Shrinking symbolic regression over medical and physiological signals

Medical embedded systems of the present and future are recording vast sets of data related to medical conditions and physiology. Linear modeling techniques are proposed as a means to help explain relationships between two or more medical or physiological signal measurements from the same human subject. In this paper a statistical regression algorithm is explored for use in medical monitoring, telehealth, and medical research applications. An essential element in applying linear modeling to physiological data is determining functional forms for the predictor signals. In this paper we demonstrate an efficient method for symbolic regression and model selection among possible transformation functions for the predictor variables. The three-stage method uses LASSO shrinkage regression to select a brief functional form and performs an polynomial lag regression with this form. This method is applied to medical and physiological time series data exploring the link between respiration and blood oxygen saturation percentage in sleep apnea patients. We found that our method for selecting a functional transformation of the predictor variable dramatically improved the goodness of fit of the model according to standard analysis of variance measures. In the dataset examined, the model achieved a multiple R2 of 0.3373, while a plain time-lagged model without transformation or polynomial lags had a R2 of only 0.016. All of the variables in the model produced by the algorithm had high scores in t tests for validity.