Limitations of PKPD Modeling using Surrogate Markers

1. Validation/Evaluation of Surrogate Endpoints: What is the relationship between changes in (surrogate) PK/PD endpoints and clinical acceptable efficacy and/or safety outcomes? The validity of PK/PD modeling depends on both surrogate endpoint validation and PK/PD model validation. Surrogate endpoint validation is a continuous process that should start at the preclinical stage; it requires front-loading of the drug-development process.

2. Incorporation of Long-term Disease Progression and Subpopulations: If the PD endpoint is clinically meaningful (surrogate marker), the effect of disease progression in patients with the disease may have to be incorporated as baseline PD model in the PK/PD model. If possible, the endpoint should be demonstrated to be meaningful across subpopulations of patients.

3. Long-term Changes in PK or PK/PD Relationship (Time-invariance): Typically, the PK model and the population parameter estimates are obtained from single-dose or short repeated-dose studies, which do not reflect the reality of chronic treatment of most chronic diseases. However, the PK may change over time, e.g., due to autoinduction or other secondary drug-induced changes in PK.

Typically, the intrinsic ER relationship (e.g., effect-biophase concentration relationship) is assumed stationary, i.e., invariant with time [10]. This means that at (PK and PD) steady state, there is a constant relationship between effect and plasma concentration. However, there is an increasing number of drugs where this is not necessarily true, and PD tolerance or resistance develops as function of time and dosing regimen, and the "intrinsic" PK/PD relationship changes with time.

4. Empirical vs. Mechanistic PK/PD Modeling: The objective of the PK/ PD modeling exercise determines the use and validation of PK/PD models: Empirical models may be validated for their predictive ability, but do not allow interpretation of their model parameters (if parametric), i.e., the system is considered a "black box". On the other hand, mechanistic models allow estimation of meaningful PK/PD parameters, but the data obtained from typical clinical studies may prevent accurate and precise parameter estimation.

5. PK/PD Model Validation: PK/PD model validation is a clinical pharmacology issue based on statistical concepts. However, internal model validation is only a part of PK/PD model validation: The surrogate PD endpoint used has to be clinically validated (external validation), i.e., has to be linked to clinically acceptable efficacy or safety outcomes (accepted/ approved by the medical specialists). There is growing research activity attempting to link surrogate PD endpoints (typically continuously scaled variables) mathematically to clinically relevant outcomes (typically categorical variables), as shown in clinical trials simulations (e.g., QTc-prolongation and likelihood of TdP).

Any PK/PD model, be it empiric or mechanistic, parametric or nonparametric, can and has to be validated for its intended use: Validation means assessment of descriptive performance (interpolation), predictive performance (extrapolation), and estimation of meaningful PK and PK/PD parameters that can be interpreted. In general, the PK/PD models have to be predictive (within certain constraints of dosing regimens and time) to be useful, but not necessarily mechanistically interpret able.

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