Jonathan Chauvin (1), Géraldine Ayral (1), Pauline Traynard (1)
(1) Lixoft, Antony, France
Introduction/Objectives: Covariate search is a key element in the modeling process. As it involves a large number of runs, automatic covariate search procedures have been developed. The most commonly used method is SCM (stepwise covariate modeling [1]). The SCM procedure includes a forward selection, in which covariates are added one by one after evaluation of all possible additions, followed by a backward elimination. This method is effective but expensive in terms of number of runs. We propose an alternative method called COSSAC based on the individual parameter-covariate correlations observed in the current model. The method is available as an R script to be used with MonolixSuite2018R1.
Methods: The proposed method makes use of the information contained in the base model run to choose which covariate to try first (instead of trying all covariates “blindly”). Indeed, the correlation between the individual parameters (or random effects) and the covariates hints at possibly relevant parameter-covariate relationships. If the EBEs (empirical Bayes estimates) are used (as proposed in [2]), shrinkage may bias the result. We instead propose to use samples from the a posteriori conditional distribution ([3], available as “conditional distribution” task in MonolixSuite2018R1) to calculate the correlation between the random effects and covariates. A p-value can be derived using the Pearson’s correlation test for continuous covariate and ANOVA for categorical covariate. The p-values are used to sort all the random effect-covariate relationships. Relationships with the lowest p-value can be added first, run and confirmed using the classical likelihood ratio test. The precise procedure is the following:
Initialization:
- Run the base model (population parameter estimation, conditional distribution sampling, and log-likelihood estimation)
- Calculate the p-values of all the parameter-covariate relationships using Pearson’s correlation tests and ANOVA (done automatically in MonolixSuite2018R1)
Forward selection:
- Add the covariate with the smallest p-value (among the remaining parameter-covariate relationships) to the model
- Run the model
- Accept/reject the relationship based on the likelihood ratio test
- Go back to step 1 until no significant p-values remain
Backward selection: same methodology as the forward step but sorting the p-value (of the correlation between the covariate and the parameter (not the random effect)) from the highest to the lowest
Results: This methodology was tested using MonolixSuite2018R1 and compared to the classical Stepwise Covariate Model (SCM) building on two examples:
- A densely sampled PK data set for remifentanil [4]. Remifentanil is an opioid analgesic drug among other used for sedation. Its PK can be modeled by a 3 compartment model (6 population parameters). The data set contains 6 correlated covariates.
- A time-to-event data set of survival for lung cancer [5]. The data is modeled with a Gompertz model (2 population parameter) and the data set contains 5 covariates.
For both strategies, log-likelihood ratio test is used to accept or reject the parameter-covariate relationship. The inclusion and exclusion criteria on the p-value are set at 0.1 and 0.05 respectively. The criteria to test the inclusion of a covariate in the proposed procedure is 4 times higher than the inclusion criteria (i.e 0.4).
For both data sets, we obtain the same final model using either the SCM and the hereby proposed procedure. However the total number of runs is much lower using the proposed algorithm:
- On the remifentanil projects (36 possible relationships), the proposed algorithm needs 32 runs, while the SCM algorithm needs 246.
- On the lung cancer event project (10 possible relationships), the proposed algorithm needs 15 runs, while the SCM algorithm needs 51.
Conclusions: We propose an efficient covariate search procedure based on the Pearson’s correlation test between individual parameters randomly drawn from the conditional distribution and the covariates. Instead of comparing all parameter-covariate relationships, we test in priority the relationships with the most relevant correlation. This greatly shortens the total number of runs needed and opens the way to the selection of covariates from large covariates lists (such as genomic information).
References:
[1] Byon, W., et al. “Establishing best practices and guidance in population modeling: an experience with an internal population pharmacokinetic analysis guidance.” CPT: Pharmacometrics & Systems Pharmacology 2.7 (2013): 1-8.
[2] Mandema, J. W., Verotta, D., & Sheiner, L. B. (1992). Building population pharmacokineticpharmacodynamic models. I. Models for covariate effects. Journal of Pharmacokinetics and Biopharmaceutics, 20(5), 511–528.
[3] Lavielle, M., & Ribba, B. (2016). Enhanced Method for Diagnosing Pharmacometric Models: Random Sampling from Conditional Distributions. Pharmaceutical Research.
[4] Influence of age and gender on the pharmacokinetics and pharmacodynamics of remifentanil. I. Model development. Anesthesiology, Minto, et al. (1997)
[5] Loprinzi et al. (1994). Prospective evaluation of prognostic variables from patient-completed questionnaires. North Central Cancer Treatment Group. Journal of Clinical Oncology : Official Journal of the American Society of Clinical Oncology, 12(3), 601–607.
Reference: PAGE 27 (2018) Abstr 8624 [www.page-meeting.org/?abstract=8624]
Poster: Methodology - Covariate/Variability Models