Covariance Modelling for Longitudinal Studies

Speaker: Professor Gilbert MacKenzie, Centre of Biostatistics, Dept. of Mathematics & Statistics, University of Limerick

Time: 4.00PM

Date: Thursday 1st May 2014

Location: Seminar Room L503, 5th floor, Library Building

Abstract:

The conventional approach to modelling longitudinal RCT data places considerable emphasis on estimation of the mean structure and much less on the covariance structure, between repeated measurements on the same subject. Often, the covariance structure is thought to be a "nuisance parameter" or at least not to be of primary scientific interest. For example, the idea that intervention in an RCT might affect the covariance structure rather than, or as well as, the mean rarely intrudes.

We shall argue that these ideas are rather passe and that from an inferential standpoint the problem is symmetrical in both parameters. Throughout, we will distinguish carefully between joint estimation which is now relatively routine and joint model selection which is not.

Our technique is based on a modified Cholesky decomposition of the usual marginal covariance matrix, sigma. The decomposition leads to a reparametrization of sigma, in which the new parameters have an obvious statistical interpretation in terms of the natural logarithms of the innovation variances, and autoregressive coefficients. These unconstrained parameters are modelled, parsimoniously, as different polynomial functions of time.

In this talk we trace the history of the development of joint mean-covariance modelling over the last decade to recent times and discuss current research in this paradigm. In particular, we focus on modelling bivariate continuous responses in the longitudinal setting..

Reference: Xu, J. and MacKenzie, G. (2012). Modelling covariance structure in bivariate marginal models for longitudinal data. Biometrika, 99, 3, 649–-662

Series: Statistics Seminar Series