Generalisation of T-optimality for discriminating between competing models - an application to paracetamol overdose
Venkata Pavan Kumar Vajjah, Stephen B Duffull
School of Pharmacy, University of Otago, Dunedin, New Zealand
Background and Objectives: The T-optimality criterion for model discrimination were introduced by Atkinson and Fedorov . 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 [2, 3]. 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  and nonlinear elimination  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 . Simulations were conducted to find values of Vmax and Km values 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 assuming that either M1 or M2 were correct. 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. The D3 design performed acceptably to either models being correct model.
Conclusions: The assumption inherent with local T-optimality, that one of the two competing models is true, may result in poor study power. A robust T-optimality method is described that relaxes this assumption which when combined using a hybrid DT-optimality had good power to distinguish between the models without assuming one of the two competing models is true.
. Atkinson A, Fedorov VV. The design of experiments for discriminating between two rival models. Biometrika 1975; 62: 57-70.
. McGree JM, Eccleston JA, Duffull SB. Compound optimal design criteria for nonlinear models. J Biopharm Stat 2008; 18: 646-61.
. Waterhouse TH. Optimal experimental design for nonlinear and genreralised linear models. Brisbane: University of Queensland, 2005.
. Anderson BJ, Holford NH, Armishaw JC, Aicken R. Predicting concentrations in children presenting with acetaminophen overdose. J Pediatr 1999; 135: 290-5.
. Slattery JT, Koup JR, Levy G. Acetaminophen pharmacokinetics after overdose. Clin Toxicol 1981; 18: 111-7.
. Anderson BJ, Holford NH. Mechanistic basis of using body size and maturation to predict clearance in humans. Drug Metab Pharmacokinet 2009; 24: 25-36.
. Lee KF, Duffull S. Methods of robust design of nonlinear models with an application to pharmacokinetics. J Biopharm Stat (in press).
. Waterhouse TH, Eccleston JA, Duffull SB. Optimal design criteria for discrimination and estimation in nonlinear models. J Biopharm Stat 2009; 19: 386-402.