Figure 2.

Individualized rate of chronic obstructive pulmonary disease (COPD) exacerbation (episodes/year) (A) and individualized ratio of severe exacerbations to total exacerbations (B), MACRO Study, 2006–2010. Values are model-estimated $e^{\delta .\mathbf{\beta }.{\mathit{X}}_i+\delta .z_i}$ for the rate component and $e^{\mathbf{\beta }\mathbf{\prime }.{\mathit{X}}_{\mathit{i}}+{z\prime }_i}/(1+e^{\mathbf{\beta }\mathbf{\prime }.{\mathit{X}}_{\mathit{i}}+{z\prime }_i})$ for the severity component (see text and Web Appendix 1 for full description). Values for random-effect terms (z_i and ${z\prime }_i$) were obtained using the empirical Bayes method, implemented with the PREDICT statement of SAS PROC NLMIXED.