Modeling the oxygen uptake kinetics during exercise testing of patients with chronic obstructive pulmonary diseases using nonlinear mixed models

Florent Baty, Christian Ritz, Arnoldus van Gestel, Martin Brutsche, Daniel Gerhard

The six-minute walk test (6MWT) is commonly used to quantify exercise capacity in patients with several cardio-pulmonary diseases. Oxygen uptake ([Formula: see text]O2) kinetics during 6MWT typically follow 3 distinct phases (rest, exercise, recovery) that can be modeled by nonlinear regression. Simultaneous modeling of multiple kinetics requires nonlinear mixed models methodology. To the best of our knowledge, no such curve-fitting approach has been used to analyze multiple [Formula: see text]O2 kinetics in both research and clinical practice so far. In the present study, we describe functionality of the R package medrc that extends the framework of the commonly used packages drc and nlme and allows fitting nonlinear mixed effects models for automated nonlinear regression modeling. The methodology was applied to a data set including 6MWT [Formula: see text]O2 kinetics from 61 patients with chronic obstructive pulmonary disease (disease severity stage II to IV). The mixed effects approach was compared to a traditional curve-by-curve approach. A six-parameter nonlinear regression model was jointly fitted to the set of [Formula: see text]O2 kinetics. Significant differences between disease stages were found regarding steady state [Formula: see text]O2 during exercise, [Formula: see text]O2 level after recovery and [Formula: see text]O2 inflection point in the recovery phase. Estimates obtained by the mixed effects approach showed standard errors that were consistently lower as compared to the curve-by-curve approach. Hereby we demonstrate the novelty and usefulness of this methodology in the context of physiological exercise testing.