Trial-Level Surrogacy: Binary-Ordinal Setting
A two-stage approach to determining trial-level 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 trial-specific treatment effects Д and ai:
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 trial-specific treatment effects в and ai are regressed on each other to estimate Rht:
In (11.7), NT is the total sample size across all trials. G2, the difference in —2 x log-likelihood between (11.6) and a null (intercept only) model, can be calculated and the LRF applied as in (11.7) to estimate Rht.
The standard approach to confidence interval estimation introduced in Chapter 4 also applies in this context, although the rescaling that takes place for individual-level surrogacy (11.3) also needs to be applied to the individual- level confidence intervals.