Validation Methods In Population Pharmacokinetics: A New Approach Based On Predictive Distributions With An Evaluation By Simulation
Mentré F, Escolano S
INSERM U 436, CHU Pitié-Sâlpétrière, 91 Bd de l'Hôpital, 75013 Paris, France
We developed a validation approach based on predictive distributions for nonlinear mixed- -effects models. This validation method is to be applied on a separate data set not used for estimation. We evaluated this method by simulation on data mimicking a population pharmacokinetic analysis.
For each observation of the validation set, we defined a pseudo-residual based on the associated predictive cumulative distribution function evaluated at the observation [Gelfand at al., 1992]. We proposed to compute them using Monte Carlo integration. If the model is valid, these pseudo-residuals for the observations of the validation set should be random with an uniform distribution. The trends in the pseudo-residuals can be evaluated by several plots: histogram, qqplots, plots versus time or versus prediction. If the observations are independent, a one-sample Kolmogorov Smirnov test can be performed.
This new validation approach was evaluated by simulation. A one compartment model with first order absorption was assumed. The variance of the error had a constant coefficient of variation and exponential random effects were added for the three PK parameters. Various sampling times were simulated. We have evaluated the actual type I error (for tests at the 0.05 level) and the power of the proposed procedure by simulation of 1000 validation sets using correct or alternative population models.
We simulated sets with 300 observations either from 300 patients, either from 100 patients with 3observations. For 300 independent observations, the type I error was close to 0.05 and the power was found satisfactory in several cases of departure from the simulated population model. When non-independent observations are simulated (100 individuals with 3 measurements), we proposed to evaluate a Monte Carlo p-value because the type I error was increased.
In conclusion, we have proposed an approach to compute pseudo-residuals in nonlinear mixed-effects models. The evaluation on simulated data showed that this approach is promising for validation from a separate data set. This method was also applied for the validation of the population pharmacokinetic analysis of mizolastine on a separate group of 340 observations from 250 patients using a nonparametric estimation method [Mesnil et al., 1998].
Gelfand AE, Det DK, Chang H (1992): Model determination using predictive distributions with implementation via sampling-based methods. In JM Bernardo, JO Berger, AP David and AFM Smirths (ed), Bayesian statistics 4, Oxford University Press, pp. 147-167.
Mesnil F, Mentré F, Dubruc C, Thenot JL, Mallet A (1998). Population pharmacokinetic analysis of mizolastine and validation from sparse data on patients using the nonparametric maximum likelihood method. Journal of Pharmacokinetics and Biopharmaceutics, 26, 133-161.