The analysis of very small samples of repeated measurements I: An adjusted sandwich estimator

The statistical analysis of repeated measures or longitudinal data always requires the accommodation of the covariance structure of the repeated measurements at some stage in the analysis. The general linear mixed model is often used for such analyses, and allows for the specification of both a mean model and a covariance structure. Often the covariance structure itself is not of direct interest, but only a means to producing valid inferences about the response. Existing methods of analysis are often inadequate where the sample size is small. More precisely, statistical measures of goodness of fit are not necessarily the right measure of the appropriateness of a covariance structure and inferences based on conventional Wald-type procedures do not approximate sufficiently well their nominal properties when data are unbalanced or incomplete. This is shown to be the case when adopting the Kenward–Roger adjustment where the sample size is very small. A generalization of an approach to Wald tests using a bias-adjusted empirical sandwich estimator for the covariance matrix of the fixed effects parameters from generalized estimating equations is developed for Gaussian repeated measurements. This is shown to attain the correct test size but has very low power