Application of Sampling Importance Resampling to estimate parameter uncertainty distributions
Anne-Gaëlle Dosne (1), Martin Bergstrand (1), Mats O. Karlsson (1)
(1) Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Objectives: Develop a method to assess parameter uncertainty for non-linear mixed effects (NLME) models based on Sampling Importance Resampling (SIR) . Compare this method to existing methods for real and simulated data.
The uncertainty in parameter estimates in NLME models is commonly computed using the asymptotic covariance matrix. A well-known limitation of this method is the lack of considering any asymmetry in the parameter uncertainty. In this work, a method based on SIR was developed to improve uncertainty estimation based on the covariance matrix while limiting computational burden.
Methods: A high number (2000-10000) of parameter vectors were sampled from the covariance matrix. For each parameter vector, an importance ratio (IR) was computed by weighting the fit to the original data by the probability density value for the vector given the estimated covariance matrix. Non-parametric uncertainty distributions were then obtained by resampling parameter vectors according to probabilities proportional to the IR. The SIR method was applied to NLME models for real [2-4] and simulated data. Parameter confidence intervals (CIs) and density distributions obtained with SIR were compared to those obtained based on likelihood profiling (LLP), covariance matrix and bootstrap using the FOCEI method in NONMEM 7.2.
Results: Compared to CIs based on the covariance matrix, SIR provided a closer agreement with LLP, especially for parameters showing asymmetric CIs. SIR CIs were in agreement with CIs based on the covariance matrix when the uncertainty was symmetric. SIR also led to CIs in closer agreement to LLP for real data examples where the bootstrap confidence intervals were shown to be inflated .
Conclusions: SIR appears as a promising approach to assess parameter uncertainty. While based on the covariance matrix, it can address asymmetry in parameter uncertainty. As opposed to LLP, it directly generates a distribution that can be used for clinical trial simulation. In comparison to a bootstrap SIR allows every parameter vector to be evaluated using all data, which is valuable when the data set is not very large, yet at a very limited computational burden.
Acknowledgements: This work was supported by the DDMoRe (http://www.ddmore.eu/) project.
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