Abstract
With the increasing popularity of optimal design in drug development it is important to understand how the approximations and implementations of the Fisher information matrix (FIM) affect the resulting optimal designs. The aim of this work was to investigate the impact on design performance when using two common approximations to the population model and the full or block-diagonal FIM implementations for optimization of sampling points. Sampling schedules for two example experiments based on population models were optimized using the FO and FOCE approximations and the full and block-diagonal FIM implementations. The number of support points was compared between the designs for each example experiment. The performance of these designs based on simulation/estimations was investigated by computing bias of the parameters as well as through the use of an empirical D-criterion confidence interval. Simulations were performed when the design was computed with the true parameter values as well as with misspecified parameter values. The FOCE approximation and the Full FIM implementation yielded designs with more support points and less clustering of sample points than designs optimized with the FO approximation and the block-diagonal implementation. The D-criterion confidence intervals showed no performance differences between the full and block diagonal FIM optimal designs when assuming true parameter values. However, the FO approximated block-reduced FIM designs had higher bias than the other designs. When assuming parameter misspecification in the design evaluation, the FO Full FIM optimal design was superior to the FO block-diagonal FIM design in both of the examples.
Highlights
Optimal design of clinical trials has become an increasingly popular and important tool in drug development to reduce the cost and increase informativeness of the study [1]
The optimizations using the full Fisher information matrix (FIM) implementation increased the number of support points and reduced sample clustering when compared to the block-diagonal FIM implementations
The optimizations using the first order conditional estimate (FOCE) approximation increased the number of support points and reduced sample clustering when compared to the First Order (FO) approximation
Summary
Optimal design of clinical trials has become an increasingly popular and important tool in drug development to reduce the cost and increase informativeness of the study [1]. By utilizing a nonlinear mixed effects model (NLMEM) to describe the pharmacokinetic (PK) and pharmacodynamic (PD) properties of the drug, the Fisher information matrix (FIM) can be calculated for a set of design variables [2]. One of the simplest and most common design criteria is called D-Optimality which compares designs using the determinant of the FIM under the assumption that all estimated parameters are of equal importance. The individual response, yi, given the individual design vector, ni, can, for a NLMEM, be written as yi 1⁄4 fðhi; niÞ þ hðhi; ni; eiÞ where f(.) is the structural model, h(.) is the residual error model and ei is the residual error vector. The Fisher information matrix for the ith individual with the vector of design variables ni and expected response. The j between subject variability (BSV) terms and the k residual unexplained variability (RUV) terms are assumed to be normally distributed with mean zero and respective covariance matrices
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