A novel score test-based method for efficient covariate selection in population pharmacokinetic analysis
Yixuan Zou (1), Chee M. Ng (1)
(1) University of Kentucky College of Pharmacy, Lexington, KY, USA
Objectives:
Originally proposed Wald’s approximation method (WAM) [1], least absolute shrinkage and selection operator (LASSO) [2] and stepwise covariate method (SCM) [3] are three common covariate model selection approaches in population pharmacokinetic (PPK) analysis. However, covariance matrix of the full PPK covariate model for WAM calculation is very sensitive to study design/model selection and can be difficult to obtain in PPK analysis. LASSO has poor performance in PPK analysis with large datasets and also requires running the full PPK covariate model with constraints on all parameters. The number of NONMEM runs for SCM can be prohibitively large with increasing number of tested covariates and model parameters. Therefore, the objective of this study was to develop an innovative and efficient covariate screening method using score test with the base PPK model without covariates to overcome the drawbacks of WAM, LASSO and SCM in PPK.
Methods:
First, the score test-based method used second order finite difference to calculate the score function and observed fisher information matrix (FIM) at the covariate parameter value of zero in the base PPK model without any covariates. No actual model run was needed to obtain the score function and observed FIM. The obtained score function and observed FIM were then used to determine the score statistic for covariate model selection. Two different model/study design scenarios each with 20 simulated datasets were used. The first scenario was a one-compartment linear PK model with intensive sampling design (number of simulated subjects or N=50, 100, and 200). Among the six covariates used in this scenario, the model parameters clearance (CL) and volume (V) were only affected by weight and gender. The second scenario was an original PK sampling design of a phase II clinical study used to develop the two-compartment PPK model of rituximab [4] (N=107). Thirteen covariates were evaluated in this scenario and both CL and central volume (Vc) were affected by body surface area and gender. Two different score test-based methods were developed and compared to SCM. In the first approach (score test coupled with SCM, or SSCM), forward selection (FS) based on score statistic was used to efficiently yield the preliminary covariate model that was subject to SCM with actual NONMEM runs for final covariate model selection. The second approach (score test coupled with backward elimination, or SBE) used the same score statistic-based FS but was followed by backward elimination (BE) with actual NONMEM runs for final covariate model selection. Relatively less stringent model selection criteria (p=0.2) was used in FS of the score-test covariate screening process as the score statistic has been shown to be more conservative than the likelihood ratio test in linear models [5]. SBE used a significance level of 0.01 in BE after the score test screening. SSCM used a significance level 0.05 in FS and 0.01 in BE after the score test screening. SCM used the same significance levels in FS and BE as SSCM.
Number of correct (true positive) and incorrect (false positive) covariates included for the three methods were used to assess the accuracy of the method in covariate selection. In addition, the average numbers of actual NONMEM runs were also recorded and compared. R (version 3.4.3) and Python (version 2.7.14) were used for covariates simulation and automated NONMEM (version 7.30) runs, respectively.
Results:
For the first scenario, SSCM and SBE achieved comparable accuracy with significant fewer actual NONMEM runs compared to SCM. The following table shows the average actual NONMEM runs for final model covariate selection for different methods:
|
Number of simulated subjects |
SBE |
SSCM |
SCM |
|
50 |
17 |
25 |
49 |
|
100 |
9 |
17 |
46 |
|
200 |
13 |
20 |
48 |
For the second scenario, the SCM identified more true positive and fewer false positive covariates compared to SSCM and SBE but at the expense of more actual NONMEM runs (39[SBE]<58[SSCM] <132[SCM]).
Conclusions:
In this study, two innovative score test-based covariate model development methods (SSCM and SBE) were developed. Both of these models needed fewer actual NONMEM runs compared to SCM and were very useful for covariate model development in presence of large number of covariates and long computation time of a single NOMEM run in complex quantitative system pharmacology analysis.
References:
[1] Kowalski, Kenneth G., and Matthew M. Hutmacher. "Efficient screening of covariates in population models using Wald's approximation to the likelihood ratio test." Journal of pharmacokinetics and pharmacodynamics 28.3 (2001): 253-275.
[2] Ribbing, Jakob, et al. "The lasso—a novel method for predictive covariate model building in nonlinear mixed effects models." Journal of pharmacokinetics and pharmacodynamics 34.4 (2007): 485-517.
[3] Jonsson, E. Niclas, and Mats O. Karlsson. "Automated covariate model building within NONMEM." Pharmaceutical research 15.9 (1998): 1463-1468.
[4] Ng, Chee M., et al. "Population pharmacokinetics of rituximab (anti-CD20 monoclonal antibody) in rheumatoid arthritis patients during a phase II clinical trial." The Journal of Clinical Pharmacology 45.7 (2005): 792-801.
[5] Berndt, Ernst R., and N. Eugene Savin. "Conflict among criteria for testing hypotheses in the multivariate linear regression model." Econometrica: Journal of the Econometric Society (1977): 1263-1277.
