Classical Model
Compartments: 3
Fractional Model (authors)
Compartments: 1
Parameters: four fewer
Reported by the authors
not re-analysed by FractaLPK
The authors implemented fractional differential equations in NONMEM (FDE4NONMEM). For diazepam, they report that a one-compartment fractional model performed similarly to a three-compartment classical model (diagnostic plots and Visual Predictive Check) with four fewer parameters.
Classical Model
Compartments: 2
Fractional Model (authors)
Compartments: 2
Order: one, shared
Reported by the authors
not re-analysed by FractaLPK
In a bioequivalence trial of two slow-release 100 mg formulations (12 healthy volunteers), the authors fitted a two-compartment model with fractional derivatives of the same order by least squares, and report a better fit than the classical two-compartment model. As they note, the classical model is a special case of the fractional one, so a better fit alone is expected.
Classical Model
Profiles: mostly decreasing
Fractional Model (authors)
Fits: non-monotonic profiles
Reported by the authors
not re-analysed by FractaLPK
In high-dose methotrexate in children with acute lymphoblastic leukaemia, the authors observed local maxima in some treatments and report that their fractional model can recognise and better fit this non-monotonic behaviour.
Classical Model (α=1)
Tumor growth: logistic ODE
Evaluable patients: 17/18
Fractional Model (RPSM+Cp5)
Preferred by ΔAIC ≥ 4: 1/17
α on the optimiser bound (0.3): 9/18
r on the optimiser bound (0.01): 13/18
Inconclusive
☆☆☆☆☆
no fractional advantage shown
No evidence of a fractional advantage in this re-analysis. The fractional logistic model contains the classical one (α = 1), so it lowers MSE almost always — that alone is not evidence. Penalising the extra parameter (ΔAIC ≥ 4), it is preferred in 1 of 17 evaluable patients. α sits on the optimiser’s lower bound in 9 of 18 patients, so its value is not interpretable; the growth rate r sits on its lower bound (0.01) in 13 of 18. Median 6 measurements per patient.
Classical Model (α=1)
Tumor growth: logistic ODE
Evaluable patients: 34/34
Fractional Model (RPSM+Cp5)
Preferred by ΔAIC ≥ 4: 4/34
α on the optimiser bound (0.3): 16/34
r on the optimiser bound (0.01): 19/34
Inconclusive
☆☆☆☆☆
no fractional advantage shown
No evidence of a fractional advantage in this re-analysis. The fractional logistic model contains the classical one (α = 1), so it lowers MSE almost always — that alone is not evidence. Penalising the extra parameter (ΔAIC ≥ 4), it is preferred in 4 of 34 evaluable patients. α sits on the optimiser’s lower bound in 16 of 34 patients, so its value is not interpretable; the growth rate r sits on its lower bound (0.01) in 19 of 34. Median 6.5 measurements per patient. Comparing α between arms (the earlier p = 0.46) is not meaningful while α sits on the bound.
Classical Model (α=1)
Tumor growth: logistic ODE
Evaluable patients: 8/8
Fractional Model (RPSM+Cp5)
Preferred by ΔAIC ≥ 4: 0/8
α on the optimiser bound (0.3): 4/8
r on the optimiser bound (0.01): 6/8
Inconclusive
☆☆☆☆☆
no fractional advantage shown
No evidence of a fractional advantage in this re-analysis. The fractional logistic model contains the classical one (α = 1), so it lowers MSE almost always — that alone is not evidence. Penalising the extra parameter (ΔAIC ≥ 4), it is preferred in 0 of 8 evaluable patients. α sits on the optimiser’s lower bound in 4 of 8 patients, so its value is not interpretable; the growth rate r sits on its lower bound (0.01) in 6 of 8. Median 4.5 measurements per patient.