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

Table 2 Comparison of the estimates provided by the joint mixed model approach and the curve-by-curve approach

Parameter	Disease stage	Joint mixed model		Curve-by-curve
		Estimate	Std. error	Estimate	Std. error
τ ₁	II	84.15	10.14	82.42	18.15
	III	74.97	8.43	82.28	24.35
	IV	97.12	15.78	128.45	32.58
\(\dot {\mathrm {V}}\mathrm {O}_{2}rest\)	II	282.9	13.27	284.52	13.62
	III	288.82	11.09	284.04	18.27
	IV	266.79	19.25	283.08	24.44
\(\dot {\mathrm {V}}\mathrm {O}_{2}ss\)	II	1029.6	55.17	1007.7	58.46
	III	948.53	46.14	940.83	78.43
	IV	737.07	79.94	815.41	104.93
τ ₂	II	–3.77	0.28	–4.68	0.41
	III	–2.91	0.23	–3.74	0.54
\(\dot {\mathrm {V}}\mathrm {O}_{2}recovery\)	II	276.03	7.51	301.3	18.8
	III	242.53	9.8	276.03	25.22
	IV	209.71	15.03	294.65	33.75
T\(_{1/2} \dot {\mathrm {V}}\)O₂	II	129.14	9.9	127.65	9.53
	III	134.7	8.46	136.51	12.79
	IV	178.82	15.27	161.6	17.11

τ ₁: growth rate of the mono-exponential \(\dot {\mathrm {V}}\)O₂ function during 6MWT; \(\dot {\mathrm {V}}\mathrm {O}_{2}rest\), \(\dot {\mathrm {V}}\mathrm {O}_{2}ss\) and \(\dot {\mathrm {V}}\mathrm {O}_{2}recovery\): oxygen level at rest, steady state during exercise and recovery, respectively; τ ₂: steepness of the exponential decay during the recovery phase; \(\mathrm {T}_{1/2}\dot {\mathrm {V}}\mathrm {O}_{2}\): time for half decrease of the \(\dot {\mathrm {V}}\)O₂ level in the recovery phase

ISSN: 1471-2288