Two bootstrapping routines for obtaining imprecision estimates for nonparametric parameter distributions in nonlinear mixed effects models |
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Authors: | Paul G Baverel Radojka M Savic Mats O Karlsson |
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Institution: | (1) Department of Pharmaceutical Biosciences, Uppsala University, Box 591, 75124 Uppsala, Sweden |
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Abstract: | When parameter estimates are used in predictions or decisions, it is important to consider the magnitude of imprecision associated
with the estimation. Such imprecision estimates are, however, presently lacking for nonparametric algorithms intended for
nonlinear mixed effects models. The objective of this study was to develop resampling-based methods for estimating imprecision
in nonparametric distribution (NPD) estimates obtained in NONMEM. A one-compartment PK model was used to simulate datasets
for which the random effect of clearance conformed to a (i) normal (ii) bimodal and (iii) heavy-tailed underlying distributional shapes. Re-estimation was conducted assuming normality under FOCE, and NPDs were
estimated sequential to this step. Imprecision in the NPD was then estimated by means of two different resampling procedures.
The first (full) method relies on bootstrap sampling from the raw data and a re-estimation of both the preceding parametric
(FOCE) and the nonparametric step. The second (simplified) method relies on bootstrap sampling of individual nonparametric
probability distributions. Nonparametric 95% confidence intervals (95% CIs) were obtained and mean errors (MEs) of the 95%
CI width were computed. Standard errors (SEs) of nonparametric population estimates were obtained using the simplified method
and evaluated through 100 stochastic simulations followed by estimations (SSEs). Both methods were successfully implemented
to provide imprecision estimates for NPDs. The imprecision estimates adequately reflected the reference imprecision in all
distributional cases and regardless of the numbers of individuals in the original data. Relative MEs of the 95% CI width of
CL marginal density when original data contained 200 individuals were equal to: (i) −22 and −12%, (ii) −22 and −9%, (iii) −13 and −5% for the full and simplified (n = 100), respectively. SEs derived from the simplified method were consistent
with the ones obtained from 100 SSEs. In conclusion, two novel bootstrapping methods intended for nonparametric estimation
methods are proposed. In addition of providing information about the precision of nonparametric parameter estimates, they
can serve as diagnostic tools for the detection of misspecified parameter distributions. |
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