Evaluation of an extended grid method for estimation using nonparametric distributions.

A nonparametric population method with support points from the empirical Bayes estimates (EBE) has recently been introduced (default method). However, EBE distribution may, with sparse and small datasets, not provide a suitable range of support points. This study aims to develop a method based on a prior parametric analysis capable of providing a nonparametric grid with adequate support points range. A new method extends the nonparametric grid with additional support points generated by simulation from the parametric distribution, hence the name extended-grid method. The joint probability density function is estimated at the extended grid. The performance of the new method was evaluated and compared to the default method via Monte Carlo simulations using simple IV bolus model and sparse (200 subject, two samples per subject) or small (30 subjects, three samples per subjects) datasets and two scenarios based on real case studies. Parameter distributions estimated by the default and the extended-grid method were compared to the true distributions; bias and precision were assessed at different percentiles. With small datasets, the bias was similar between methods (<10%); however, precision was markedly improved with the new method (by 43%). With sparse datasets, both bias (from 5.9% to 3%) and precision (by 60%) were improved. For simulated scenarios based on real study designs, extended-grid predictions were in a good agreement with true values. A new approach to obtain support points for the nonparametric method has been developed, and it displayed good estimation properties. The extended-grid method is automated, using the program PsN, for implementation into the NONMEM.