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Stat Methods Med Res. 2018 Mar;27(3):701-714. doi: 10.1177/0962280217742539. Epub 2017 Nov 28.

Estimating diagnostic accuracy for clustered ordinal diagnostic groups in the three-class case-Application to the early diagnosis of Alzheimer disease.

Xiong C1,2, Luo J3,4, Chen L1, Gao F3,4, Liu J3,4, Wang G1,2, Bateman R2, Morris JC2,5.

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1 Division of Biostatistics, Washington University in St. Louis, St. Louis, MO, USA.
2 Department of Neurology, Washington University in St. Louis, St. Louis, MO, USA.
3 Division of Public health, Department of Surgery, Washington University in St. Louis, St. Louis, MO, USA.
4 Biostatistics Core, Siteman Cancer Center, Washington University in St. Louis, St. Louis, MO, USA.
5 Department of Pathology and Immunology, Washington University in St. Louis, St. Louis, MO, USA.


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.


Alzheimer’s disease; clustered study; general linear mixed models; maximum likelihood estimate; receiver operating characteristic surface; sensitivity; specificity; volume under ROC Surface

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