Generalisation of T-optimality for discriminating between competing models – an application to paracetamol overdose

Background and objectives: The T-optimality criterion for model discrimination was introduced by Atkinson and Fedorov [1]. Application of this method required the condition that one of the competing models is correct. We term this criterion local T-optimality. In addition, T-optimal designs are generally not efficient for parameter estimation. The aims of current work are (1) to develop and assess a robust T-optimal method that relaxes the requirement that one of the candidate models is true and (2) to combine this robust T-optimal method with robust D-optimality for parameter estimation. The motivating example is paracetamol in overdose. Reports on the pharmacokinetics (PK) of paracetamol in overdose are conflicting with authors describing both linear [2] and nonlinear elimination [3] disposition. This has significant implications for the use of N-acetylcysteine as an antidote in treatment of patients who take an overdose of paracetamol.

Methods: The two competing models for the PK of paracetamol in overdose were; (1) a 2-compartment model with linear elimination (M1); (2) a 2-compartment model with Michaelis-Menten elimination (M2). The population PK parameters for M1 were available from the literature from paracetamol at therapeutic doses [4]. Simulations were conducted to find values of Vmax and Km such that the PK profile of paracetamol using M2 looks similar to M1 at therapeutic doses (up to 2g/dose) but would yield different profiles after overdose (e.g. 30g). A HClnD-optimal design was obtained for both the models using WinPOPT. Three hybrid DT designs were constructed: (1) using local T-optimality assuming M1 to be correct (D1), (2) using local T-optimality assuming M2 to be correct (D2) and, (3) robust T-optimality where either M1 or M2 could be correct (D3). Using NONMEM VI, 100 data sets were simulated and estimated under each of D1, D2 and D3 with either M1 or M2 being the true model. The power was calculated as the proportion of times that the correct model was identified based on a likelihood ratio test. The number of subjects in each simulated data set was calibrated so that the power was close to 60% in order to see a signal from the different designs.

Results: The Vmax and Km values obtained in simulation study are 3540 mg/h and 200 mg/L, respectively. The Hybrid local DT-optimal designs D1 and D2 were not similar indicating that assuming either M1 or M2 is true could be misleading. The power of D1, D2 and D3 if M1 was correct was 70%, 40% and 52% respectively. The power of D1, D2 and D3 if M2 was correct was 13%, 87% and 87% respectively.

Conclusions: The assumption inherent with local T-optimality, that one of the two competing models is true, may result in poor study power when the supposed correct model is incorrect. The robust T-optimality method had good power to distinguish between the models without assuming either of the two competing models is true.


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