A nonlinear mixed model approach to predict energy expenditure from heart rate

Objective. Heart rate (HR) monitoring provides a convenient and inexpensive way to predict energy expenditure (EE) during physical activity. However, there is a lot of variation among individuals in the EE-HR relationship, which should be taken into account in predictions. The objective is to develop a model that allows the prediction of EE based on HR as accurately as possible and allows an improvement of the prediction using calibration measurements from the target individual. Approach. We propose a nonlinear (logistic) mixed model for EE and HR measurements and an approach to calibrate the model for a new person who does not belong to the dataset used to estimate the model. The calibration utilizes the estimated model parameters and calibration measurements of HR and EE from the person in question. We compare the results of the logistic mixed model with a simpler linear mixed model for which the calibration is easier to perform. Main results. We show that the calibration is beneficial already with only one pair of measurements on HR and EE. This is an important benefit over an individual-level model fitting, which requires a larger number of measurements. Moreover, we present an algorithm for calculating the confidence and prediction intervals of the calibrated predictions. The analysis was based on up to 11 pairs of EE and HR measurements from each of 54 individuals of a heterogeneous group of people, who performed a maximal treadmill test. Significance. The proposed method allows accurate energy expenditure predictions based on only a few calibration measurements from a new individual without access to the original dataset, thus making the approach viable for example on wearable computers.