Background
A key element of pharmacometrics analyses is explaining part of the observed population variability via individual level covariates effects on the PK or PK/PD model parameters. When the resulting effects of covariates on exposures are important, and when supported by the specific E-R relationships, a dose alteration might be warranted. Ultimately this might lead to a drug label where an approved dose can depend on a specific value/range of one or multiple covariates. Earlier in the drug development program, covariate effects can be utilized for clinical study planning in various demographic subgroups, dose selection, and dose individualization. The Food and Drug Administration (FDA) population PK guidance for industry details the various cases where a covariate analysis can be used to establish dosing recommendation whether stand-alone specific subpopulation studies are available or not. Despite the availability of recent tutorials on software and workflows on how to apply the FDA proposal on constructing, illustrating, and reporting covariate analyses, there is still confusion in the community on what level of variability to include and a tendency to 1) only use the posthocs empirical Bayesian estimates (EBE) from the current population rather than conducting simulation and 2) avoid using “marginal” effects i.e. illustrating the effect of one covariate at a time holding the other at reference and favor using a distribution of correlated covariates and 3) avoid using uncertainty since it can be time consuming and not easy to implement.
Methods
In this work, we develop a step-by-step workflow comparing the use of EBE (what happened in the clinical trials) versus simulating from the estimated between subject variability (BSV) (what will happen in future trials and patients). In a second step we remove the between subject variability and include the uncertainty of the parameter estimates combined with correlated covariate distributions to adequately quantify the uncertainty of our predictions and the joint effects of covariates on exposures. The R packages mrgsolve and foreach are used for simulations and coveffectsplot for visualization and communication.
The population pk simulation was done using Phoenix NLME, using a one compartment model (CL= 2, V = 10) with first order absorption (Ka =0.2) and between subject variability on CL and V, with an omega of 0.09, 0.1, 0.16.
The data had 50 subjects, a multiple oral dosing regimen of 100 mg QD for 6 days and PK sampling at predose, 0.5,1,2,3,4,6,8,10,12,18,24,48,72,96,120,120.5,121,122,123,124,126,128,122 and 148 hours. The model included simulated continuous covariates: Weight = normal with mean of 70 range (40-88 Kg) and eGFR = unif between 18-120 with EM probability of 30 % and Patients probability of 50 %. Covariate effects were included on the equation of CL and V as per the following equations: Cl= tvCl *((Weight/70)^0.75)*((eGFR/90)^1 * exp(0.693*(EM==1)) * exp(-0.223*(PAT==1)) / V = tvV *((Weight/70)^1)* exp(1.2*(PAT==1)).
The simulation model was fitted on the generated data and uncertainty generated using a 500 bootstrap sample. We follow the vignettes of the the coveffectsplot package and toease the clinical interpretation in each subpopulation cut we use one of the categories as the reference rather than all patients for example when we split weight into tertiles (T1, T2, T3) we use the middle category T2 as reference to compute the ratio of T1/T2 and T3/T2.
Results
The fitted model could estimate the parameter used in the simulation with acceptable bias and precision < 10% except for the effect of EM on Clerance > 50 % due to the small sample size.
The R workflow was validated by comparing phoenix NLME PRED and IPRED to the ones generated with mrgsolve.
We show that if the goal is to illustrate the range of possible individual exposure in the future simulation with covariates and OMEGA should be used while the most common use case of illustrating covariate effects should not include BSV (no EBE, no OMEGA).
Conclusion
To evaluate the performance of new dosing regimens for inclusion in drug label, simulation based on fixed-effect estimates with uncertainty are recommended (univariate “marginal” and multivariate “joint”). To illustrate the range of individual ranges of pk parameters in the studied population, simulation with OMEGA is preferred over EBE and if we want to extrapolated into future populations uncertainty should be incorporated.
References
- FDA Population Pharmacokinetics Guidance for Industry, 2022
- Hu C. Variability and uncertainty: interpretation and usage of pharmacometric simulations and intervals. J Pharmacokinet Pharmacodyn. 2022 Oct;49(5):487-491. doi: 10.1007/s10928-022-09817-9. Epub 2022 Aug 4. PMID: 35927373.
- Marier JF, Teuscher N, Mouksassi MS. Evaluation of covariate effects using forest plots and introduction to the coveffectsplot R package. CPT Pharmacometrics Syst Pharmacol. 2022 Oct;11(10):1283-1293. doi: 10.1002/psp4.12829. Epub 2022 Jun 27. PMID: 35670230; PMCID: PMC9574733.
