Determination of Appropriate Settings in the Assessment of Parameter Uncertainty Distributions using Sampling Importance Resampling (SIR)
Anne-Gaëlle Dosne (1), Martin Bergstrand (1), Mats O. Karlsson (1)
(1) Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Objectives: Sampling Importance Resampling (SIR)  has been proposed as a method for assessment of parameter uncertainty without the need for repeated parameter estimation and making no assumptions regarding the uncertainty distribution . A number of questions are likely to arise when performing SIR. The objectives of this work were to develop criteria to select appropriate settings for the SIR method in terms of number of initial samples and proposal uncertainty distribution, as well as to investigate the impact of replacement on SIR results.
Methods: SIR was performed using NONMEM 7.3 on three real data examples [3-5] with 2000, 4000, 6000, 8000 and 10,000 initial vectors, i.e. 2, 4, 6, 8 and 10-fold the number of resampled parameters (1000 in this case). Initial parameter vectors were sampled on inflations or deflations of the asymptotic covariance matrix, for which all variances were multiplied by factors of 0.5, 0.75, 1, 1.5, and 2 while correlations between them remained unchanged. Parameter vectors were allowed to be resampled with no, limited (to 5 times) or unlimited replacement. dOFV quantile distribution curves of the resampled parameters, the value of the integration of these curves between the 2.5th and 97.5th quantiles (dOFVint) and the value of importance ratios (IR) over parameter value of the initial samples were investigated as criteria potentially qualified to judge the appropriateness of SIR settings.
Results: The convergence of dOFV quantile distributions and their location in relationship to the reference chi-squared distribution was used as a graphical indicator of when a sufficient number of initial samples was reached and whether the proposal uncertainty was appropriate. dOFVint was used to confirm this quantitatively. Trends in IR over parameter plots enabled to assess potential needs for inflation on the parameter level. Limited replacement was shown to increase SIR efficiency.
Conclusions: Quantitative and qualitative criteria to determine whether the number of initial samples and the proposal uncertainty distribution are appropriate when using SIR were developed. These criteria are easy to use and will facilitate reliable use of the SIR method. SIR is readily implemented in PsN  and automation of the choice of initial settings based on the developed criteria will be considered.
Acknowledgments: This work was supported by the DDMoRe (www.ddmore.eu) project and the FP7-HEALTH-2013-602552.
 Rubin DB, Bayesian Statistics. 1988;3:395-402
 PAGE 22 (2013) Abstr 2907 [www.page-meeting.org/?abstract=2907]
 Karlsson et al., J Pharmacokinet Biopharm. 1998;26(2):207–46
 Wählby et al., Br J Clin Pharmacol. 2004;58(4):367–77
 Grasela et al., Dev Pharmacol Ther. 1985;8(6):374–83
 Lindbom et al., Comput Methods Programs Biomed. 2004 Aug;75(2):85-94. 4–83