期刊
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
卷 112, 期 519, 页码 1156-1168出版社
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2016.1194846
关键词
Excess risk; Functional regression; Generalized scalar-on-image regression; Prediction; Total variation
资金
- NSF [DMS1042967, CMMI1030246, SES-1357666, DMS-1407655, DMS-1127914]
- NIH [MH086633, 1UL1TR001111]
- Cancer Prevention Research Institute of Texas
- NATIONAL CANCER INSTITUTE [P30CA016672] Funding Source: NIH RePORTER
- NATIONAL CENTER FOR ADVANCING TRANSLATIONAL SCIENCES [UL1TR001111] Funding Source: NIH RePORTER
- NATIONAL INSTITUTE OF MENTAL HEALTH [R01MH086633] Funding Source: NIH RePORTER
The use of imaging markers to predict clinical outcomes can have a great impact in public health. The aim of this article is to develop a class of generalized scalar-on-image regression models via total variation (GSIRM-TV), in the sense of generalized linear models, for scalar response and imaging predictor with the presence of scalar covariates. A key novelty of GSIRM-TV is that it is assumed that the slope function (or image) of GSIRM-TV belongs to the space of bounded total variation to explicitly account for the piecewise smooth nature of most imaging data. We develop an efficient penalized total variation optimization to estimate the unknown slope function and other parameters. We also establish nonasymptotic error bounds on the excess risk. These bounds are explicitly specified in terms of sample size, image size, and image smoothness. Our simulations demonstrate a superior performance of GSIRM-TV against many existing approaches. We apply GSIRM-TV to the analysis of hippocampus data obtained from the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset. Supplementary materials for this article are available online.
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