Scientific Director Pharmetheus AB Uppsala, United States
Disclosure(s):
E. Niclas Jonsson, PhD: No financial relationships to disclose
Objectives: Pharmacometric models use covariates to explain variability, provide mechanistic insight, inform dosing recommendations and to increase its relevance across different patient populations. Typically, the estimated covariate coefficients are used for the communication of covariate effect sizes. If only one covariate is included on a parameter, its coefficient represents an unconditional effect. Conversely, inclusion of correlated covariates on the same parameter will make the coefficients conditional on the other covariates and can differ substantially from the unconditional coefficients. The aims of this study are to investigate the consequences of misinterpreting conditional coefficients as unconditional for the understanding and communication of covariate effect sizes, and to investigate if unconditional covariate effects can be used instead of the full model for regulatory and clinical decision making.
Methods: The influence of correlated covariates on the estimated coefficients on pharmacokinetic parameters was investigated theoretically using standard principles from linear and nonlinear regression[1]. The theoretical findings were verified using simulation and re-estimations in NONMEM. Simulations were also used to compare exposure predictions for dose selection based on conditional, unconditional and full covariate models. Finally, the use of conditional and unconditional covariate coefficients were compared to the full model for the selection of individual doses from a finite set of available dose levels, in a model informed precision dosing setup.
Results: The theoretical investigations, confirmed by NONMEM simulations, show that the conditional coefficients are sensitive to the inclusion of correlated covariates. The impact depends on the relative size of the coefficients and standard deviations (SDs) of the covariates. In the case of coefficients with the same size and sign and equal covariate SDs, correlations of -0.5, -0.3, 0.3 and 0.5 led to conditional coefficients that were 2.0, 1.4, 0.8 and 0.7 times the corresponding coefficient, respectively. In an exponential model, in which the unconditional effect of weight on clearance was 10% between 60-100 kg, the conditional impact of weight were 21%, 15%, 7.6% and 6.6% for the same correlations, respectively.
The conditional model's exposure predictions were sensitive to covariate correlations, unlike the unconditional model, which was insensitive and similar to the full model. The unconditional model had minor bias compared to the full model, while the conditional model's bias varied with the correlation.
Conclusions: Unconditional covariate effects are easier to communicate than conditional effects from a multivariable model, are sufficient for common decisions and are likely what the audience implicitly assumes is communicated. Using conditional covariate coefficients incorrectly can lead to misunderstandings and potentially incorrect decisions. Modelers should understand the difference between conditional and unconditional estimates and consider reporting both.
Citations: [1] Wooldridge, Jeffrey M. 2012. “Introductory Econometrics: A Modern Approach.”
