# SAS Code for the Reduced Mixed-Effects Model

The SAS code to fit the reduced mixed-effects model is:

proc mixed data=dataset covtest; class endp patid trial;

model outcome = endp endp*treat / solution noint; random endp*treat / subject=trial type=un; repeated endp / type=un subject=patid(trial); ods output solutionF=fix CovParms=covar SolutionR=eb; run;

Note that, compared with the full mixed-effects model, the RANDOM statement was changed from RANDOM endp endp*treat / subject=trial type=un to RANDOM endp*treat / subject=trial type=un, while the MODEL and REPEATED statements remain the same. This implies that the covariance matrix for the trial-specific treatment effects is a 2 x 2 covariance matrix, while the repeated statement defines the error covariance matrix ? in (12.2). The estimated matrices are shown in Figure 12.18. Trial-level surrogacy is esti-

FIGURE 12.17

*Empirical Bayes estimates for the trial-specific random effects.*

FIGURE 12.18

*Covariance matrices, reduced mixed-effects model.*

mated using equation (12.15).

and individual-level surrogacy is derived as follows (see equation 12.15):

FIGURE 12.19

*Data structure for two survival time endpoints.*