# Data Analysis and Output

Due to convergence problems with the full random effects, a simulated set of data was used to generate numerical and graphical outputs. The following parameters were used to simulate the data: 1000 observations from 50 trials were generated from a multivariate normal distribution with the mean vector

FIGURE 12.13

*Surrogacy measures with their 95% C.I., full mixed-effects model.*

FIGURE 12.14

*Trial-specific random-effects plot.*

(p* _{s}, Мт*, а,

*в)*= (5, 5, 5, 5), and covariance matrices given by

As shown in Figure 12.13, the surrogacy measures are equal to R?_{ndiv} = 0.6260 (0.5893, 06628) and *Rt _{lia}* = 0.7655 (0.6483, 0.8828). Figure 12.14 shows the empirical Bayes estimates for the trial-specific random treatment effects.

FIGURE 12.15

*Covariance matrices, full mixed-effects model.*

# SAS Code for the Full Mixed-Effects Model

The full mixed-effects model can be fitted using procedure MIXED. Possible code is given by

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

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

The data structure and variables are identical to those outlined in Section 12.3.1. The MODEL statement defines the 4 fixed effects in the mean structure, (p_{T}, , а, в), while the RANDOM statement defines the structure of the

covariance matrix D for the random effects, and the REPEATED statement builds up the error covariance matrix *E* in (12.2). The estimated covariance matrices are shown in Figure 12.15. The lower panel presents the parameter estimates of the covariance matrix D (given in 4.2).

The trial-level surrogacy measure is estimated by (4.4):

The estimated covariance matrix for the residuals (defined in (12.2)) is given by

and individual-level surrogacy is derived according to (4.9):