A novel covariate search method intended for PKPD models with nonparametric parameter distributions
Paul G. Baverel (1), Radojka M. Savic (1), Scott F. Marshall (2), Mats O. Karlsson (1)
(1) Dept of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University, Uppsala, Sweden; (2) Dept of Pharmacometrics, Pfizer Ltd, Sandwich, United Kingdom
Objectives: To develop a new covariate modeling approach adapted for nonparametric parameter distributions and to evaluate its statistical properties in terms of power and type-I error rate of covariate inclusion.
Methods: The proposed methodology is articulated around the decomposition of the nonparametric joint density obtained in NONMEM into a set of unique individual probability density distributions. These individual probabilities are then exported into R and used as weighting factors of a generalized additive model (GAM) regressing support points on covariate distributions. A calibration of the method is undertaken by means of 1000 randomization tests automated with GAM analyses to derive a decision criterion based on the Akaike’s information criterion (AIC) given the null hypothesis and a user-defined confidence level α. Statistical properties of the proposed methodology were then evaluated through Monte-Carlo simulations with α=5%. Eight scenarios of 1000 stochastic simulations followed by estimations (SSEs) were performed under FOCE-NONP given a 1-compartment PK model and an informative design. Estimates of the statistical power of inclusion of both a continuous and a categorical covariate with varying correlation to CL were obtained with associated estimates of type-I error rate. A comparison was then performed with likelihood ratio test statistics (LRTs) given FOCE parameter distributions. Errors in estimates of correlation coefficients were further assessed.
Results: The methodology was successfully implemented by means of a Perl script calling PsN, NONMEM and R. Estimates of statistical power and type-I error rate of the proposed method were in close agreement with LRT statistics under ideal conditions of hypothesis-testing for the latter, and this, regardless of the correlation strengths and of the nature of the covariate distribution investigated. Estimates of regression coefficients presented negligible bias and were as precise as the ones obtained with parametric models.
Conclusions: The set of covariate analysis tools is extended with a new, calibrated, covariate identification technique intended for nonparametric population models.