NOPAPROD non-parametric testing on projections from multivariate data. Applications to near infrared spectroscopy in clinical studies

Clinical studies may be carried out using non-invasively collected near infrared spectra of patient skin. Two problems encountered are: (1) data reduction to go from thousands of wavelengths to some clinically relevant estimator and (2) getting statistical significance from noisy data with sometimes very skewed distributions. The problem of data reduction can usually be solved by principal component analysis to get a few meaningful components. In the space spanned by these components, a direction of discrimination may have to be found, typically discrimination between treated and control. A visual difference in a score plot is often not enough; statistical significance has to be demonstrated. Once a univariate estimator is found, non-parametric testing can show significant differences, even if the data are noisy and have an unknown and skewed distribution. The NOPRAPOD method combines the actions of finding a direction in a reduced data space and performing the non-parametric significance testing by producing a disk of significance. Two examples are included. Example one is from a study of diabetes-related neuropathy where it is shown that significant differences show up in the NIR spectra. Example two is from a study of post-operative radiation treatment of breast cancer patients, where it is shown that radiation effects (erythema) and the effect of Lotion can be determined with an indication of significance from the NIR spectra.