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Individual-level surrogacy

As shown in Table 4.2, the point estimates of Rndiv that were obtained in the different models ranged between 0.4866 and 0.5469, and their 95% confidence intervals largely overlapped. Notice that the point estimates for R?ndiv are identical in the weighted and unweighted scenarios for all models (see Table 4.2). This result is expected, because the choice for a weighted versus unweighted model only affects the Stage 2 models (upon which the estimation of Rrial is based) but not the Stage 1 models (upon which the estimation of Rndiv is based). Overall, the results indicate that S = visual acuity after 24 weeks is a moderate surrogate for T = visual acuity after 52 weeks at the level of individual patients.

FIGURE 4.3

Age-Related Macular Degeneration Trial. Scatter plot of the treatment effects on the true endpoint against the treatment effects on the surrogate endpoint in the ARMD data (gray circles), the expected treatment effect on T in a new trial where ao = —1 (black circle), and the 95% confidence interval around the expected treatment effect in the new trial (dashed black line).

Individual-level surrogacy can be graphically illustrated based on a scatter plot that depicts the treatment- and trial-corrected residuals for T (i.e., ?Tij) against the treatment- and trial-corrected residuals for S (i.e., ?Sij) for the Ntotal = 181 patients. By means of illustration, Figure 4.2 provides such a plot using the (weighted or unweighted) reduced bivariate fixed-effects model. This plot is in line with the earlier conclusion that the accuracy by which T can be predicted based on S (taking treatment and trial into account) is moderate (i.e., there remains substantial variability in ?Tij for a given value

of ? Sij ) .

The expected treatment effect on T in a new trial

The main motivation to evaluate a surrogate endpoint is to be able to predict the treatment effect on T based on the treatment effect on S in a new trial i = 0. For example, suppose that a new clinical trial was conducted that is similar to the ARMD study in which only S (and not T) is measured. Figure 4.3 presents a scenario in which in the new trial it is found that a0 = —1, i.e., the estimated treatment effect on visual acuity measured after 24 weeks equals —1. Interest is in the prediction of the expected treatment effect after 52 weeks.

Here, the prediction is made based on the results of the weighted reduced bivariate fixed-effects model.

Using (4.15), it follows that the expected treatment effect on T equals E (p + b0 | a0 = —1) = -1.9324. As was shown in Table 4.2, the Rriai of the model equaled 0.6585 and was thus moderate. Consequently, the uncertainty in the expected treatment effect E (в + b0 | a0 = —1) is large, i.e., its 95% confidence interval is [—11.7592; 7.8944]. Figure 4.3 shows the trial-specific treatment effects on T and S as obtained in the ARMD dataset (gray circles), the expected treatment effect on T in the hypothetical new trial i = 0 (black circle), and the 95% confidence interval around the expected treatment effect on T in the new trial (black dashed line).

 
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