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Concluding Remarks

The joint model specified in Section 17.4 was developed in order to model the association between MRI and histology, taking into account the disease progression effects on both endpoints. The observation unit that we have used in this chapter is the triplet (Genotype^., MRU, Histology^.). Figure 17.23 illustrates the two sources of association presented in this chapter. For a given age, the effect of the disease on MRI аг and the effect of the disease on histology is represented by the shift in the distribution of both MRI and histology parameters as illustrated in panel b. Panel a illustrates the genotype- specific association in the residuals after adjusting for the disease effects аг and вг.

We have shown that, using a two-stage approach, we can estimate a genotype-specific adjusted association pW and pA using the joint model (17.1) in the first stage, while the prediction of the disease progression effects on histology can be done in the second stage using a linear regression model for вг and аг. Although, the experimental setting discussed in this chapter is completely different from the one discussed in Chapter 4, the same association structure (as illustrated in Figure 17.23a) implies that the same modeling

FIGURE 17.23

Illustration of the joint modeling framework: The association between MRI and histology after adjusting for the disease effects.

approach can be used in order to evaluate the quality of MRI as a biomarker for histology. We have shown that the use of MRI as a biomarker for histology depends on the brain region, MRI parameters, and histology staining.

The case studies presented in this chapter posed two challenges with regard to sample size: (1) there were only five age groups, which implies that estimation of the linear regression line in the second stage is based on only five observations and (2) there were only two control mice at each age group. Therefore, the genotype-specific coefficients in (17.2) are based on two observations, hence they may have higher variability.

 
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