Nonlinear mixed effects modelling for the analysis of longitudinal body core temperature data in healthy volunteers

Abstract

Many longitudinal studies have collected serial body core temperature (Tc) data to understand thermal work strain of workers under various environmental and operational heat stress environments. This provides the opportunity for the development of mathematical models to analyse and forecast temporal Tc changes across populations of subjects. Such models can reduce the need for invasive methods that continuously measure Tc. This current work sought to develop a nonlinear mixed effects modelling framework to delineate the dynamic changes of Tc and its association with a set of covariates of interest (e.g. heart rate, chest skin temperature), and the structure of the variability of Tc in various longitudinal studies. Data to train and evaluate the model were derived from two laboratory investigations involving male soldiers who participated in either a 12 (N = 18) or 15 km (N = 16) foot march with varied clothing, load and heat acclimatisation status. Model qualification was conducted using nonparametric bootstrap and cross validation procedures. For cross validation, the trajectory of a new subject’s Tc was simulated via Bayesian maximum a posteriori estimation when using only the baseline Tc or using the baseline Tc as well as measured Tc at the end of every work (march) phase. The final model described Tc versus time profiles using a parametric function with its main parameters modelled as a sigmoid hyperbolic function of the load and/or chest skin temperature. Overall, Tc predictions corresponded well with the measured data (root mean square deviation: 0.16 °C), and compared favourably with those provided by two recently published Kalman filter models.