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Two Levels of Surrogacy

Panels a and b in Figure 17.3 show an illustrative example in which a histology feature is plotted against a specific MRI parameter at 2 and 8 months, respectively. The effect of the disease progression is translated to a shift in

FIGURE 17.3

Illustrative example: The effect of AD progression on an MRI parameter and a specific histology feature at two time points for simulated data. The solid line connects the means of the two genotypes. Gray symbols: wildtype mice. Black symbols: transgenic mice.

both the MRI parameter and histology feature in the transgenic group. Panels a and b of Figure 17.4 show the data at 2 and 8 months respectively, which will be analyzed in this chapter. Note that the slope of the lines connecting the means of the two clouds in panel b of Figures 17.3 and 17.4 corresponds to the relative effect (RE), discussed in Chapter 3.

Figures 17.5 and 17.6 illustrate two aspects of the association between an

FIGURE 17.4

Illustrative example: The effect of AD progression on an MRI parameter and a specific histology feature at two time points for real data. The solid line connects means of the two genotypes. Gray symbols: wildtype mice. Black symbols: transgenic mice.

MRI parameter and a given histology feature: the effect of AD progression (characterized by continual amyloid-beta deposition) and the correlation between the two variables. Panels a and b show the data and the residuals after subtracting the means, respectively. From Figure 17.5, the AD progression

effect can be seen clearly in panel a, while panel b indicates that, conditional on AD progression effect, the two variables are not correlated. Using surrogacy terminology, Figure 17.5b indicates that, on an individual level, MRI is a poor biomarker for histology. A second illustrative example is shown in Figures 17.6a and b. For this example, the AD progression effect (shown in Figure 17.6a) has the same magnitude of the effects as in the first example. Note that the relative effects in the two examples are similar. Figure 17.6b reveals a substantial difference between the two examples on an individual level. For the second example, after adjusting for the AD progression effects, MRI and histology are correlated (Figure 17.6b). Hence, at an individual level, MRI is a good biomarker for histology. Note that we can use the adjusted association, discussed in Chapter 3, to evaluate MRI as a biomarker for histology at an individual level.

In the next example, presented in Figures 17.7 and 17.8, we “translate” the two aspects of the association between MRI and histology into two surrogacy measures: individual-level surrogacy and disease-level surrogacy. The latter corresponds to the trial-level surrogacy, discussed in Chapter 4. The examples presented in Figures 17.5 and 17.6 correspond to a single-trial setting and allow us to evaluate the quality of MRI as a biomarker for histology only at the individual level. On the other hand, the animal model for AD allows us to estimate surrogacy measures in both levels since MRI parameters and histology features are measured at 5 time points. Figure 17.7 shows a scenario in which an MRI parameter and a histology feature are not correlated, given the progression effect of AD but the disease effects (on both MRI and histology), shown in panel (c), are correlated. This suggests a scenario for which the disease-level surrogacy is high while individual-level surrogacy is low. In other words, the effect of AD progression on histology features can be predicted using the AD progression effects observed on MRI parameters, while at individual level, MRI values are not predictive for histology features. A scenario in which MRI parameters and histology features are associated at both disease and individual levels is shown in Figure 17.8.

FIGURE 17.5

Illustrative examples demonstrating the effect of AD progression on an MRI parameter and a histology feature at two time points, without correlation between MRI and histology parameters. Larger symbols denote the group means. Gray symbols: wildtype mice. Black symbols: transgenic mice.

FIGURE 17.6

Illustrative examples demonstrating the effect of AD progression on an MRI parameter and a histology feature at two time points, with correlation between MRI and histology parameters. Larger symbols denote the group means. Gray symbols: wildtype mice. Black symbols: transgenic mice.

 
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