Fig. 3

Histograms of estimated random effects with superimposed approximating normal densities (A), pairwise scatterplots of estimated random effects with 95% confidence ellipses (B), and histograms of marginal predicted mean outcomes (C). Estimated random effects (\(\widehat{Z}_{B,i}\), \(\widehat{Z}_{W,i}\), and \(\widehat{Z}_{S,i}\)) are obtained using the empirical Bayes method, implemented with the PREDICT statement of SAS PROC NLMIXED. As the random effect estimates of the duration and severity submodels are meaningful only for patients with at least one exacerbation during the follow-up period, only such patients are included in these plots