The Northern Ireland group held a meeting at 4pm on Thursday the 13th of June, 2013 in the David Bates Building in Queen's University Belfast. The speaker was Dr Daniel Farewell of Cardiff University, Wales.
Working within a generalised estimating equation (GEE) framework in longitudinal randomised controlled trials (RCTs), Daniel described a class of generalised inverses of singular working correlation matrices that allowed flexible modelling of covariance within a subject's responses while offering robustness to certain kinds of informative observation. He demonstrated how this class corresponds to dynamic models of the increments in the longitudinal responses, and illustrated its application to a randomised trial of quetiapine in the treatment of delirium.
The first part of the talk dealt with a general approach involving two fundamental ideas which were to use: (a) the working covariance structure to control bias and (b) the choice of path to limit to improve efficiency. A key development was the use of Linear Increment models which Daniel showed in the case of a random intercept model led to increments which were missing completely at random. The underlying concept had been described by Diggle et al. (2007, JRSSC) in terms of martingales. A generalised version of proposed methods with a damped exponential working correlation structure:
corr(yj,yk) = rjk = γ|j-k|α
was applied to the randomised trial of quetiapine in the treatment of delirium with advantage.
The second part of the talk, which Daniel emphasised was work in progress, focussed on exploring use of a modified Cholesky decomposition, LRL' = D, of the working correlation matrix R. It was shown that the choice of α was equivalent to a choice of L. Concentrating on the choice of L and D a key question was how much residual flexibility remained as R → J, the unit matrix? it was shown that under some restrictions a linear increment model involving the elements of L emerged. Daniel proposed to estimate these elements using the GEE method of Ye and Pan (Biometrika, 2006). He then went on to generalise the problem and to propose a mathematical statistical solution.
While this interesting talk was relatively technical, it was quite different in focus from the talk on covariance modelling given to the group by Professor MacKenzie earlier in the year.
It led to a detailed discussion of several key issues.