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Reduced MixedEffects ModelAn elaborate discussion about the reduced mixedeffects model is given in Chapter 4. Briefly, a joint model if formulated for the true and the surrogate endpoints in which trialspecific treatment effects are assumed to be random:
is used to estimate the surrogacy measures. Trial and individuallevel surrogacy measures are given, respectively, by (see 4.14 and 4.9 for more details):
The SAS Macro %CONTRANREDThe macro %CONTRANRED is used to conduct the analysis. %CONTRANRED(data=simreduced,true=true,surrog=surr,trt=treat, trial=trial,patid=patientld,looa=0). The macro’s arguments are presented in Section 12.2. FIGURE 12.16 Surrogacy measures with their 95% C.I, reduced mixedeffects model. Data Analysis and OutputSimilar to full random effects models, convergence problems arise. Simulated data were used to generate numerical and graphical output. 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 (p_{S}, а, в) = (5, 3, 5,4), and covariance matrices given by
Parameter estimates for trial and individuallevel surrogacy measures obtained for the reduced mixedeffects model are equal to R?2riai(r) = 0.8144 (0.7186, 0.9102) and R?_{1}^{2}ndiv = 0.6241 (0.5872, 0.6609), respectively (Figure 12.16). Figure 12.17 shows the empirical Bayes estimates for the random effects. 
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