### 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 |

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### Keywords

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

### Cite this

*Physiological Measurement*,

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

}

*Physiological Measurement*, vol. 25, no. 6, pp. 1425-1436. https://doi.org/10.1088/0967-3334/25/6/008

**Models for estimating the change-point in gas exchange data.** / Kelly, G. E.; Lindsey, J. K.; Thin, A. G.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Models for estimating the change-point in gas exchange data

AU - Kelly, G. E.

AU - Lindsey, J. K.

AU - Thin, A. G.

PY - 2004/12

Y1 - 2004/12

N2 - 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?CO2) relative to the rate of increase of oxygen uptake (V?O2). 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?O2) are more appropriate. This is because V?O2 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?CO2 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.

AB - 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?CO2) relative to the rate of increase of oxygen uptake (V?O2). 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?O2) are more appropriate. This is because V?O2 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?CO2 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.

KW - Change-point

KW - Gas exchange threshold

KW - Hidden Markov models

KW - Statistical modelling

UR - http://www.scopus.com/inward/record.url?scp=12344257635&partnerID=8YFLogxK

U2 - 10.1088/0967-3334/25/6/008

DO - 10.1088/0967-3334/25/6/008

M3 - Article

VL - 25

SP - 1425

EP - 1436

JO - Physiological Measurement

JF - Physiological Measurement

SN - 0967-3334

IS - 6

ER -