Age-Specific Parameters for Histology in the Wild- type Group
A partial print of the dataset for the model with age-specific parameters for histology in the wildtype group is shown below.
animalid age genotype endpoint response
- 30 1 10 TRANSGENIC true 17.4715576
- 81 1 10 TRANSGENIC surrogate 0.8114934
- 31 2 10 TRANSGENIC true 16.5277908
- 82 2 10 TRANSGENIC surrogate 0.7101217
- 32 3 10 TRANSGENIC true 14.3902328
- 83 3 10 TRANSGENIC surrogate 0.8296881
The model is fitted using age and endpoint as factor variables. The interaction term endpoint:age denotes the age-specific average readout for MRI and histology in wildtype mice, while the three-way interaction term endpoint:genotype:age denotes the age-specific disease effect (transgenic compared to wildtype mice).
fit2 <- gls(response~endpoint:age+endpoint:genotype:age -1, data=MriHistData,
correlation=corSymm( form = ~ 1| animalid ), weight=varIdent(form=~1|endpoint*genotype))
Parameter estimates are shown in Figure 17.22. Note that in this case, the coefficients for histology in wildtype mice are more imprecise (since at each age, only two observations are available). The estimation of disease-level surrogacy follows as in the previous case of the model with a common histology parameter in wildtype mice.
R gls output for the age-specific surrogacy model.