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

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

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
  1. 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