Sparse statistical health monitoring: A novel variable selection approach to diagnosis and follow-up of individual patients

- An l1-norm constrained Mahalanobis distance metric is presented.
- This combines estimation of Mahalanobis distances with variable selection.
- Metabolomics data of individual patients is compared to a normal reference range.
- The variable selection step allows for better identification of abnormal variables.
- Several inborn errors of metabolism are diagnosed.

The -omics technologies are becoming increasingly important in health care and are expected to contribute to personalized health care. In a typical experiment, cases and controls are compared as a two-class classification problem. This approach is often unsuitable, for example, because the classes are not well defined due to associated populations being biologically too heterogeneous. Recently, statistical health monitoring (SHM) was introduced as a complementary approach to allow for predictions at the individual level. This approach could be of use in all sorts of applications such as diagnosis of rare diseases, analysis of individual patterns in disease manifestation, disease monitoring, or personalized therapy.SHM uses the framework of statistical process monitoring (SPM) in a clinical setting. The method essentially combines estimation of Mahalanobis distances (MD) with principal component analysis (PCA) to evaluate the difference in the -omics data of an individual subject to a normal reference range (normal operating conditions). It is well known from SPM, however, that reliable identification of the variables primarily responsible for this difference is hampered by the smearing effect, which is a result of the PCA step. To avoid this problem, we propose to combine estimation of the MD with variable selection via an l1-norm penalty instead of using dimension reduction. This way a sparse MD metric is obtained.The effectiveness of this method is illustrated by several simulation studies and its application to urine 1H-NMR metabolomics data for diagnosis of multiple inborn errors of metabolism.