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Journal Article•DOI•

Marginally specified logistic-normal models for longitudinal binary data.

Patrick J. Heagerty1•
University of Washington1
01 Sep 1999-Biometrics (Blackwell Publishing Ltd)-Vol. 55, Iss: 3, pp 688-698
TL;DR: In this manuscript, an alternative parameterization of the logistic-normal random effects model is adopted, and both likelihood and estimating equation approaches to parameter estimation are studied.
Abstract: Summary. Likelihood-based inference for longitudinal binary data can be obtained using a generalized linear mixed model (Breslow, N. and Clayton, D. G., 1993, Journal of the American Statistical Association88, 9–25; Wolfinger, R. and O'Connell, M., 1993, Journal of Statistical Computation and Simulation48, 233–243), given the recent improvements in computational approaches. Alternatively, Fitzmaurice and Laird (1993, Biometrika80, 141–151), Molenberghs and Lesaffre (1994, Journal of the American Statistical Association89, 633–644), and Heagerty and Zeger (1996, Journal of the American Statistical Association91, 1024–1036) have developed a likelihood-based inference that adopts a marginal mean regression parameter and completes full specification of the joint multivariate distribution through either canonical and/or marginal higher moment assumptions. Each of these marginal approaches is computationally intense and currently limited to small cluster sizes. In this manuscript, an alternative parameterization of the logistic-normal random effects model is adopted, and both likelihood and estimating equation approaches to parameter estimation are studied. A key feature of the proposed approach is that marginal regression parameters are adopted that still permit individual-level predictions or contrasts. An example is presented where scientific interest is in both the mean response and the covariance among repeated measurements.
Citations
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Journal Article•DOI•
The Prevention and Treatment of Missing Data in Clinical Trials

[...]

Roderick J. A. Little1, Ralph B. D'Agostino2, Michael L. Cohen3, Kay Dickersin4, Scott S. Emerson5, John T. Farrar6, Constantine Frangakis4, Joseph W. Hogan7, Geert Molenberghs8, Susan A. Murphy1, James D. Neaton9, Andrea Rotnitzky10, Daniel O. Scharfstein4, Weichung Joe Shih11, Jay P. Siegel12, Hal S. Stern13 •
University of Michigan1, Boston University2, National Research Council3, Johns Hopkins University4, University of Washington5, University of Pennsylvania6, Brown University7, University of Hasselt8, University of Minnesota9, Torcuato di Tella University10, Rutgers University11, Johnson & Johnson12, University of California, Irvine13
04 Oct 2012-The New England Journal of Medicine
TL;DR: Methods for preventing missing data and, failing that, dealing with data that are missing in clinical trials are reviewed.
Abstract: Missing data in clinical trials can have a major effect on the validity of the inferences that can be drawn from the trial. This article reviews methods for preventing missing data and, failing that, dealing with data that are missing.

1,553 citations

Journal Article•DOI•
Nonlinear models for repeated measurement data: An overview and update

[...]

Marie Davidian1, David M. Giltinan2•
North Carolina State University1, Genentech2
01 Dec 2003-Journal of Agricultural Biological and Environmental Statistics
TL;DR: An overview of the formulation, interpretation, and implementation of nonlinear mixed effects models and surveys recent advances and applications is presented.
Abstract: Nonlinear mixed effects models for data in the form of continuous, repeated measurements on each of a number of individuals, also known as hierarchical nonlinear models, are a popular platform for analysis when interest focuses on individual-specific characteristics. This framework first enjoyed widespread attention within the statistical research community in the late 1980s, and the 1990s saw vigorous development of new methodological and computational techniques for these models, the emergence of general-purpose software, and broad application of the models in numerous substantive fields. This article presentsan overview of the formulation, interpretation, and implementation of nonlinear mixed effects models and surveys recent advances and applications.

383 citations

Cites background from "Marginally specified logistic-norma..."

  • ...Fang and Bailey (2001) and Hall and Bailey (2001) describe nonlinear models for these measures as a function of time that depend on meaningful parameters such as asymptotic growth or yield and rates of change....

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  • ...Thus, for nonlinear models, the interpretation of β in SS and PA models cannot be the same in general; see Heagerty (1999) for related discussion....

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Journal Article•DOI•
Laryngoscopic intubation: learning and performance.

[...]

Julian T. Mulcaster1, Joanna Mills1, Orlando Hung1, Kirk MacQuarrie1, J. Adam Law1, Saul Pytka1, David Imrie1, Chris Field1 •
McMaster University1
01 Jan 2003-Anesthesiology
TL;DR: It is determined that traditional LEI teaching for nonanesthesia personnel using manikin alone is inadequate, and a reevaluation of current standards in LEI Teaching for non anesthesiologists is required.
Abstract: BackgroundMany healthcare professionals are trained in direct laryngoscopic tracheal intubation (LEI), which is a potentially lifesaving procedure. This study attempts to determine the number of successful LEI exposures required during training to assure competent performance, with special emphasis

350 citations

Journal Article•DOI•
An Introduction to Generalized Estimating Equations and an Application to Assess Selectivity Effects in a Longitudinal Study on Very Old Individuals

[...]

Paolo Ghisletta, Dario Spini
21 Dec 2004-Journal of Educational and Behavioral Statistics
TL;DR: In this paper, an analysis of selectivity effects in the Swiss Interdisciplinary Longitudinal Study on the Oldest Old is presented, where the authors provide a concise, non-statistical introduction to generalized estimating equations (GEE).
Abstract: Correlated data are very common in the social sciences. Most common applications include longitudinal and hierarchically organized (or clustered) data. Generalized estimating equations (GEE) are a convenient and general approach to the analysis of several kinds of correlated data. The main advantage of GEE resides in the unbiased estimation of population-averaged regression coefficients despite possible misspecification of the correlation structure. This article aims to provide a concise, nonstatistical introduction to GEE. To illustrate the method, an analysis of selectivity effects in the Swiss Interdisciplinary Longitudinal Study on the Oldest Old is presented.

332 citations

Cites background or methods from "Marginally specified logistic-norma..."

  • ...Second, it is possible to reinterpret the marginal parameters as cluster-specific parameters, permitting us to address simultaneously both population-level and individual-level conclusions (Heagerty, 1999; see also, Diggle et al., 2002)....

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  • ...Heagerty (1999) and Heagerty and Zeger (2000) have shown that a model analogous to GEE can be specified by combining a marginal regression with a random effects model....

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Journal Article•DOI•
Correlation and studies of habitat selection: problem, red herring or opportunity?

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John R Fieberg1, Jason Matthiopoulos2, Mark Hebblewhite3, Mark S. Boyce4, Jacqueline L. Frair5 •
Minnesota Department of Natural Resources1, University of St Andrews2, University of Montana3, University of Alberta4, State University of New York Upstate Medical University5
27 Jul 2010-Philosophical Transactions of the Royal Society B
TL;DR: Analytical methods for dealing with correlated data in the context of resource selection are reviewed, including post hoc variance inflation techniques, ‘two-stage’ approaches based on models fit to each individual, generalized estimating equations and hierarchical mixed-effects models.
Abstract: With the advent of new technologies, animal locations are being collected at ever finer spatio-temporal scales. We review analytical methods for dealing with correlated data in the context of resource selection, including post hoc variance inflation techniques, ‘two-stage’ approaches based on models fit to each individual, generalized estimating equations and hierarchical mixed-effects models. These methods are applicable to a wide range of correlated data problems, but can be difficult to apply and remain especially challenging for use–availability sampling designs because the correlation structure for combinations of used and available points are not likely to follow common parametric forms. We also review emerging approaches to studying habitat selection that use fine-scale temporal data to arrive at biologically based definitions of available habitat, while naturally accounting for autocorrelation by modelling animal movement between telemetry locations. Sophisticated analyses that explicitly model correlation rather than consider it a nuisance, like mixed effects and state-space models, offer potentially novel insights into the process of resource selection, but additional work is needed to make them more generally applicable to large datasets based on the use–availability designs. Until then, variance inflation techniques and two-stage approaches should offer pragmatic and flexible approaches to modelling correlated data.

286 citations

References
More filters
Journal Article•DOI•
Handbook of Mathematical Functions

[...]

Milton Abramowitz, Irene A. Stegun, Donald A. McQuarrie
01 Feb 1966-American Journal of Physics

46,339 citations

Journal Article•DOI•
Longitudinal data analysis using generalized linear models

[...]

Kung Yee Liang1, Scott L. Zeger1•
Johns Hopkins University1
01 Apr 1986-Biometrika
TL;DR: In this article, an extension of generalized linear models to the analysis of longitudinal data is proposed, which gives consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence.
Abstract: SUMMARY This paper proposes an extension of generalized linear models to the analysis of longitudinal data. We introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence. The estimating equations are derived without specifying the joint distribution of a subject's observations yet they reduce to the score equations for multivariate Gaussian outcomes. Asymptotic theory is presented for the general class of estimators. Specific cases in which we assume independence, m-dependence and exchangeable correlation structures from each subject are discussed. Efficiency of the proposed estimators in two simple situations is considered. The approach is closely related to quasi-likelih ood. Some key ironh: Estimating equation; Generalized linear model; Longitudinal data; Quasi-likelihood; Repeated measures.

17,111 citations

Handbook of Mathematical Functions

[...]

Milton Abramowitz, Irene A. Stegun
01 Jan 1972

9,153 citations

Journal Article•DOI•
Approximate inference in generalized linear mixed models

[...]

Norman E. Breslow1, D. G. Clayton•
University of Washington1
01 Mar 1993-Journal of the American Statistical Association
TL;DR: In this paper, generalized linear mixed models (GLMM) are used to estimate the marginal quasi-likelihood for the mean parameters and the conditional variance for the variances, and the dispersion matrix is specified in terms of a rank deficient inverse covariance matrix.
Abstract: Statistical approaches to overdispersion, correlated errors, shrinkage estimation, and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model (GLMM). Given an unobserved vector of random effects, observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function, known prior weights and a scale factor. The random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components. For problems involving time series, spatial aggregation and smoothing, the dispersion may be specified in terms of a rank deficient inverse covariance matrix. Approximation of the marginal quasi-likelihood using Laplace's method leads eventually to estimating equations based on penalized quasilikelihood or PQL for the mean parameters and pseudo-likelihood for the variances. Im...

4,317 citations

"Marginally specified logistic-norma..." refers methods in this paper

  • ...Marginal models (Liang and Zeger, 1986) and generalized linear mixed models (Breslow and Clayton, 1993) are two major regression approaches for the analysis of longitudinal data....

    [...]

  • ...(1988) and discussed by Breslow and Clayton (1993). However, by using numerical integration to compute the first and second moments, we are able to obtain a consistent estimation of both mean and variance component parameters....

    [...]

  • ...(1988) and discussed by Breslow and Clayton (1993). However, by using numerical integration to compute the first and second moments, we are able to obtain a consistent estimation of both mean and variance component parameters. The likelihood approach that we adopt is also related to methods described in Drum and McCullagh (1993), who restricted their attention to models for which the marginal mean can be represented as a linear function of the fixed effects....

    [...]

  • ...(1988) and discussed by Breslow and Clayton (1993). However, by using numerical integration to compute the first and second moments, we are able to obtain a consistent estimation of both mean and variance component parameters. The likelihood approach that we adopt is also related to methods described in Drum and McCullagh (1993), who restricted their attention to models for which the marginal mean can be represented as a linear function of the fixed effects. Also, the estimating equations approach is similar to that proposed by Qu et al. (1992), who included random effects on the probit scale....

    [...]

  • ...This model was introduced by Pierce and Sands (1975), and estimation methods have been summarized by Breslow and Clayton (1993). The model can be written as...

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Journal Article•DOI•
Models for longitudinal data: a generalized estimating equation approach.

[...]

Scott L. Zeger1, Kung-Yee Liang1, Paul S. Albert1•
Johns Hopkins University1
01 Dec 1988-Biometrics
TL;DR: This article discusses extensions of generalized linear models for the analysis of longitudinal data in which heterogeneity in regression parameters is explicitly modelled and uses a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes.
Abstract: This article discusses extensions of generalized linear models for the analysis of longitudinal data. Two approaches are considered: subject-specific (SS) models in which heterogeneity in regression parameters is explicitly modelled; and population-averaged (PA) models in which the aggregate response for the population is the focus. We use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes. When the subject-specific parameters are assumed to follow a Gaussian distribution, simple relationships between the PA and SS parameters are available. The methods are illustrated with an analysis of data on mother's smoking and children's respiratory disease.

4,303 citations

Related Papers (5)
Longitudinal data analysis using generalized linear models

[...]

01 Apr 1986-Biometrika
Kung Yee Liang, Scott L. Zeger
Models for longitudinal data: a generalized estimating equation approach.

[...]

01 Dec 1988-Biometrics
Scott L. Zeger, Kung-Yee Liang, Paul S. Albert
Approximate inference in generalized linear mixed models

[...]

01 Mar 1993-Journal of the American Statistical Association
Norman E. Breslow, D. G. Clayton
Analysis of longitudinal data

[...]

01 Jan 1994
Peter J. Diggle, Patrick J. Heagerty, Kung-Yee Liang, Scott L. Zeger 
Generalized Linear Models

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01 Jan 1983
Peter McCullagh, John A. Nelder