Interpretable High-Dimensional Inference Via Score Projection With an Application in Neuroimaging

ABSTRACT

In the fields of neuroimaging and genetics, a key goal is testing the association of a single outcome with a very high-dimensional imaging or genetic variable. Often, summary measures of the high-dimensional variable are created to sequentially test and localize the association with the outcome. In some cases, the associations between the outcome and summary measures are significant, but subsequent tests used to localize differences are underpowered and do not identify regions associated with the outcome. Here, we propose a generalization of Rao’s score test based on projecting the score statistic onto a linear subspace of a high-dimensional parameter space. The approach provides a way to localize signal in the high-dimensional space by projecting the scores to the subspace where the score test was performed. This allows for inference in the high-dimensional space to be performed on the same degrees of freedom as the score test, effectively reducing the number of comparisons. Simulation results demonstrate the test has competitive power relative to others commonly used. We illustrate the method by analyzing a subset of the Alzheimer’s Disease Neuroimaging Initiative dataset. Results suggest cortical thinning of the frontal and temporal lobes may be a useful biological marker of Alzheimer’s disease risk. Supplementary materials for this article are available online.

KEYWORDS:

• Alzheimer’s disease
• Association test
• Cortical thickness
• Neuroimaging
• Post hoc inference
• Score test

Supplementary Materials

Proofs of all theorems and additional simulations are included in the Supplementary Material.

Acknowledgments

The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The authors thank Wei Pan and Haochang Shou for helpful discussions related to this work. Code to perform the analyses in this manuscript is provided at https://bitbucket.org/simonvandekar/pst. The investigators within the ADNI contributed to the design and implementation of ADNI and provided data, but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf. The data used in this manuscript are publicly available at http://adni.loni.usc.edu/

Additional information

Funding

SNV was supported by NIMH grant T32MH065218-11; PTR was supported by NIMH grant R01MH095836 and Israel Science Foundation grant 1777/16; RTS was supported by NINDS grant R01NS085211, R21NS093349, and R01NS060910, as well as NIMH grant R01MH112847.