A novel bootstrap method for obtaining uncertainty measurement around the nonparametric distribution
R.M. Savic (1), P.G. Baverel (1), M.O. Karlsson
Dept of Pharmaceutical Biosciences, Uppsala University, Sweden
Objectives: : Nonparametric methods are powerful tools in population analysis for detecting non-normal distributions of random effects.(1-3) However the wide application of these methods is limited for various reasons, one of them being the lack of imprecision measurement. The aim of this work is to develop a novel method for obtaining the uncertainty around the nonparametric distribution (NPD).
Methods: Original dataset (D) containing J individuals are bootstrapped with replacement n times. This creates n bootstrapped datasets (B1-n) each containing less number of unique individuals than the original number J. Bootstrap sample key, i.e. scheme of included individuals in each B is recorded. The final model is run n times with B1-n and n sets of final parameter estimates (P1-n) are obtained. Each P is used to estimate NPD using final model and D. This further results in n sets of NPD1-n. Each NPD corresponds to P1-n , but it is defined at J number of support points as D is used as the dataset for its estimation. The individual contributions, i.e. probabilities to each NPD are computed. These are summarized as table T1-n with dimensions JxJ with columns representing points of support and rows containing vectors of individual probabilities, J in total. According to the bootstrap sample key, individual probability vectors corresponding to individuals contained in B1-n are sampled from T1-n. This result in n sets of new NPD (NPDnew1-n) based exclusively on information from individuals contained in dataset B1-n but defined at J number of points of support. NPDnew1-n are used to construct 95% CI around the original NPD.
Results: The method has been successfully developed and tested using nonparametric estimation method in NONMEM VI. Being a computer intensive method, automation using Perl and PsN was necessary. A shorter version has been developed which involves obtaining individual probability vectors for original NPD only. These vectors could be bootstrapped with replacement on its own which can be further used to construct confidence intervals around NPD.
Conclusions: A novel method for uncertainty measurement around NPD is developed. The implementation of the method is available for software NONMEM; however the principle can be applied within other nonparametric software framework. The method facilitates wider use of nonparametric methods for population analyses in future.
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 Savic R.M., Kjellsson M.C., Karlsson M.O. Evaluation of the nonparametric estimation method in NONMEM VI beta. In; 2006; PAGE 15 (2006) Abstr 937 [www.page-meeting.org/?abstract=937]