Genotype-Specific Individual-Level Surrogacy
Based on the covariance matrices specified in (17.3), we can derive the adjusted correlation between an MRI parameter and a specific histology feature for each genotype given by
The genotype-specific adjusted correlations p_{W} and p_{T} measure the association between the two endpoints adjusted for the time evolution of the disease and can be interpreted in the same way as the adjusted association in the surrogacy model presented in Chapter 3. A large absolute values of the adjusted correlation implies a better surrogacy at an individual level. Note that, in contrast with the models discussed in Chapter 4, we do not assume that the association between MRI and histology is equal in the two groups.
Disease-Level Surrogacy
The joint model specified in (17.1) allows us to estimate the age and genotype- specific parameters (а,а_{2},а_{3},а_{4},а_{б}) and (@1, @2, вз, @4, вб). Our aim is to establish a relationship between a_{i} and @_{i}, and in particular, to assess whether AD evolution observed for the MRI parameter is predictive for the AD evolution observed for a particular histology feature. In other words, we wish to evaluate whether an MRI parameter can be used as a biomarker for a given histology feature in an AD mouse model at a disease level. Disease-level surrogacy can be measured using R^{2} obtained from the regression model in a similar way as done in Chapter 4 for trial-level surrogacy. From (17.5), n and Y are regression coefficients, while e_{i} denotes the measurement error for the regression model:
TABLE 17.2
The motor cortex region: Parameter estimate (standard error) of AD progression effects. в: the disease effect on GFAP percentage of area stained. a: the disease effects on MRI-AK.
Age |
/3 (s.e.) |
a (s.e.) |
2 |
-0.35 (0.51) |
-0.01 (0.02) |
4 |
1.58 (0.51) |
0.03 (0.02) |
6 |
5.43 (0.53) |
0.03 (0.02) |
8 |
11.83 (0.53) |
0.05 (0.02) |
10 |
15.43 (0.92) |
0.08 (0.03) |