Modelling of covariance structures in generalised estimating equations for longitudinal data

Abstract

When modelling longitudinal data generalised estimating equations specify a working structure to the within-subject covariance matrices, aiming to produce efficient parameter estimates. Misspecification of the working covariance structure, however, may lead to a great loss of efficiency of the mean parameter estimates. In this paper we propose an approach for joint modelling of the mean and covariance structures of longitudinal data within the framework of generalised estimating equations. The resulted estimates for the mean and covariance parameters are shown to be consistent and asymptotically Normally distributed. Real data analysis and simulation studies show that the proposed approach yields efficient estimates for both of the mean and covariance parameters.

Modelling Mean-Covariance Structures in the Growth Curve Model

“…For example, within the framework of generalized estimating equations (GEE) Wang and Carey (2003) showed that misspecification of covariance structures produces too large standard deviations for regression coefficients and hence results in inefficient estimates. Ye and Pan (2004a) further modeled the mean and covariance structures in GEE using regression models. Very recently they (Ye and Pan, 2004b) proposed to use local-likelihood estimation approach developed by Fan et al (1998) to nonparametrically model the mean and covariance structures for large longitudinal data.…”

jmcm: An R Package for Joint Mean-Covariance Modeling of Longitudinal Data

“…Since the solutions satisfy Equation 17 and the parameters β, λ, γ are asymptotically independent (Ye and Pan 2006), the three parameters can also be sequentially solved one by one with the other parameters kept fixed. More specifically, we apply the following algorithm.…”

“…Moreover, owing to the decomposition, the resulting correlation function of MCD depends on both the innovation variance and autoregressive parameters, indicating that MCD is not robust against the misspecification of the innovation variance when the correlation is the main interest (Maadooliat et al 2013). We also need to note that MCD is the most computationally efficient approach among the three approaches due to the fact that its Fisher information matrix is block diagonal (Ye and Pan 2006).…”

“…In this section, we apply the proposed joint mean-covariance modeling approach to an unbalanced CD4 + cell dataset analyzed by Ye and Pan (2006) and Zhang et al (2015). The dataset comprises a total of 2376 CD4 + cell counts of 369 HIV-infected men covering a period of approximately eight and half years.…”

A cautionary note on generalized linear models for covariance of unbalanced longitudinal data

“…This unconstrained reparameterization and its statistical interpretability makes it easy to incorporate covariates in covariance modeling and to cast the joint modeling of mean and covariance into the generalized linear model framework. The methodology has proved to be useful in recent literature; see for example, Pourahmadi and Daniels (2002), Pan and MacKenzie (2003), Ye and Pan (2006), Daniels (2006), Huang et al (2006), Levina et al (2008), Yap et al (2009), and Lin and Wang (2009).…”