PCA-based modelling in antidepressant trials: a pre-mechanistic approach

Objectives: For many diseases, such as psychiatric ones, mechanistic knowledge of the progression of the disease and the interaction between disease and drug action is often very limited or absent. The empirical models, adopted to describe the evolution of clinical endpoints [1], are characterized by arbitrarily chosen basis functions and are usually dataset-specific. This motivates the development of a flexible and general-purpose "pre-mechanistic" technique to be used for exploratory analysis and as a touchstone for subsequent mechanistic model building. Along this direction, the aim of this work is to introduce a method, based on Principal Component Analysis (PCA), that automatically provides regression functions reflecting the informative content of the data: the PCA-based approach [2]. Methods: Population analyses of simulated and experimental datasets were performed. Three parametric models were used to simulate 50 datasets (100 subjects per dataset): Weibull, Inverse Bateman and Weibull + linear models. The experimental dataset was obtained from a Phase II depression trial. The proposed approach provides the principal functions of the unobservable true signal through the singular value decomposition of the covariance matrix of data. The number of components was selected through either Mallows' Cp criterion [3] or random crossvalidation. The new PCA-based approach and the three parametric models were compared in simulation in terms of "denoising", i.e. the ability to reconstruct the true individual profiles. Moreover, we evaluated the crossvalidatory RMSE on both simulated and experimental data. Parameter estimation was carried out with R 2.13.1 [4], according to the empirical Bayes paradigm. Results: The PCA-based approach provided satisfactory denoising perfomances and good predictive ones, in all the 150 simulated datasets. In the experimental scenario, the PCA-based model with 3 principal functions was chosen according to the order selection procedure. The proposed approach achieved very satisfactory individual fittings and crossvalidatory performances. Conclusions: The proposed PCA-based approach can be valuable when the mechanistic knowledge of the disease is limited or absent. It automatically provides basis functions suitable to develop parsimonious population models and yields reliable reconstructions of individual profiles. This approach is useful for exploratory analysis and as a touchstone in order to benchmark the performances of mechanistic models. References: [1] Gomeni R, Lavergne A, Merlo-Pich E (2009), Modelling placebo response in depression trials using a longitudinal model with informative dropout, European Journal of Pharmaceutical Science 36, pp. 4-10. [2] Abdi H, Williams Lynne J (2010), Principal component analysis, WIREs Computational Statistics 2, pp. 433-459 [3] Mallows C L (1973), Some comments on Cp, Technometrics 15, pp. 661-675 [4] R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2011). http://www.r-project.org/.