A New Exact Test for the Evaluation of Population Pharmacokinetic and/or Pharmacodynamic Models Using Random Projections

Abstract

Purpose Within-subject dependency of observations has a strong impact on the evaluation of population pharmacokinetic (PK) and/or pharmacodynamic (PD) models. To our knowledge, none of the current model evaluation tools correctly address this issue. We present a new method with a global test and easy diagnostic plot which relies on the use of a random projection technique that allows the analysis of dependent data. Methods For each subject, the vector of standardised residuals is calculated and projected onto many random directions drawn uniformly from the unit sphere. Our test compares the empirical distribution of projections with their distribution under the model. Simulation studies assess the level of the test and compare its performance with common metrics including normalised prediction distribution errors and different types of weighted residuals. An application to real data is performed. Results In contrast to other evaluated methods, our test shows adequate level for all models and designs investigated, which confirms its good theoretical properties. The weakness of other methods is demonstrated and discussed. ConclusionsThis new test appears promising and could be used in combination with other tools to drive model evaluation in population PK/PD analyses. KEY WORDS

Enhanced Method for Diagnosing Pharmacometric Models: Random Sampling from Conditional Distributions

“…Then, it cannot be used for model building, but only for validating the nal model. Another method for a global test and which relies on the use of a random projection technique is described in [20].…”

Model Evaluation of Continuous Data Pharmacometric Models: Metrics and Graphics

“…We may compare the observed statistics or observations with their distribution via graphical assessment or statistical tests. The use of statistical tests is not considered in this tutorial but is discussed in several papers 6, 11, 15, 16, 17…”

“…The use of statistical tests is not considered in this tutorial but is discussed in several papers. 6,11,[15][16][17] Visual and numeric predictive check The VPC offers a graphical comparison of the distribution of observations and the distribution of predictions vs. an independent variable, such as time, dose, or other covariates. 8 It comprises in comparing the distribution of the observations with that of the predictions using different percentiles of the distributions.…”

Extension of NPDE for evaluation of nonlinear mixed effect models in presence of data below the quantification limit with applications to HIV dynamic model

“…Under the null hypothesis, we expect pde to follow the distribution U[0, 1] and npde to follow the distribution N (0, 1). However, one should bear in mind that npde are uncorrelated but not totally independent as observations in NLMEM are not Gaussian [18,28]. To use statistical tests on npde, we have to assume that the decorrelation step renders the pde independent.…”

“…To use statistical tests on npde, we have to assume that the decorrelation step renders the pde independent. This can sometimes cause type I errors to be higher than the nominal level [28]. Also, it should be noted that with the proposed method, left censored observations in the validation datasets are imputed using the model to be evaluated and this could lead to loss of power if the model is wrong.…”