Many medical diagnostic studies involve three ordinal diagnostic populations in 
which the diagnostic accuracy can be summarized by the volume or partial volume 
under the receiver operating characteristic surface for a diagnostic marker. 
When the diagnostic populations are clustered, e.g. by families, we propose to 
model the diagnostic marker by a general linear mixed model that takes into 
account of the correlation on the diagnostic marker from members of the same 
clusters. This model then facilitates the maximum likelihood estimation and 
statistical inferences of the diagnostic accuracy for the diagnostic marker. 
This approach naturally allows the incorporation of covariates as well as 
missing data when some clusters do not have subjects on all diagnostic groups in 
the estimation of, and the subsequent inferences on the diagnostic accuracy. We 
further study the performance of the proposed methods in a large simulation 
study with clustered data. Finally, we apply the proposed methodology to the 
data of several biomarkers collected by the Dominantly Inherited Alzheimer 
Network, an international family-clustered registry to study autosomal dominant 
Alzheimer disease which is a rare form of Alzheimer disease caused by mutations 
in any of the three genes including the amyloid precursor protein, presenilin 1 
and presenilin 2. We estimate the accuracy of several cerebrospinal fluid and 
neuroimaging biomarkers in differentiating three diagnostic and genetic 
populations: normal non-mutation carriers, asymptomatic mutation carriers, and 
symptomatic mutation carriers.