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TrialLevel Surrogacy: BinaryOrdinal SettingA twostage approach to determining triallevel surrogacy enables the computational issues, such as those illustrated in Section 11.2.2, to be overcome. In stage one, a generalized linear model is fitted to the binary S regressed on treatment Z separately for each trial i, as in (11.4). Similarly, a proportional odds model is fitted, for each trial i, to the ordinal T regressed on treatment Z in (11.5). This estimates the trialspecific treatment effects Д and a_{i}:
where w = 1,... ,W — 1; W is the number of categories in T, is the set of intercept parameters for each of the W — 1 cut points of T; and all other parameters are the same as in the continuous case (Section 10.2). In stage two, the estimates of the trialspecific treatment effects в and a_{i }are regressed on each other to estimate Rh_{t}:
In (11.7), N_{T} is the total sample size across all trials. G^{2}, the difference in —2 x loglikelihood between (11.6) and a null (intercept only) model, can be calculated and the LRF applied as in (11.7) to estimate Rh_{t}. Confidence IntervalsThe standard approach to confidence interval estimation introduced in Chapter 4 also applies in this context, although the rescaling that takes place for individuallevel surrogacy (11.3) also needs to be applied to the individual level confidence intervals. 
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