rates and transition probabilities). Model building and comparisons was guided by reference to the deviance information criteria (DIC). Of the four proportional hazards models considered, exponential regression was preferred because it led to the smallest deviances. Adding random effects further improved the model fit. Of the covariates considered, only age, infarct size, and baseline functional status were significant. By using our final model we were able to make individual predictions about functional recovery in stroke patients.

A random effects four-part model, with application to correlated medical costs

Lei Liu — 2008-07-22T05:13:41-00:00

Computational Statistics & Data Analysis, Vol. 52, No. 9. (15 May 2008), pp. 4458-4473.

In this paper we propose a four-part random effects model, with application to correlated medical cost data. Four joint equations are used to model respectively: (1) the probability of seeking medical treatment, (2) the probability of being hospitalized (conditional on seeking medical treatment), and the actual amount of (3) outpatient and (4) inpatient costs. Our model simultaneously takes account of the inter-temporal (or within-cluster) correlation of each patient and the cross-equation correlation of the four equations, by means of joint linear mixed models and generalized linear mixed models. The estimation is accomplished by the high-order Laplace approximation technique in Raudenbush et al. [Raudenbush, S.W., Yang, M., Yosef, M., 2000. Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation. Journal of Computational and Graphical Statistics 9, 141-157] and Olsen and Schafer [Olsen, M.K., Schafer, J.L., 2001. A two-part random effects model for semicontinuous longitudinal data. Journal of the American Statistical Association 96, 730-745]. Our model is used to analyze monthly medical costs of 1397 chronic heart failure patients from the clinical data repository (CDR) at the University of Virginia.

A distribution-free test of constant mean in linear mixed effects models.

J Lim — 2008-07-22T04:26:24-00:00

Statistics in medicine, Vol. 27, No. 19. (30 August 2008), pp. 3833-3846.

We propose a distribution-free procedure, an analogy of the DIP test in non-parametric regression, to test whether the means of responses are constant over time in repeated measures data. Unlike the existing tests, the proposed procedure requires very minimal assumptions to the distributions of both random effects and errors. We study the asymptotic reference distribution of the test statistic analytically and propose a permutation procedure to approximate the finite-sample reference distribution. The size and power of the proposed test are illustrated and compared with competitors through several simulation studies. We find that it performs well for data of small sizes, regardless of model specification. Finally, we apply our test to a data example to compare the effect of fatigue in two different methods used for cardiopulmonary resuscitation. Copyright (c) 2008 John Wiley & Sons, Ltd.

A multi-level two-part random effects model, with application to an alcohol-dependence study.

Lei Liu — 2008-04-30T09:33:54-00:00

Statistics in medicine (25 January 2008)

Two-part random effects models (J. Am. Statist. Assoc. 2001; 96:730-745; Statist. Methods Med. Res. 2002; 11:341-355) have been applied to longitudinal studies for semi-continuous outcomes, characterized by a large portion of zero values and continuous non-zero (positive) values. Examples include repeated measures of daily drinking records, monthly medical costs, and annual claims of car insurance. However, the question of how to apply such models to multi-level data settings remains. In this paper, we propose a novel multi-level two-part random effects model. Distinct random effects are used to characterize heterogeneity at different levels. Maximum likelihood estimation and inference are carried out through Gaussian quadrature technique, which can be implemented conveniently in freely available software-aML. The model is applied to the analysis of repeated measures of the daily drinking record in a randomized controlled trial of topiramate for alcohol-dependence treatment. Copyright (c) 2008 John Wiley & Sons, Ltd.

Linear mixed models

2008-07-22T02:51:43-00:00

A comparison of methods for estimating the random effects distribution of a linear mixedmodel.

Wendimagegn Ghidey — 2008-07-22T01:55:54-00:00

Statistical methods in medical research (18 June 2008)

This article reviews various recently suggested approaches to estimate the random effects distribution in a linear mixed model, i.e. (1) the smoothing by roughening approach of Shenand Louis,(1) (2) the semi-non-parametric approach of Zhang and Davidian,(2) (3) the heterogeneity model of Verbeke and Lesaffre(3) and (4) a flexible approach of Ghidey et al.(4) These four approaches are compared via an extensive simulation study. We conclude that for the considered cases, the approach of Ghidey et al.(4) often shows to have the smallest integrated mean squared error for estimating the random effects distribution. An analysis of a longitudinal dental data set illustrates the performance of the methods in a practical example.

Bliese-Multilevel Modeling in R

2008-07-20T04:59:14-00:00

The Analysis of Longitudinal Data Using Mixed Model L-Splines

Welham — 2006-06-20T11:02:42-00:00

Biometrics, Vol. 62, No. 2. (June 2006), pp. 392-401.

A family of tests to detect misspecifications in the random-effects structure of generalized linear mixed models

A Alonso — 2008-07-18T00:50:41-00:00

Computational Statistics & Data Analysis, Vol. 52, No. 9. (15 May 2008), pp. 4474-4486.

Estimation in generalized linear mixed models for non-Gaussian longitudinal data is often based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. It is known that the results obtained from these models are not always robust against misspecification of the random-effects structure. Therefore, diagnostic tools for the detection of this misspecification are of the utmost importance. Three diagnostic tests, based on the eigenvalues of the variance-covariance matrices for the fixed-effects parameters estimates, are proposed in the present work. The power and type I error rate of these tests are studied via simulations. A very acceptable performance was observed in many cases, especially for those misspecifications that can have a big impact on the maximum likelihood estimators.

The impact of a misspecified random-effects distribution on estimation in generalized linear mixed models

2008-07-18T00:51:40-00:00

Analysis and Sensitivity Analysis for Incomplete Longitudinal Data

2008-07-18T00:50:00-00:00

Longitudinal and Incomplete Data Analysis

Geert Verbeke — 2008-07-18T00:40:31-00:00

Mixed modeling and multiple imputation for unobservable genotype clusters.

AS Foulkes — 2008-07-15T06:35:56-00:00

Statistics in medicine, Vol. 27, No. 15. (10 July 2008), pp. 2784-2801.

Understanding the genetic contributions to complex diseases will require consideration of interaction across multiple genes and environmental factors. At the same time, capturing information on allelic phase, that is, whether alleles within a gene are in cis (on the same chromosome) or in trans (on different chromosomes), is critical when using haplotypic approaches in disease association studies. This paper proposes a combination of mixed modeling and multiple imputation for assessing high-order genotype-phenotype associations while accounting for the uncertainty in phase inherent in population-based association studies. This method provides a flexible statistical framework for controlling for potential confounders and assessing gene-environment and gene-gene interactions in studies of unrelated individuals where the haplotypic phase is generally unobservable. The proposed method is applied to a cohort of 626 subjects with human immunodeficiency virus (HIV) to assess the potential contribution of four genes, apolipoprotein-C-III, apolipoprotein-E, endothelial lipase and hepatic lipase in predicting lipid abnormalities. A simulation study is also presented to describe the method performance.

Sample size and power calculations based on generalized linear mixed models with correlated binary outcomes.

Q Dang — 2008-07-11T03:30:10-00:00

Computer methods and programs in biomedicine, Vol. 91, No. 2. (August 2008), pp. 122-127.

The generalized linear mixed model (GLIMMIX) provides a powerful technique to model correlated outcomes with different types of distributions. The model can now be easily implemented with SAS PROC GLIMMIX in version 9.1. For binary outcomes, linearization methods of penalized quasi-likelihood (PQL) or marginal quasi-likelihood (MQL) provide relatively accurate variance estimates for fixed effects. Using GLIMMIX based on these linearization methods, we derived formulas for power and sample size calculations for longitudinal designs with attrition over time. We found that the power and sample size estimates depend on the within-subject correlation and the size of random effects. In this article, we present tables of minimum sample sizes commonly used to test hypotheses for longitudinal studies. A simulation study was used to compare the results. We also provide a Web link to the SAS macro that we developed to compute power and sample sizes for correlated binary outcomes.

FUNCTIONAL LINEAR REGRESSION ANALYSIS FOR LONGITUDINAL DATA1

2008-07-07T04:21:57-00:00

Sequential analysis of latent variables using mixed-effect latent variable models: Impact of non-informative and informative missing data.

V Sébille — 2008-07-07T04:15:15-00:00

Statistics in medicine, Vol. 26, No. 27. (30 November 2007), pp. 4889-4904.

Sequential methods allowing for early stopping of clinical trials are widely used in various therapeutic areas. These methods allow for the analysis of different types of endpoints (quantitative, qualitative, time to event) and often provide, in average, substantial reductions in sample size as compared with single-stage designs while maintaining pre-specified type I and II errors. Sequential methods are also used when analysing particular endpoints that cannot be directly measured, such as depression, quality of life, or cognitive functioning, which are often measured through questionnaires. These types of endpoints are usually referred to as latent variables and should be analysed with latent variable models. In addition, in most clinical trials studying such latent variables, incomplete data are not uncommon and the missing data process might also be non-ignorable. We investigated the impact of informative or non-informative missing data on the statistical properties of the double triangular test (DTT), combined with the mixed-effects Rasch model (MRM) for dichotomous responses or the traditional method based on observed patient's scores (S) to the questionnaire. The achieved type I errors for the DTT were usually close to the target value of 0.05 for both methods, but increased slightly for the MRM when informative missing data were present. The DTT was very close to the nominal power of 0.95 when the MRM was used, but substantially underpowered with the S method (reduction of about 23 per cent), irrespective of whether informative missing data were present or not. Moreover, the DTT using the MRM allowed for reaching a conclusion (under H(0) or H(1)) with fewer patients than the S method, the average sample number for the latter increasing importantly when the proportion of missing data increased. Incorporating MRM in sequential analysis of latent variables might provide a more powerful method than the traditional S method, even in the presence of non-informative or informative missing data.

Bayesian semiparametric regression for longitudinal binary processes with missing data.

L Su — 2008-06-26T02:33:27-00:00

Statistics in medicine, Vol. 27, No. 17. (30 July 2008), pp. 3247-3268.

Longitudinal studies with binary repeated measures are widespread in biomedical research. Marginal regression approaches for balanced binary data are well developed, whereas for binary process data, where measurement times are irregular and may differ by individuals, likelihood-based methods for marginal regression analysis are less well developed. In this article, we develop a Bayesian regression model for analyzing longitudinal binary process data, with emphasis on dealing with missingness. We focus on the settings where data are missing at random (MAR), which require a correctly specified joint distribution for the repeated measures in order to draw valid likelihood-based inference about the marginal mean. To provide maximum flexibility, the proposed model specifies both the marginal mean and serial dependence structures using nonparametric smooth functions. Serial dependence is allowed to depend on the time lag between adjacent outcomes as well as other relevant covariates. Inference is fully Bayesian. Using simulations, we show that adequate modeling of the serial dependence structure is necessary for valid inference of the marginal mean when the binary process data are MAR. Longitudinal viral load data from the HIV Epidemiology Research Study are analyzed for illustration. Copyright (c) 2008 John Wiley & Sons, Ltd.

Semiparametric Stochastic Mixed Models for Longitudinal Data-spmm.sas

Daowen Zhang — 2008-06-25T15:02:48-00:00

Journal of the American Statistical Association, Vol. 93, No. 442. (1998), pp. 710-719.

We consider inference for a semiparametric stochastic mixed model for longitudinal data. This model uses parametric fixed effects to represent the covariate effects and an arbitrary smooth function to model the time effect. The within-subject correlation is modeled using random effects and a stationary or nonstationary stochastic process. We derive maximum penalized likelihood estimators of the regression coefficients and the nonparametric function. The resulting estimator of the nonparametric...

Semi-parametric mixed models (spmm.sas)

2008-06-25T14:49:19-00:00

Missing data and the trouble with LOCF.

DL Streiner — 2008-06-23T14:20:36-00:00

Evidence-based mental health, Vol. 11, No. 1. (February 2008), pp. 3-5.

Statistical choices can affect inferences about treatment efficacy: a case study from obsessive-compulsive disorder research.

HB Simpson — 2008-06-23T14:15:02-00:00

Journal of psychiatric research, Vol. 42, No. 8. (July 2008), pp. 631-638.

Longitudinal clinical trials in psychiatry have used various statistical methods to examine treatment effects. The validity of the inferences depends upon the different method's assumptions and whether a given study violates those assumptions. The objective of this paper was to elucidate these complex issues by comparing various methods for handling missing data (e.g., last observation carried forward [LOCF], completer analysis, propensity-adjusted multiple imputation) and for analyzing outcome (e.g., end-point analysis, repeated-measures analysis of variance [RM-ANOVA], mixed-effects models [MEMs]) using data from a multi-site randomized controlled trial in obsessive-compulsive disorder (OCD). The trial compared the effects of 12 weeks of exposure and ritual prevention (EX/RP), clomipramine (CMI), their combination (EX/RP&CMI) or pill placebo in 122 adults with OCD. The primary outcome measure was the Yale-Brown Obsessive Compulsive Scale. For most comparisons, inferences about the relative efficacy of the different treatments were impervious to different methods for handling missing data and analyzing outcome. However, when EX/RP was compared to CMI and when CMI was compared to placebo, traditional methods (e.g., LOCF, RM-ANOVA) led to different inferences than currently recommended alternatives (e.g., multiple imputation based on estimation-maximization algorithm, MEMs). Thus, inferences about treatment efficacy can be affected by statistical choices. This is most likely when there are small but potentially clinically meaningful treatment differences and when sample sizes are modest. The use of appropriate statistical methods in psychiatric trials can advance public health by ensuring that valid inferences are made about treatment efficacy.

Assessing and interpreting treatment effects in longitudinal clinical trials with missing data.

CH Mallinckrodt — 2008-06-23T14:12:06-00:00

Biological psychiatry, Vol. 53, No. 8. (15 April 2003), pp. 754-760.

Treatment effects are often evaluated by comparing change over time in outcome measures; however, valid analyses of longitudinal data can be problematic, particularly if some data are missing. For decades, the last observation carried forward (LOCF) approach has been a common method of handling missing data. Considerable advances in statistical methodology and our ability to implement those methods have been made in recent years. Thus, it is appropriate to reconsider analytic approaches for longitudinal data. This review examines the following from a clinical perspective: 1) the characteristics of missing data that influence analytic choices; 2) the attributes of common methods of handling missing data; and 3) the use of the data characteristics and the attributes of the various methods, along with empirical evidence, to develop a robust approach for the analysis and interpretation of data from longitudinal clinical trials. We propose that, in many settings, the primary efficacy analysis should use a repeated measures, likelihood-based, mixed-effects modeling approach, with LOCF used as a secondary, composite measure of efficacy, safety, and tolerability. We illustrate how repeated-measures analyses can be used to enhance decision-making, and we review the caveats that remain regarding the use of LOCF as a composite measure.

Repeated Measures Lecture 2

2008-06-23T14:08:24-00:00

High dimensional multivariate mixed models for binary questionnaire data

Fieuws — 2006-07-24T03:25:28-00:00

Journal of the Royal Statistical Society: Series C (Applied Statistics), Vol. 55, No. 4. (August 2006), pp. 449-460.

Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles

Fieuws — 2006-06-20T11:02:40-00:00

Biometrics, Vol. 62, No. 2. (June 2006), pp. 424-431.

A high-dimensional joint model for longitudinal outcomes of different nature.

Christel Faes — 2008-06-22T07:27:55-00:00

Statistics in medicine (12 June 2008)

In repeated dose-toxicity studies, many outcomes are repeatedly measured on the same animal to study the toxicity of a compound of interest. This is only one example in which one is confronted with the analysis of many outcomes, possibly of a different type. Probably the most common situation is that of an amalgamation of continuous and categorical outcomes. A possible approach towards the joint analysis of two longitudinal outcomes of a different nature is the use of random-effects models (Models for Discrete Longitudinal Data. Springer Series in Statistics. Springer: New York, 2005). Although a random-effects model can easily be extended to jointly model many outcomes of a different nature, computational problems arise as the number of outcomes increases. To avoid maximization of the full likelihood expression, Fieuws and Verbeke (Biometrics 2006; 62:424-431) proposed a pairwise modeling strategy in which all possible pairs are modeled separately, using a mixed model, yielding several different estimates for the same parameters. These latter estimates are then combined into a single set of estimates. Also inference, based on pseudo-likelihood principles, is indirectly derived from the separate analyses. In this paper, we extend the approach of Fieuws and Verbeke (Biometrics 2006; 62:424-431) in two ways: the method is applied to different types of outcomes and the full pseudo-likelihood expression is maximized at once, leading directly to unique estimates as well as direct application of pseudo-likelihood inference. This is very appealing when interested in hypothesis testing. The method is applied to data from a repeated dose-toxicity study designed for the evaluation of the neurofunctional effects of a psychotrophic drug. The relative merits of both methods are discussed. Copyright (c) 2008 John Wiley & Sons, Ltd.

A mixed model-based variance estimator for marginal model analyses of cluster randomized trials.

TM Braun — 2008-06-14T08:41:37-00:00

Biometrical journal. Biometrische Zeitschrift, Vol. 49, No. 3. (June 2007), pp. 394-405.

Generalized estimating equations (GEE) are used in the analysis of cluster randomized trials (CRTs) because: 1) the resulting intervention effect estimate has the desired marginal or population-averaged interpretation, and 2) most statistical packages contain programs for GEE. However, GEE tends to underestimate the standard error of the intervention effect estimate in CRTs. In contrast, penalized quasi-likelihood (PQL) estimates the standard error of the intervention effect in CRTs much better than GEE but is used less frequently because: 1) it generates an intervention effect estimate with a conditional, or cluster-specific, interpretation, and 2) PQL is not a part of most statistical packages. We propose taking the variance estimator from PQL and re-expressing it as a sandwich-type estimator that could be easily incorporated into existing GEE packages, thereby making GEE useful for the analysis of CRTs. Using numerical examples and data from an actual CRT, we compare the performance of this variance estimator to others proposed in the literature, and we find that our variance estimator performs as well as or better than its competitors.

ML-DEs: a program for designing efficient multilevel studies.

W Cools — 2008-06-14T03:49:44-00:00

Behavior research methods, Vol. 40, No. 1. (February 2008), pp. 236-249.

The multilevel model is increasingly used as a flexible tool in the statistical analysis of dependent behavioral research data. A drawback of this model's flexibility is that it complicates designing the study. For example, an important additional consideration in the design of a multilevel study is choosing the number and the size of the clusters to sample to ensure sufficient efficiency as quantified by precision, bias, or statistical power. To help researchers in designing their multilevel study, a user-friendly simulation tool is introduced (Multilevel Design Efficiency Using Simulation, or ML-DEs), also allowing for design questions that have not been dealt with analytically in the literature, while avoiding complex specifications of simulation studies. ML-DEs generates MLwiN macros for running the simulations and handles its output using R scripts to compare the designs' efficiencies for both fixed and random parameters, allowing for small sample sizes, unbalanced data, and more than two levels.

Multilevel modelling of medical data.

H Goldstein — 2007-04-30T15:15:28-00:00

Stat Med, Vol. 21, No. 21. (15 November 2002), pp. 3291-3315.

This tutorial presents an overview of multilevel or hierarchical data modelling and its applications in medicine. A description of the basic model for nested data is given and it is shown how this can be extended to fit flexible models for repeated measures data and more complex structures involving cross-classifications and multiple membership patterns within the software package MLwiN. A variety of response types are covered and both frequentist and Bayesian estimation methods are described.

A comparison between traditional methods and multilevel regression for the analysis of multicenter intervention studies.

M Moerbeek — 2008-06-13T04:45:51-00:00

Journal of clinical epidemiology, Vol. 56, No. 4. (April 2003), pp. 341-350.

This article reviews three traditional methods for the analysis of multicenter trials with persons nested within clusters, i.e., centers, namely naïve regression (persons as units of analysis), fixed effects regression, and the use of summary measures (clusters as units of analysis), and compares these methods with multilevel regression. The comparison is made for continuous (quantitative) outcomes, and is based on the estimator of the treatment effect and its standard error, because these usually are of main interest in intervention studies. When the results of the experiment have to be valid for some larger population of centers, the centers in the intervention study have to present a random sample from this population and multilevel regression may be used. It is shown that the treatment effect and especially its standard error, are generally incorrectly estimated by the traditional methods, which should, therefore, not in general be used as an alternative to multilevel regression.

Methods for pooling results from multi-center studies.

H Worthington — 2008-06-13T02:46:50-00:00

Journal of dental research, Vol. 83 Spec No C (2004)

A multi-center study is one conducted simultaneously in several participating centers following an agreed protocol, where the randomization has been carried out independently within each center. The main consideration for pooling the data from the individual centers is the choice between a weighted analysis, which weights centers relative to the number of patients in them, or an unweighted analysis as the primary statistical method. The unweighted analysis is used to investigate whether there was an interaction between the centers and study groups. Another issue is whether a fixed- or random-effects model should be used. There is unresolved controversy among statisticians about whether to use a weighted (type II) or unweighted analysis (type III), since there are advantages and disadvantages to the use of either method. The weighted analysis provides the most powerful test of the treatment contrast if there is no interaction between treatment and center. If there is an interaction, the unweighted analysis leads to unbiased estimates. Although, from an estimation and hypothesis testing standpoint, there is no need to balance the number of patients between the sites, it is sensible to avoid major imbalances among the study sites. There is agreement among statisticians that a fixed-effects model should be used.

Modelling covariance structure in the analysis of repeated measures data.

RC Littell — 2007-12-21T14:46:05-00:00

Stat Med, Vol. 19, No. 13. (15 July 2000), pp. 1793-1819.

The term 'repeated measures' refers to data with multiple observations on the same sampling unit. In most cases, the multiple observations are taken over time, but they could be over space. It is usually plausible to assume that observations on the same unit are correlated. Hence, statistical analysis of repeated measures data must address the issue of covariation between measures on the same unit. Until recently, analysis techniques available in computer software only offered the user limited and inadequate choices. One choice was to ignore covariance structure and make invalid assumptions. Another was to avoid the covariance structure issue by analysing transformed data or making adjustments to otherwise inadequate analyses. Ignoring covariance structure may result in erroneous inference, and avoiding it may result in inefficient inference. Recently available mixed model methodology permits the covariance structure to be incorporated into the statistical model. The MIXED procedure of the SAS((R)) System provides a rich selection of covariance structures through the RANDOM and REPEATED statements. Modelling the covariance structure is a major hurdle in the use of PROC MIXED. However, once the covariance structure is modelled, inference about fixed effects proceeds essentially as when using PROC GLM. An example from the pharmaceutical industry is used to illustrate how to choose a covariance structure. The example also illustrates the effects of choice of covariance structure on tests and estimates of fixed effects. In many situations, estimates of linear combinations are invariant with respect to covariance structure, yet standard errors of the estimates may still depend on the covariance structure.

Multiple imputation inference for multivariate multilevel continuous data with ignorable non-response.

RM Yucel — 2008-06-10T04:10:03-00:00

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences, Vol. 366, No. 1874. (13 July 2008), pp. 2389-2403.

Methods specifically targeting missing values in a wide spectrum of statistical analyses are now part of serious statistical thinking due to many advances in computational statistics and increased awareness among sophisticated consumers of statistics. Despite many advances in both theory and applied methods for missing data, missing-data methods in multilevel applications lack equal development. In this paper, I consider a popular inferential tool via multiple imputation in multilevel applications with missing values. I specifically consider missing values occurring arbitrarily at any level of observational units. I use Bayesian arguments for drawing multiple imputations from the underlying (posterior) predictive distribution of missing data. Multivariate extensions of well-known mixed-effects models form the basis for simulating the posterior predictive distribution, hence creating the multiple imputations. The discussion of these topics is demonstrated in an application assessing correlates to unmet need for mental health care among children with special health care needs.

Predicting renal graft failure using multivariate longitudinal profiles

Steffen Fieuws — 2008-06-10T03:56:16-00:00

Biostat (3 December 2007), kxm041.

Patients who have undergone renal transplantation are monitored longitudinally at irregular time intervals over 10 years or more. This yields a set of biochemical and physiological markers containing valuable information to anticipate a failure of the graft. A general linear, generalized linear, or nonlinear mixed model is used to describe the longitudinal profile of each marker. To account for the correlation between markers, the univariate mixed models are combined into a multivariate mixed model (MMM) by specifying a joint distribution for the random effects. Due to the high number of markers, a pairwise modeling strategy, where all possible pairs of bivariate mixed models are fitted, is used to obtain parameter estimates for the MMM. These estimates are used in a Bayes rule to obtain, at each point in time, the prognosis for long-term success of the transplant. It is shown that allowing the markers to be correlated can improve this prognosis. 10.1093/biostatistics/kxm041

Discriminant Analysis for Longitudinal Data with Multiple Continuous Responses and Possibly Missing Data.

Guillermo Marshall — 2008-06-10T03:55:53-00:00

Biometrics (24 March 2008)

Multiple outcomes are often used to properly characterize an effect of interest. This article discusses model-based statistical methods for the classification of units into one of two or more groups where, for each unit, repeated measurements over time are obtained on each outcome. We relate the observed outcomes using multivariate nonlinear mixed-effects models to describe evolutions in different groups. Due to its flexibility, the random-effects approach for the joint modeling of multiple outcomes can be used to estimate population parameters for a discriminant model that classifies units into distinct predefined groups or populations. Parameter estimation is done via the expectation-maximization algorithm with a linear approximation step. We conduct a simulation study that sheds light on the effect that the linear approximation has on classification results. We present an example using data from a study in 161 pregnant women in Santiago, Chile, where the main interest is to predict normal versus abnormal pregnancy outcomes.

Random-effects models for multivariate repeated measures.

S Fieuws — 2008-06-10T03:54:54-00:00

Statistical methods in medical research, Vol. 16, No. 5. (October 2007), pp. 387-397.

Mixed models are widely used for the analysis of one repeatedly measured outcome. If more than one outcome is present, a mixed model can be used for each one. These separate models can be tied together into a multivariate mixed model by specifying a joint distribution for their random effects. This strategy has been used for joining multivariate longitudinal profiles or other types of multivariate repeated data. However, computational problems are likely to occur when the number of outcomes increases. A pairwise modeling approach, in which all possible bivariate mixed models are fitted and where inference follows from pseudo-likelihood arguments, has been proposed to circumvent the dimensional limitations in multivariate mixed models. An analysis on 22-variate longitudinal measurements of hearing thresholds illustrates the performance of the pairwise approach in the context of multivariate linear mixed models. For generalized linear mixed models, a data set containing repeated measurements of seven aspects of psycho-cognitive functioning will be analyzed.

The effect of miss-specified baseline characteristics on inference for longitudinal trends in linear mixed models.

G Verbeke — 2008-06-08T04:07:45-00:00

Biostatistics (Oxford, England), Vol. 8, No. 4. (October 2007), pp. 772-783.

The main advantage of longitudinal studies is that they can distinguish changes over time within individuals (longitudinal effects) from differences among subjects at the start of the study (baseline characteristics, cross-sectional effects). Often, especially in observational studies, longitudinal trends are studied after correction for many potentially important baseline differences between subjects. We show that, in the context of linear mixed models, inference for longitudinal trends is in general biased if a wrong model for the baseline characteristics is used. However, we will argue that this bias is small in most practical situations and completely vanishes in the special case of a growth curve model for complete balanced data. In the latter case, inference for longitudinal trends is completely independent of additional baseline covariates that might have been omitted from the model.

Small sample inference for fixed effects from restricted maximum likelihood.

MG Kenward — 2008-06-08T00:53:20-00:00

Biometrics, Vol. 53, No. 3. (September 1997), pp. 983-997.

Restricted maximum likelihood (REML) is now well established as a method for estimating the parameters of the general Gaussian linear model with a structured covariance matrix, in particular for mixed linear models. Conventionally, estimates of precision and inference for fixed effects are based on their asymptotic distribution, which is known to be inadequate for some small-sample problems. In this paper, we present a scaled Wald statistic, together with an F approximation to its sampling distribution, that is shown to perform well in a range of small sample settings. The statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias. This approach has the advantage that it reproduces both the statistics and F distributions in those settings where the latter is exact, namely for Hotelling T2 type statistics and for analysis of variance F-ratios. The performance of the modified statistics is assessed through simulation studies of four different REML analyses and the methods are illustrated using three examples.

The Analysis of Repeated Measurements with Mixed-Model Adjusted F Tests

Rhonda Kowalchuk — 2008-06-07T16:36:02-00:00

Educational and Psychological Measurement, Vol. 64, No. 2. (1 April 2004), pp. 224-242.

One approach to the analysis of repeated measures data allows researchers to model the covariance structure of their data rather than presume a certain structure, as is the case with conventional univariate and multivariate test statistics. This mixed-model approach, available through SAS PROC MIXED, was compared to a Welch-James type statistic. The Welch-James approach is known to provide generally robust tests of treatment effects in a repeated measures between-by within-subjects design under assumption violations given certain sample size requirements. The mixed-model F tests were based on Kenward-Roger's adjusted degrees of freedom solution, an approach specifically proposed for small sample settings. The authors investigated Type I error control for repeated measures main and interaction effects in unbalanced designs when normality and covariance homogeneity assumptions did not hold. The mixed-model Kenward-Roger's adjusted F tests showed superior Type I error control in small sample size conditions in which the Welch-James type statistic was nonrobust; power rates, however, did not favor one approach over the other. 10.1177/0013164403260196

Recent advances in fitting mixed-effects models

2008-06-07T16:34:29-00:00

Fixed vs random effects meta-analysis in rare event studies: the rosiglitazone link with myocardial infarction and cardiac death.

JJ Shuster — 2008-06-07T13:15:08-00:00

Statistics in medicine, Vol. 26, No. 24. (30 October 2007), pp. 4375-4385.

Meta-analyses can be powerful tools to combine the results of randomized clinical trials and observational studies to make consensus inferences about a medical issue. It will be demonstrated that a common practice of testing for homogeneity of effect size, and acting upon the inference to decide between fixed vs random effects, can lead to potentially misleading results. A by-product of this paper is a new ratio estimator approach to random effects meta-analysis of a large set of studies with low event rates. As a case study, we shall use the recent Rosiglitazone example, where diagnostic testing failed to reject homogeneity, leading the investigators to use fixed effects. The results for the fixed and random effects analyses are discordant. In the fixed (random) effects analysis, the p-values for myocardial infarction were 0.03 (0.11) while those for cardiac death were 0.06 (0.0017). Had the fixed effects analysis controlled the study error for multiple testing via a Bonferonni correction, the joint 95+ per cent confidence rectangle for the two outcomes would have included odds ratios of (1.0, 1.0). For the Rosiglitazone example, random effects analysis, where all studies receive the same weight, is the superior choice over fixed effects, where two large studies dominate.

Assessing surrogates as trial endpoints using mixed models.

EL Korn — 2008-06-06T14:48:07-00:00

Statistics in medicine, Vol. 24, No. 2. (30 January 2005), pp. 163-182.

Having a surrogate for a definitive endpoint in a clinical trial can sometimes be useful when it is impractical, invasive or very time consuming to obtain the definitive endpoint. This paper discusses methods for assessing whether the surrogate-endpoint results of a trial can be used in place of definitive-endpoint results. It is important when examining this trial-level surrogacy to include the possibility of trial-level effects and to distinguish whether the treatment arms are naturally ordered, e.g. A vs A+B rather than A vs B. Methods using mixed models of trial-level summaries are discussed and compared to fixed-effects models and to the possibility of using models of individual-level data. We give estimators for definitive-endpoint results of a trial that are predicted from the surrogate-endpoint results of the trial and a set of results from previous trials in which both the definitive and surrogate trial results were available. Graphical displays are also suggested. Two sets of trial results previously analysed for trial-level surrogacy are used as examples.

Type I and Type II Error Under Random-Effects Misspecification in Generalized Linear Mixed Models

Litiere — 2007-12-07T02:26:55-00:00

Biometrics, Vol. 63, No. 4. (December 2007), pp. 1038-1044.

The impact of a misspecified random-effects distribution on the estimation and the performance of inferential procedures in generalized linear mixed models.

S Litière — 2008-06-06T14:41:31-00:00

Statistics in medicine (11 December 2007)

Estimation in generalized linear mixed models (GLMMs) is often based on maximum likelihood theory, assuming that the underlying probability model is correctly specified. However, the validity of this assumption is sometimes difficult to verify. In this paper we study, through simulations, the impact of misspecifying the random-effects distribution on the estimation and hypothesis testing in GLMMs. It is shown that the maximum likelihood estimators are inconsistent in the presence of misspecification. The bias induced in the mean-structure parameters is generally small, as far as the variability of the underlying random-effects distribution is small as well. However, the estimates of this variability are always severely biased. Given that the variance components are the only tool to study the variability of the true distribution, it is difficult to assess whether problems in the estimation of the mean structure occur. The type I error rate and the power of the commonly used inferential procedures are also severely affected. The situation is aggravated if more than one random effect is included in the model. Further, we propose to deal with possible misspecification by way of sensitivity analysis, considering several random-effects distributions. All the results are illustrated using data from a clinical trial in schizophrenia. Copyright (c) 2007 John Wiley & Sons, Ltd.

Joint Models for a Primary Endpoint and Multiple Longitudinal Covariate Processes

Li — 2007-12-07T02:26:54-00:00

Biometrics, Vol. 63, No. 4. (December 2007), pp. 1068-1078.

Move over ANOVA: progress in analyzing repeated-measures data and its reflection in papers published in the Archives of General Psychiatry.

R Gueorguieva — 2008-05-24T09:26:20-00:00

Archives of general psychiatry, Vol. 61, No. 3. (March 2004), pp. 310-317.

BACKGROUND: The analysis of repeated-measures data presents challenges to investigators and is a topic for ongoing discussion in the Archives of General Psychiatry. Traditional methods of statistical analysis (end-point analysis and univariate and multivariate repeated-measures analysis of variance [rANOVA and rMANOVA, respectively]) have known disadvantages. More sophisticated mixed-effects models provide flexibility, and recently developed software makes them available to researchers. OBJECTIVES: To review methods for repeated-measures analysis and discuss advantages and potential misuses of mixed-effects models. Also, to assess the extent of the shift from traditional to mixed-effects approaches in published reports in the Archives of General Psychiatry. DATA SOURCES: The Archives of General Psychiatry from 1989 through 2001, and the Department of Veterans Affairs Cooperative Study 425. STUDY SELECTION: Studies with a repeated-measures design, at least 2 groups, and a continuous response variable. DATA EXTRACTION: The first author ranked the studies according to the most advanced statistical method used in the following order: mixed-effects model, rMANOVA, rANOVA, and end-point analysis. DATA SYNTHESIS: The use of mixed-effects models has substantially increased during the last 10 years. In 2001, 30% of clinical trials reported in the Archives of General Psychiatry used mixed-effects analysis. CONCLUSIONS: Repeated-measures ANOVAs continue to be used widely for the analysis of repeated-measures data, despite risks to interpretation. Mixed-effects models use all available data, can properly account for correlation between repeated measurements on the same subject, have greater flexibility to model time effects, and can handle missing data more appropriately. Their flexibility makes them the preferred choice for the analysis of repeated-measures data.

A comparison of the general linear mixed model and repeated measures ANOVA using a dataset with multiple missing data points.

C Krueger — 2008-05-24T09:25:51-00:00

Biological research for nursing, Vol. 6, No. 2. (October 2004), pp. 151-157.

Longitudinal methods are the methods of choice for researchers who view their phenomena of interest as dynamic. Although statistical methods have remained largely fixed in a linear view of biology and behavior, more recent methods, such as the general linear mixed model (mixed model), can be used to analyze dynamic phenomena that are often of interest to nurses. Two strengths of the mixed model are (1) the ability to accommodate missing data points often encountered in longitudinal datasets and (2) the ability to model nonlinear, individual characteristics. The purpose of this article is to demonstrate the advantages of using the mixed model for analyzing nonlinear, longitudinal datasets with multiple missing data points by comparing the mixed model to the widely used repeated measures ANOVA using an experimental set of data. The decision-making steps in analyzing the data using both the mixed model and the repeated measures ANOVA are described.

Analyzing Change: A Primer on Multilevel Models with Applications to Nephrology.

Jocelyn E Holden — 2008-05-24T09:22:56-00:00

American journal of nephrology, Vol. 28, No. 5. (10 May 2008), pp. 792-801.

The analysis of change is central to the study of kidney research. In the past 25 years, newer and more sophisticated methods for the analysis of change have been developed; however, as of yet these newer methods are underutilized in the field of kidney research. Repeated measures ANOVA is the traditional model that is easy to understand and simpler to interpret, but it may not be valid in complex real-world situations. Problems with the assumption of sphericity, unit of analysis, lack of consideration for different types of change, and missing data, in the repeated measures ANOVA context are often encountered. Multilevel modeling, a newer and more sophisticated method for the analysis of change, overcomes these limitations and provides a better framework for understanding the true nature of change. The present article provides a primer on the use of multilevel modeling to study change. An example from a clinical study is detailed and the method for implementation in SAS is provided.

Biometrical Modeling of Twin and Family Data Using Standard Mixed Model Software

S Rabe-Hesketh — 2007-06-06T08:33:30-00:00

Biometrics (2 May 2007)

Abstract: Biometrical genetic modeling of twin or other family data can be used to decompose the variance of an observed response or 'phenotype' into genetic and environmental components. Convenient parameterizations requiring few random effects are proposed, which allow such models to be estimated using widely available software for linear mixed models (continuous phenotypes) or generalized linear mixed models (categorical phenotypes). We illustrate the proposed approach by modeling family data on the continuous phenotype birth weight and twin data on the dichotomous phenotype depression. The example data sets and commands for Stata and R/S-PLUS are available at the Biometrics website.

Efficient Estimation for Patient-Specific Rates of Disease Progression Using Nonnormal Linear Mixed Models

Zhang — 2008-03-01T14:23:56-00:00

Biometrics, Vol. 64, No. 1. (March 2008), pp. 29-38.