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The Full Fixed-Effects Model

Model Formulation

The two-stage 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 pSi and pTi are trial-specific intercepts for S and T, ai and Д are trial- specific treatment effects on the surrogate and the true endpoint, respectively. The error terms, ?Sij and ?Tij, are bivariate normally distributed with zero mean and covariance matrix given by

As pointed out in Chapter 4, individual-level surrogacy is assessed by the squared correlation between S and T after adjusting for trial-specific treat-

FIGURE 12.2

A leave-one-out evaluation procedure.

ment effects, that is,

For the full fixed-effects model, the trial-level 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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