Asymptotic results with generalized estimating equations for longitudinal data

Balan, Raluca M.; Şchiopu-Kratina, Ioana

doi:10.1214/009053604000001255

Cited by 40 publications

(54 citation statements)

References 15 publications

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“…Remark 1. The first part of condition (A5) is similar to the condition in Lemma 2 of Xie and Yang (2003) and condition (Ñ δ ) in Balan and Schiopu-Kratina (2005); the second part is satisfied for Gaussian distribution, sub-Gaussian distribution, and Poisson distribution, etc. Condition (A6) requires μ (k ) ij (X T ij β n ), which denotes the kth derivative of μ ij (t) evaluated at X T ij β n , to be uniformly bounded when β n is in a local neighborhood around β n 0 , k = 1, 2, 3.…”

Section: Asymptotic Theory For High-dimensionalmentioning

confidence: 78%

Penalized Generalized Estimating Equations for High‐Dimensional Longitudinal Data Analysis

2011

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We consider the penalized generalized estimating equations (GEEs) for analyzing longitudinal data with high-dimensional covariates, which often arise in microarray experiments and large-scale health studies. Existing high-dimensional regression procedures often assume independent data and rely on the likelihood function. Construction of a feasible joint likelihood function for high-dimensional longitudinal data is challenging, particularly for correlated discrete outcome data. The penalized GEE procedure only requires specifying the first two marginal moments and a working correlation structure. We establish the asymptotic theory in a high-dimensional framework where the number of covariates p(n) increases as the number of clusters n increases, and p(n) can reach the same order as n. One important feature of the new procedure is that the consistency of model selection holds even if the working correlation structure is misspecified. We evaluate the performance of the proposed method using Monte Carlo simulations and demonstrate its application using a yeast cell-cycle gene expression data set.

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Section: Asymptotic Theory For High-dimensionalmentioning

confidence: 78%

Penalized Generalized Estimating Equations for High‐Dimensional Longitudinal Data Analysis

2011

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“…But, in practice, centralized and normalized covariates will trivially satisfy (C3), which empirically justifies its usage. Condition (C4) is similar to the condition in Lemma 2 of Xie and Yang (2003), condition ( Ñ δ ) in Balan and Schiopu-Kratina (2005), and condition (A5) in Wang (2011), which usually holds for outcome Y i of a variety of types, including binary, Poisson and Gaussian. With ḡ j (0) = tr{ A 1/2 (0) R̄ −1 A −1/2 (0) Cov(μ(β 0 ), x j )}, condition (C5) is similar to the condition in Theorem 3 of Fan and Song (2010), ensuring the marginal signals are stronger than the stochastic noise as shown in Web Appendix A.…”

Section: Sure Screening Properties Of Geesmentioning

confidence: 81%

Ultrahigh dimensional time course feature selection

Zhu

2014

Biometrics

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Statistical challenges arise from modern biomedical studies that produce time course genomic data with ultrahigh dimensions. In a renal cancer study that motivated this paper, the pharmacokinetic measures of a tumor suppressor (CCI-779) and expression levels of 12625 genes were measured for each of 33 patients at 8 and 16 weeks after the start of treatments, with the goal of identifying predictive gene transcripts and the interactions with time in peripheral blood mononuclear cells for pharmacokinetics over the time course. The resulting dataset defies analysis even with regularized regression. Although some remedies have been proposed for both linear and generalized linear models, there are virtually no solutions in the time course setting. As such, a novel GEE-based screening procedure is proposed, which only pertains to the specifications of the first two marginal moments and a working correlation structure. Different from existing methods that either fit separate marginal models or compute pairwise correlation measures, the new procedure merely involves making a single evaluation of estimating functions and thus is extremely computationally efficient. The new method is robust against the mis-specification of correlation structures and enjoys theoretical readiness, which is further verified via Monte Carlo simulations. The procedure is applied to analyze the aforementioned renal cancer study and identify gene transcripts and possible time-interactions that are relevant to CCI-779 metabolism in peripheral blood.

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“…And under the conditions defined in Balan and Schiopu-Kratina (2005), specifically: And under the conditions defined in Balan and Schiopu-Kratina (2005), specifically:…”

Section: Theoretical Properties Of And̃matricesmentioning

confidence: 99%

“…T A B L E 1 0 ( ) estimates for = 6 Estimates of ( ) for true structure of correlation so that for the normalized residues, * =Â i (̂) −1∕2 (̂), ( * * ) =R ( ). And under the conditions defined in Balan and Schiopu-Kratina (2005), specifically:…”

Section: Theoretical Properties Of And̃matricesmentioning

confidence: 99%

Selection criterion of work matrix as a function of limiting estimates of the covariance matrix of correlated data in GEE

Silva

Cirillo

2018

Biometrical J

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The modeling of generalized estimating equations used in the analysis of longitudinal data whether in continuous or discrete variables, necessarily requires the prior specification of a correlation matrix in its iterative process in order to obtain the estimates of the regression parameters. Such a matrix is called working correlation matrix and its incorrect specification produces less efficient estimates for the model parameters. Due to this fact, this study aims to propose a selection criterion of working correlation matrix based on the covariance matrix estimates of correlated responses resulting from the limiting values of the association parameter estimates. For validation of the criterion, we used simulation studies considering normal and binary correlated responses. Compared to some criteria in the literature, it was concluded that the proposed criterion resulted in a better performance when the correlation structure for exchangeable working correlation matrix was considered as true structure in the simulated samples and for large samples, the proposed criterion showed similar behavior to the other criteria, resulting in higher success rates.

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Asymptotic results with generalized estimating equations for longitudinal data

Cited by 40 publications

References 15 publications

Penalized Generalized Estimating Equations for High‐Dimensional Longitudinal Data Analysis

Penalized Generalized Estimating Equations for High‐Dimensional Longitudinal Data Analysis

Ultrahigh dimensional time course feature selection

Selection criterion of work matrix as a function of limiting estimates of the covariance matrix of correlated data in GEE

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