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The Full FixedEffects ModelModel FormulationThe twostage approach for two normally distributed endpoints was discussed in Chapter 4. Briefly, the first stage consists of a joint model for the surrogate and true endpoints given by
where p_{Si} and p_{Ti} are trialspecific intercepts for S and T, a_{i} and Д are trial specific treatment effects on the surrogate and the true endpoint, respectively. The error terms, ?_{Si}j and ?_{Ti}j, are bivariate normally distributed with zero mean and covariance matrix given by
As pointed out in Chapter 4, individuallevel surrogacy is assessed by the squared correlation between S and T after adjusting for trialspecific treat FIGURE 12.2 A leaveoneout evaluation procedure. ment effects, that is, For the full fixedeffects model, the triallevel surrogacy is estimated using the coefficient of determination obtained by fitting the following model:
where /?*, Ms*, and Sj are the parameter estimates obtained from the joint model specified in (12.1). A weighted analysis, which takes into account the sample size in each trial (see also Section 4.3.4), can be used as well. The standard error for R?_{ndiv} and R^_{rial} can be calculated using the delta method. 
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