Model-based optimal robust design in pharmacometrics
Giulia Lestini, Sebastian Ueckert, France Mentré
IAME, UMR 1137, INSERM, University Paris Diderot, Paris, France
Objectives: Optimal design requires prior information on models and parameters, which may be difficult to guess. Robust design approaches have been developed for taking into account the uncertainty of parameters [1,2]. Our aims were i) to compare various robust design criteria for design in nonlinear mixed effect models (NLMEM) for a PKPD example with continuous data; ii) to evaluate robust designs using a new method for the evaluation of the Fisher information matrix (FIM) for a NLMEM with discrete data.
Methods: The PKPD model was already used for evaluation of adaptive design [3]. We studied robust design assuming prior distributions for two PD parameters kout and IC50, keeping the PK fixed as in [3]. For 50 patients, 3 sampling times were optimized using D-optimality and the following robust criteria: ED (Expectation of Determinant of FIM), EID (Expectation of the Inverse Determinant), ELD (Expectation of log Determinant), and max-min (minimum of determinant). Predicted relative standard errors (pRSE) for 1000 simulated set of parameters were used for designs comparison.
A logistic model for repeated binary response [4] was defined with treatment increasing the slope of the logit of the response with time. Design evaluation was performed using a new method to compute FIM based on Adaptive Gaussian Quadrature and Quasi Random Monte Carlo[5,6]. We evaluated an equispaced design (ξES) of 4 sampling times, with 50 patients per arm. We then optimized the two intermediate times (fixing the first and the last) using standard D-optimality (ξD) or using the robust ELD criterion (ξELD) with prior uncertainties on the slope and treatment effect
Results: For the PKPD example, the different robust criteria led to different optimal designs. ξELD performed the best in terms of pRSE across the 1000 simulations, the worst was ξmax-min. For IC50 the 90% percentiles for pRSE were 26% for ξELD and 64% for ξmax-min.
The evaluation of FIM with the new approach is rather fast, allowing for the first time robust design optimization for discrete longitudinal models. ξD and ξELD were very close. ξES has a loss of efficiency of 0.82 compare to ξD. When prior uncertainty is assumed, the loss of efficiency is 0.66 compared to ξELD.
Conclusions: Robust designs criteria showed better performance of ξELD in NLMEM. Robust and optimal designs are also useful in the context of binary response studies, providing better results than equispaced design.
This work was supported by the DDMoRe project (www.ddmore.eu).
References:
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[5] Ueckert S, Mentré F. Computation of the Fisher information matrix for discrete nonlinear mixed effect models. 8th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics) University of London, UK. 2015.
[6] Ueckert S, Mentré F. Computation of the Fisher information matrix for discrete non-linear mixed effect models. Population Optimum Design of Experiments (PODE) Isaac Newton Institute for Mathematical Sciences, Cambridge. 2015.