Results

1. Two bootstrapping routines for obtaining uncertainty measurement around the nonparametric distribution obtained in NONMEM VI Paul G. Baverel 1, Radojka M. Savic 2 and Mats O. Karlsson 11 Division of Pharmacokinetics & Drug Therapy, Uppsala University, Sweden 2 INSERM U738, University Paris Diderot Paris 7, Paris, France Background Results NQuantifying uncertainty in parameter estimates is essential to support decision making throughout model building process. NDespite providing enhanced estimates of parameter distribution, nonparametric algorithms do not yet supply uncertainty metrics. • Overall, the trend and the magnitude of the 95% CI derived with the full and • the simplified nonparametric bootstrapping methods (N=100 and N=500) • matched the true 95% CI in all distributional cases and regardless of • individual numbers in original data. • The simplified version induced slightly less bias in quantifying uncertainty • (prediction errors of 95% CI width) than the full version. This is expected as • the former methodology derives uncertainty from the original data. Objectives UNDERLYING BIMODAL CLEARANCE DISTRIBUTION 200 IDs 50 IDs Prediction errors Materials and Methods N Six informative datasets of 50 or 200 individuals were simulated from an IV bolus PK model in which CL and V conformed to various underlying distributional shapes (log-normal, bimodal, heavy-tailed). Residual variability was set to 10% CV. UNDERLYING HEAVY-TAILED CLEARANCE DISTRIBUTION (200 IDs) N=100 N=500 Prediction errors N Re-estimation was conducted assuming normality under FOCE, and NPDs were estimated by applying FOCE-NONP method in NONMEM VI. • Two different permutation methods automated in PsN [1] were developed to quantify uncertainty around NPD (95% confidence interval) and nonparametric estimates (SEs and variance-covariance matrix): • The full method [2] relies on N bootstraps of the original data and a re-analysis of both the preceding parametric as well as the nonparametric step • The simplified method relies on N bootstrap samples of the vectors of individual probabilities associated with each unique support point of the NPD Figure 2. On the left : 95% confidence intervals obtained based on the full and simplified nonparametric bootstrapping methodologies in case of various underlying distributions of CL. The true 95% CI around the true parameter distribution is also represented for comparison, as well as the parametric cumulative density function. On the right: Prediction errors of the 95% CI width are displayed for each quartile of parameter distribution, the true uncertainty being taken as reference. • N matrices MN(JxJ) of individual probabilities: • Row entries J individuals • Column entries J support points Table 1. SEs of parameter estimates obtained from 100 stochastic simulations followed by estimations given the true model under FOCE, FOCE-NONP and the analytical solution under FOCE ($COVARIANCE) in NONMEM VI. The simplified methodology was applied to each simulated dataset; SEs were computed and average SEs were reported for comparison with SSE.  N sets NPDnewNdefined at J support points of NPDN NSEs obtained with the simplified methodology matched the ones obtained by SSE. • Full nonparametric bootstrapping method: 7-step procedure (CPU time: ca 4 hr.) Conclusion BOOTSTRAP* IPDNaccording to sample scheme B1...BN 5 4 PARTITIONING NPDNinto J individual probability densities IPDN BOOTSTRAP* N times original data DJ 1 2 3 PARAMETRIC ESTIMATION: B1... BN NONPARAMETRIC ESTIMATION: DJgiven (θ,Ω,σ) NTwo novel bootstrapping routines intended for nonparametric estimation methods are proposed. Their evaluation with a simple PK model in the case of informative sampling design was performed when applying FOCE- NONP in NONMEM VI but it is easily transposable to other nonparametric applications. N These tools can be used for diagnostic purpose to help detecting misspecifications with respect to the distribution of random effects. NFrom the sampling distribution obtained, standard uncertainty metrics, such as standard errors and correlation matrix can be derived in case reporting uncertainty is intended. • NxN matrices MbootNof bootstrapped IPD<J  N sets (θ,Ω,σ) each defined at <J support points  N sets NPDNdefined at J support points for <J individuals in B1...BN • Bootstrapped • data B1...BN  A single set of NPDnewNdefined at J support points of NPD • From NPDnewNconstruct nonparametric 95% CI around NPD • Derive SEs and correlation matrix of nonparametric estimates RE-ASSEMBLING bootstrapped IPD<J 6 5 7 Figure 1: Sequential steps of the operating procedure of both the full and simplified nonparametric bootstrapping methods intended for nonparametric estimation methods. • Simplified nonparametric bootstrapping method: 5-step procedure (ca 2 mn.) BOOTSTRAP IPDJ N times PARTITIONING NPDinto J individual probability densities IPDJ NONPARAMETRIC ESTIMATION: Original data DJ RE-ASSEMBLING bootstrapped IPDJ 3 2 1 4 NThe true uncertainty was derived by standard nonparametric bootstrapping (N=1000) [3] of the true individual parameters and used as reference for qualitative and quantitative assessment of the uncertainty measurements derived from both techniques. References: [1]. Perl-speaks-NONMEM (PsN software): L. Lindbom, M. Karlsson, N. Jonsson. http://psn.sourceforge.net [2]. Savic RM, Baverel PG, Karlsson MO. A novel bootstrap method for obtaining uncertainty around the nonparametric distribution. PAGE 18 (2008) Abstract 1390. [3]. Efron B. Bootstrap methods: another look at the jackknife. Ann Stat 1979;7:1-26. • N matrices MbootN of bootstrapped IPDJ • Matrice M (JxJ) of • individual probabilities: • Row entries J individuals • Column entries J support points  NPD defined at J support points