Estimating inestimable standard errors in population pharmacokinetic studies: the bootstrap with Winsorization

A simulation study was performed to determine how inestimable standard errors could be obtained when population pharmacokinetic analysis is performed with the NONMEM software on data from small sample size phase I studies. Plausible sets of concentration-time data for nineteen subjects were simulated using an incomplete longitudinal population pharmacokinetic study design, and parameters of a drug in development that exhibits two compartment linear pharmacokinetics with single dose first order input. They were analyzed with the NONMEM program. Standard errors for model parameters were computed from the simulated parameter values to serve as true standard errors of estimates. The nonparametric bootstrap approach was used to generate replicate data sets from the simulated data and analyzed with NONMEM. Because of the sensitivity of the bootstrap to extreme values, winsorization was applied to parameter estimates. Winsorized mean parameters and their standard errors were computed and compared with their true values as well as the non-winsorized estimates. Percent bias was used to judge the performance of the bootstrap approach (with or without winsorization) in estimating inestimable standard errors of population pharmacokinetic parameters. Winsorized standard error estimates were generally more accurate than non-winsorized estimates because the distribution of most parameter estimates were skewed, sometimes with heavy tails. Using the bootstrap approach combined with winsorization, inestimable robust standard errors can be obtained for NONMEM estimated population pharmacokinetic parameters with > or = 150 bootstrap replicates. This approach was also applied to a real data set and a similar outcome was obtained. This investigation provides a structural framework for estimating inestimable standard errors when NONMEM is used for population pharmacokinetic modeling involving small sample sizes.