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The Reduced FixedEffects ModelModel FormulationThe reduced fixedeffects model approach assumes common intercepts for S and T in (12.1). Hence, trialspecific and are replaced by and , respectively. The full fixedeffects model in (12.1) can be rewritten as
The term is dropped from the secondstage model, which implies that trial level surrogacy is assessed using the coefficient of determination obtained for the model Individuallevel surrogacy can be assessed using the adjusted association in (12.3). The SAS Macro %CONTCONTREDThe SAS macro %CONTCONTRED can be used to fit the reduced joint model specified in (12.6). For the ARMD data we use FIGURE 12.9 Surrogacy measures with 95% C.I; reduced fixed effects model. %CONTCONTRED(data=armd,true=diff52,surrog=diff24,trt=treat, trial=center,patid=patientId,weighted=1, looa=1) The specification of the macro’s arguments is the same as the specification presented in Section 12.2. Data Analysis and OutputSurrogacy measures obtained from the reduced fixedeffect model are shown below. Similar to the results presented in Section 12.3.1, the surrogacy measures R2_{ndiv} = 0.5318 (0.4315,0.6321) and R_{t}^{2}rial(r) = 0.6585 (0.4695,0.8476) indicated that visual acuity after 24 weeks after starting the interferona treatment is a surrogate of moderate value for the visual acuity at 52 weeks after starting the interferona treatment. Trialspecific parameter estimates for treatment effects are shown in Figure 12.10. The regression line fitted at the second stage is added. The circle sizes in the plot are proportional to the number of patients from a given trial. Similar to the analysis presented in the previous section, if the argument looa=1 is used, a “leaveoneout” analysis is performed. 
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