Models for estimating the change-point in gas exchange data

In subjects undertaking an incremental exercise test to exhaustion, the onset of metabolic acidosis can be detected by an increased rate of carbon dioxide output (VCO2) relative to the rate of increase of oxygen uptake (VO2). To locate the change-point (the gas exchange threshold) in such subjects, a two-line regression model relating these two quantities has been used, where the location of the change-point is unknown. We argue that statistical models where the change-point is set on time (rather than VO2) are more appropriate. This is because VO2 is not monotone in time. We use novel statistical methodology of hidden Markov models to demonstrate the existence of the change-point. We use time series models, to estimate the position of the change-point. In these models distributions other than the multivariate normal are considered. For some subjects, the variance of VCO2 increases with time because of increasing ventilation and this is also modelled. The results are illustrated using gas exchange data on three healthy subjects who performed a 20 W min(-1) workrate ramp test.