SADDLE_RESET: more robust parameter estimation with a check for local practical identifiability
Henrik Bjugård Nyberg[1], Andrew C. Hooker[1], Robert J. Bauer[2], Yasunori Aoki[3]
[1] Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden [2] Pharmacometrics R&D, ICON plc., Gaithersburg, MD, USA [3] National Institute of Informatics, Tokyo, Japan
Objectives: In the model building process finding the parameter values that best fit the data is a crucial step. Methods based on minimizing the gradient of the likelihood do not adequately evaluate the identifiability of the parameters, potentially leading to incorrect conclusions. We present an algorithm for checking local practical identifiability. The method provides higher confidence in parameter estimates, and can identify local identifiability problems for model-data combinations. We demonstrate the performance of our algorithm as implemented in NONMEM 7.4[1].
Methods:
Algorithm: Estimation utilizing gradient based optimization (e.g. FO, FOCE, LAPLACE) is performed. The result is checked for zero gradients, and if found any associated parameters are reset to their initial values. If no zero gradients are found, then the Hessian of the likelihood (R-matrix) is eigendecomposed and parameters are changed along the direction of the minimum curvature (including negative curvature) of the -2log(likelihood). Estimation is then re-initiated from the new values.
Numerical experiment: Seven example models were selected to represent likely scenarios: five published models with original data – A[2], B[3], C[4]; D – practically identifiable emax model-data, E – practically unidentifiable emax model-data, and F – structurally unidentifiable model[5]. Random perturbation using “retries” in PsN[6] was used to select 1,000 sets of initial parameter estimates within 99% of the best known estimate. Estimation was performed in NONMEM 7.4 alpha 14 from these initial values using SADDLE_RESET. An additional step was taken for models A and B to compare this new method to random perturbation within 10% of final parameter estimates instead of saddle reset in the workflow above.
Results: SADDLE_RESET improved the portion of estimations reaching lowest OFV from 81.2%, 69.8%, and 69.0% to 95.5%, 83.9%, and 77.3% for models A, B and C respectively. Random perturbation only improved percentages to 89.2% and 72.2% for models A and B. SADDLE_RESET successfully indicated local nonidentifiability by obtaining two sets of model parameters with minimum OFV in 96% and 95% of estimations for models E and F respectively.
Conclusion: Our algorithm provides an efficient and easy-to-use check for local practical identifiability of model-data combinations, thus improving confidence in parameter values. We recommend setting SADDLE_RESET to 1 whenever FO, FOCE or Laplacian estimation is performed.
References:
[1] Beal SL, Sheiner LB, Boeckmann AJ, and Bauer RJ (eds) NONMEM 7.4.0 alpha 14 Users Guides. (1989–2016). ICON plc, Gaithersburg, MD, USA. https://nonmem.iconplc.com/nonmem740alpha
[2] Jönsson et al, Population pharmacokinetic modelling and estimation of dosing strategy for NXY-059, a nitrone being developed for stroke, Clinical Pharmakocinetics (2005), 44(8):863-78
[3] Bergmann et al, Impact of CYP2C8*3 on paclitaxel clearance: a population pharmacokinetic and pharmacogenomic study in 93 patients with ovarian cancer, The Pharmacogenomics Journal (2011) 11, 113–120
[4] Wählby et al, Models for time-varying covariates in population pharmacokinetic pharmacodynamic analysis. Br J Clin Pharmacol. 2004;58:367– 77.
[5] Aoki Y, Nordgren R, Hooker AC., Preconditioning of Nonlinear Mixed Effects Models for Stabilisation of Variance-Covariance Matrix Computations., AAPS J. 2016 Mar;18(2):505-18
[6] Keizer RJ, Karlsson MO, Hooker A. Modeling and Simulation Workbench for NONMEM: Tutorial on Pirana, PsN, and Xpose. CPT Pharmacometrics Syst Pharmacol 2013, 2: e50. http://psn.sourceforge.net/
