  Motivated by two case studies using primary care records from the Clinical
Practice Research Datalink, we describe statistical methods that facilitate the
analysis of tall data, with very large numbers of observations. Our focus is on
investigating the association between patient characteristics and an outcome of
interest, while allowing for variation among general practices. We explore ways
to fit mixed effects models to tall data, including predictors of interest and
confounding factors as covariates, and including random intercepts to allow for
heterogeneity in outcome among practices. We introduce: (1) weighted regression
and (2) meta-analysis of estimated regression coefficients from each practice.
Both methods reduce the size of the dataset, thus decreasing the time required
for statistical analysis. We compare the methods to an existing subsampling
approach. All methods give similar point estimates, and weighted regression and
meta-analysis give similar standard errors for point estimates to analysis of
the entire dataset, but the subsampling method gives larger standard errors.
Where all data are discrete, weighted regression is equivalent to fitting the
mixed model to the entire dataset. In the presence of a continuous covariate,
meta-analysis is useful. Both methods are easy to implement in standard
statistical software.
