# Analysis of Case Studies: The Age-Related Macular Degeneration Trial

The use of the *RE* and p_{z} to evaluate surrogacy is again illustrated using the ARMD dataset. In the analyses, S and T are considered to be continuous normally distributed endpoints so *a* and *в* can be estimated based on model (3.5)-(3.6) and the variance-covariance matrix E of this model (see (3.7)) provides the estimates for *a _{ST}*,

*&ss*, and

*a*.

_{TT}The results in Section 3.2.2 showed that *a* = -0.8893 (s.e. 0.9509) and *в* = -1.4562 (s.e. 1.1771), so RE = -1.4562/ - 0.8893 = 1.6375 (95% delta method-based confidence interval [-0.6522, 3.9273]). The point estimate for *RE* thus indicates that the magnitude of the treatment effect on T corresponds to about 1 . 6 times the magnitude of the treatment effect on S, but the confidence limits are rather wide.

For the adjusted association, it was found that *p _{z}* = 0.7450 (95% confidence interval [0.6647; 0.8159]). This result is graphically illustrated in Figure

FIGURE 3.1

*Age-Related Macular Degeneration (ARMD) Trial. Scatterplot of the treatment-corrected residuals of T (e^j) against S (esj). The solid line results from regressing e^j on esj.*

3.1. In this figure, each circle depicts the treatment-corrected residuals for the S and T values of an individual patient j (i.e., eSj and e_{T}j, respectively). There is a moderately strong association between S and T at the level of an individual patient (taking the effect of treatment into account). Thus, for a given patient, the outcome on the true endpoint can be predicted using his/her outcome on the surrogate with a moderate level of accuracy.