A fusion learning method to subgroup analysis of Alzheimer's disease

Abstract

Uncovering the heterogeneity in the disease progression of Alzheimer's is a key factor to disease understanding and treatment development, so that interventions can be tailored to target the subgroups that will benefit most from the treatment, which is an important goal of precision medicine. However, in practice, one top methodological challenge hindering the heterogeneity investigation is that the true subgroup membership of each individual is often unknown. In this article, we aim to identify latent subgroups of individuals who share a common disorder progress over time, to predict latent subgroup memberships, and to estimate and infer the heterogeneous trajectories among the subgroups. To achieve these goals, we apply a concave fusion learning method to conduct subgroup analysis for longitudinal trajectories of the Alzheimer's disease data. The heterogeneous trajectories are represented by subject-specific unknown functions which are approximated by B-splines. The concave fusion method can simultaneously estimate the spline coefficients and merge them together for the subjects belonging to the same subgroup to automatically identify subgroups and recover the heterogeneous trajectories. The resulting estimator of the disease trajectory of each subgroup is supported by an asymptotic distribution. It provides a sound theoretical basis for further conducting statistical inference in subgroup analysis.

Keywords:

• B-spline
• concave penalty
• heterogeneity
• longitudinal trajectory
• precision medicine
• subgroup analysis

Acknowledgments

The authors are grateful to the editor, the associate editor, and two anonymous reviewers for their insightful comments that have helped us improve the article substantially.

Data collection and sharing for this project was funded by the Alzheimer's Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer's Association; Alzheimer's Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (http://www.fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimer's Therapeutic Research Institute at the University of Southern California. ADNI data are disseminated by the Laboratory for Neuro Imaging at the University of Southern California.

The authors thank Xiang Zhang and Peter F. Castelluccio, former Eli Lilly and Company employees, for their help in data organization. Yushi Liu, Bochao Jia and Luna Sun are stockholders and employees of Eli Lilly and Company.

Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or 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.

Data availability statement

The Alzheimer's disease data can be obtained from the ADNI database (adni.loni.usc.edu). And the R codes associated with this paper are available at https://doi.org/10.6084/m9.figshare.17275148.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of Mingming Liu and Shujie Ma is supported in part by the National Science Foundation [grant number 1712558 and 2014221], and the UCR Academic Senate CoR Grant. Jing Yang's research is supported by the National Natural Science Foundation of China [grant number 11801168], the Natural Science Foundation of Hunan Province [grant number 2018JJ3322], the Scientific Research Fund of Hunan Provincial Education Department [grant number 18B024], and the project of China Scholarship Council for his visiting to Professor Shujie Ma a University of California, Riverside.