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Stat Biopharm Res. 2013 Jan 1;5(1). doi: 10.1080/19466315.2012.756662.

Combining Multiple Markers to Improve the Longitudinal Rate of Progression-Application to Clinical Trials on the Early Stage of Alzheimer's Disease.

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Division of Biostatistics, Washington University, St. Louis, MO 63110, USA.
School of Public Health, Department of Biostatistics and Department of Environmental and Occupational Health Sciences, University of Washington, Seattle, WA 98195-4691.
Banner Alzheimer's Institute, Phoenix, AZ 85006.
Department of Biostatistics, SUNY at Buffalo, USA.
Division of Biostatistics, Washington University, St. Louis, MO 63110, USA ; Department of Surgery and Division of Biostatistics, Washington University, St. Louis, MO 63110, USA.
Department of Neurology, Pathology and Immunology, Washington University Alzheimer's Disease Research Center, St. Louis, MO.
Department of Medicine, University of Washington, Seattle, USA.


Clinical trials on early stage Alzheimer's disease (AD) are reaching a bottleneck because none of the current disease markers changes appreciably early in the disease process and therefore a huge sample is required to adequately power such trials. We propose a method to combine multiple markers so that the longitudinal rate of progression can be improved. The criterion is to maximize the probability that the combined marker will be decreased over time (assuming a negative mean slope for each marker). We propose estimates to the weights of markers in the optimum combination and a confidence interval estimate to the combined rate of progression through the maximum likelihood estimates and a bootstrap procedure. We conduct simulations to assess the performance of our estimates and compare our approach with the first principal component from a principal component analysis. The proposed method is applied to a real world sample of individuals with preclinical AD to combine measures from two cognitive domains. The combined cognitive marker is finally used to design future clinical trials on preclinical AD, demonstrating a significant improvement in reducing the sample sizes needed to power such trials when compared with individual markers alone.


Bootstrap estimate; Delta method; Multivariate random coefficients models; Power; Preclinical Alzheimer’s disease (AD); Randomized clinical trials (RCT); Sample size

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