### Abstract

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 (V?CO_{2}) relative to the rate of increase of oxygen uptake (V?O_{2}). 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 V?O_{2}) are more appropriate. This is because V?O_{2} 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 V?CO_{2} 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.

Original language | English |
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Pages (from-to) | 1425-1436 |

Number of pages | 12 |

Journal | Physiological Measurement |

Volume | 25 |

Issue number | 6 |

DOIs | |

Publication status | Published - Dec 2004 |

### Keywords

- Change-point
- Gas exchange threshold
- Hidden Markov models
- Statistical modelling

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## Cite this

*Physiological Measurement*,

*25*(6), 1425-1436. https://doi.org/10.1088/0967-3334/25/6/008