Optimal Sampling Design and Trial Simulation using POPT and NONMEM
Zexun Zhou, Marc Pfister, and Amit Roy
Bristol-Myers Squibb, Princeton, NJ 08807, USA
Objectives: The availability in recent years of optimal sampling design software for population analysis (PFIM_OPT and POPT) have enabled the wider application of optimal sampling methodology to the specification of sparse sampling designs. These software tools determine optimal sampling time-points by maximizing the determinant of the Population Fisher Information Matrix (D-optimal PFIM), and can also provide estimates of uncertainty in population parameters. However, these tools do not provide estimates of accuracy in population and individual parameters, and at present also do not account for interoccasion variability (IOV) and errors in recording sampling times.
Methods: The accuracy (bias) and uncertainty (standard error, SE) in population parameter estimates for an oral 2‑compartment model were examined for 5 constrained optimal sampling designs (modified for practicality), including 4 designs in which not all subjects had the same number of samples. The impact of IOV and sampling time recording errors were also examined. The bias and SE in population parameter estimates were determined by trial simulation (500 trials/design), followed by parameter estimation with NONMEM. The accuracy of individual parameter estimates (mean absolute error, MAE) was also determined for each of the 5 designs with NONMEM.
Results: The population parameters for all designs except interindividual variability of KA for designs with variable sampling times were estimated with small bias, and the CL population parameters were more accurately estimated than the other parameters. The standard error (SE) of the population parameter estimates determined by POPT were smaller than that calculated from NONMEM estimations, but the magnitude of the differences were generally small. MAEs in individual parameter estimates for the richly sampled subjects were approximately 5-10% smaller than the corresponding values for the sparsely sampled subjects.
Conclusions: POPT determined optimal designs generally resulted in accurately estimated population and individual parameters. The estimates of precision provided by POPT were smaller than, but similar in magnitude to the precision determined with NONMEM for the oral 2‑compartment model. However, examination of the efficiency of a sampling design by simulation and estimation with NONMEM is recommended to confirm that the design is robust with respect to sample time recording errors and provides accurate individual parameter estimates, especially for designs that are not exactly optimal or balanced, and for the assessment of the individual parameters.