Date Published: July 17, 2020
Publisher: Springer International Publishing
Author(s): Dan Liu, Linzhong Li, Amin Rostami-Hodjegan, Frederic Y. Bois, Masoud Jamei.
Three global sensitivity analysis (GSA) methods (Morris, Sobol and extended Sobol) are applied to a minimal physiologically based PK (mPBPK) model using three model drugs given orally, namely quinidine, alprazolam, and midazolam. We investigated how correlations among input parameters affect the determination of the key parameters influencing pharmacokinetic (PK) properties of general interest, i.e., the maximal plasma concentration (Cmax) time at which Cmax is reached (Tmax), and area under plasma concentration (AUC). The influential parameters determined by the Morris and Sobol methods (suitable for independent model parameters) were compared to those determined by the extended Sobol method (which considers model parameter correlations). For the three drugs investigated, the Morris method was as informative as the Sobol method. The extended Sobol method identified different sets of influential parameters to Morris and Sobol. These methods overestimated the influence of volume of distribution at steady state (Vss) on AUC24h for quinidine and alprazolam. They also underestimated the effect of volume of liver (Vliver) for all three drugs, the impact of enzyme intrinsic clearance of CYP2C9 and CYP2E1 for quinidine, and that of UGT1A4 abundance for midazolam. Our investigation showed that the interpretation of GSA results is not straightforward. Dismissing existing model parameter correlations, GSA methods such as Morris and Sobol can lead to biased determination of the key parameters for the selected outputs of interest. Decisions regarding parameters’ influence (or otherwise) should be made in light of available knowledge including the model assumptions, GSA method limitations, and inter-correlations between model parameters, particularly in complex models.
Sensitivity analysis, in its broad sense, has been widely used to identify and rank the most influential model parameters affecting the model outputs. Many factors determine the sensitivity of a model’s outputs to its parameters. Those are most notably: the number of input parameters, uncertainty, correlation, and interactions between them, and the non-linearity or non-monotonicity of the model (1). Correlation between two parameters means that the values of one parameter relate in some way to the values of the other, i.e., values of one parameter generally co-occur with certain values of the other. That implies that, for a given value of parameter A (correlated to parameter B) parameter B has a certain distribution, which in turn results in a given distribution of outcome C. If the value of A changes, so does the distributions of B, and the distribution of C. For example, Darwich et al. found that extremely high values of CYP3A intrinsic clearance can never occur simultaneously with high values of Michaelis-Menten constant (Km) of CYP3A and similarly no low values of CYP3A intrinsic clearance happens at the same time as having low Km (2).
Sensitivity analysis can help in narrowing down the number of parameters to be estimated prior to model calibration, avoiding model over-parameterisation, and assisting in model understanding or experimental design. In this study, Morris, Sobol, and extended Sobol methods were used to identify the most influential parameters of mPBPK models of quinidine, alprazolam, and midazolam affecting Cmax, Tmax, and AUC. We investigated the ability of the three methods to identify the contributions of all model parameters and their potential interactions to a set of specified model outputs, contributions coming not only from inter-individual variability but also from parameter correlations and model structure. Of the three drugs selected, (1) quinidine is an antiarrhythmic agent (36); (2) alprazolam one of the most commonly used drugs for short-term management of anxiety disorders with a relativley low clearance (37); (3) midazolam a widely used drug in anaesthesia (38,39) or as a preanesthetic medication (40). Although alprazolam and midazolam are both BCS class I drugs and cleared by the similar enzymes, their pharmacokinetics in the body are different, due to different clearance and volume of distribution (Vss).
We have highlighted some key areas for consideration when applying GSA to identify influential parameters in a model, namely limitations and assumptions of the applied GSA algorithms, assumptions in the investigated physiological or biological model, correlations among model parameters, and distributions or ranges of the parameters of interest. All of these may impact the outcomes, interpretation and application of GSA.