Xibei Dang: No financial relationships to disclose
Objectives: The residual error in the nonlinear mixed effects models is commonly assumed to be normally distributed with mean zero, and variance that is either constant or increases as function of the predicted value. Dosne et al (2016) have shown that this computationally convenient assumption is often violated, illustrated with several examples in which a heavier-tailed T-distribution provided a better fit to the data (as measured by improvement in log-likelihood). Here we examine the impact on estimated population and individual parameters of a population PK model in which t-distributed heteroscedastic residual error is misspecified by the corresponding normal distribution.
Methods: The population PK model consisted of a 2-compartment PK disposition model with first-order absorption, with log-normally distributed interindividual variability (IIV) in model parameters (CL, VC, Q, VP, and KA); and a t-distributed combined residual error model, with a degree-of-freedom of 3 (the most common value reported by Dosne et al.). The model was implemented in Pumas, which has native support for a comprehensive set of distributions, including the t-distribution.
The population PK model was applied to simulate data typical of a Phase-1 SAD (N=36) + MAD (N=36) study with intensive PK sampling, as well as a 4-arm Phase-2 study (N=50/arm) with sparse PK sampling (100 sets of clinical trial simulations). The data were fit to the True Model as well as a model in which the RUV was specified by a normally distributed combined error model. The -2LL objective functions were not comparable, as the True Model with the t-distributed RUV error model was required to be fit using the Laplace approximation of -2LL, whereas the model with normally distributed RUV was fit using the FOCE approximation. The bias [100 * (estimate – true)/true] and mean absolute error [ MAE = 100 * |estimate – true|/true] of the estimated population and empirical Bayes estimates (EBE) of individual PK parameter values obtained by these fits were computed and compared.
Results: The RUV model misspecification did not have a marked impact on the bias and MAE of the estimated values of the fixed-effects (typical values) of the population PK model, irrespective of whether they were estimated with intensive or sparse PK observations.
However, the mean bias and MAE of the estimated proportional error variance were markedly larger with the Misspecified RUV model compared to the True RUV model, and the bias and MAE were higher for the intensively sampled data. The bias in the estimated proportional error variance of the Misspecified and True models were ~45% and ~5% with intensive PK data, and ~18% and ~6% with sparse PK data. The magnitudes of the MAE were similar to those of the bias.
Conclusions: A heavy-tailed residual error estimated with a normally distributed RUV did not have an impact on the estimates of typical values of a population PK model. However, the MAE in EBE of CL was slightly higher with the Misspecified model, and the estimated proportional error variance was markedly higher with the Misspecified model.
Keywords: Residual Error, T-Distribution, Heavy Tails
Citations: [1] Dosne AG, Bergstrand M. and Karlsson MO. A strategy for residual error modeling incorporating scedasticity of variance and distribution shape. J Pharmacokinet Pharmacodyn 43, 137–151 (2016).
Keywords: Residual Error, T-Distribution, Heavy Tails
