Evaluation of MRI Parameters as a Biomarker for Histology Features
A Joint Model for MRI and Histology
The analysis presented in this section consists of a region/MRI/histology- specific model. Hence, for each region, 4 x 7 models are fitted. Each model is used to evaluate one MRI parameter as a biomarker for one histology feature. The observation unit for the analysis is (Xj, Yj, Zj) with Xj being the histology feature for the jth animal, j = 1,..., N at age i, i = 1,... ,1; Yj is the MRI parameter of the jth animal at age i; and Zj is an indicator variable for the genotype the animal belongs to given by
We assume that the mean structure for MRI and histology parameters, respectively, is given by
Here, and are the age-specific means for the MRI feature and histology parameter, respectively, in the wildtype mice group. Note that for the wildtype mice group, we assume that the histology feature is constant over time since the disease pathology does not vary a lot for these young ages (2-8 months) in the wildtype mice. Thus, the mean structure in (17.1) can be simplified by having only one parameter for histology staining in wildtype mice, i.e., =
. The age-specific parameters a and Д correspond to the disease effect on MRI and histology at a given age, respectively. Further, we assume that the two endpoints (histology and MRI) follow a bivariate normal distribution with genotype-specific covariance matrices, that is,
Here, E is a 2 x 2 genotype-specific covariance matrix given for transgenic and wildtype mice, respectively, by
Illustration of simulated individual- and disease-level surrogacy using the AD animal model for a scenario with low individual-level surrogacy. The solid lines in panel a connect the means of the transgenic and wildtype groups at each age. The slope of these lines is equal to the RE (at each age). Panel b shows the association between a histology feature and the MRI parameter. Panel c presents the disease effects в on a histology feature versus the disease effects a on an MRI parameter. Gray symbols: wildtype mice. Black symbols: transgenic mice.
Illustration of simulated individual and disease-level surrogacy using the AD animal model for a scenario with high individual-level surrogacy. The solid lines in panel a connect the means of the transgenic and wildtype groups at each age. The slope of these lines is equal to the RE (at each age). Panel c presents the disease effects в on a histology feature versus the disease effects a on an MRI parameter. Gray symbols: wildtype. Black symbols: transgenic.
The joint model specified in (17.1) allows us to model two sources (or aspects) of the association between a specific histology feature and an MRI parameter: (1) the association between the disease evolution effects (with respect to age) of the two endpoints and (2) the association between the two endpoints adjusted for the time evolution of the disease. In what follows, we show that the two sources of association can be interpreted as individual- and disease- level surrogacy. The latter is similar to the trial-level surrogacy discussed in Chapter 4.