Henry Hu; Ferdous Gheyas
Merck & Co., Inc., Rahway, NJ, USA
Introduction: Exposure-response (E-R) modeling plays an important role in model-informed drug development, especially in dose selection. A key step in E-R modeling is the selection of the exposure metric. If the PK driver (e.g. Cavg, Ctrough, Cmax) of a given response is known based on the mechanism of action of the drug or other existing information, this PK driver can be used as the exposure metric. However, in many instances, the PK driver is not known a priori. In such cases, E-R models are developed using all plausible exposure metrics, and the best exposure metric is chosen based on model performance including goodness-of-fit diagnostics. However, the operating characteristics of this approach have not been systematically assessed.
Objectives:
The goal of this methodological research is to evaluate
- how various factors impact the choice of exposure metric in E-R modeling
- how the choice of the exposure metric impacts the operating characteristics of E-R models including
- accuracy and precision of parameter estimates, and
- conclusions based on E-R modeling, especially dose selection
Methods:
Monte Carlo simulations were conducted to assess how the operating characteristics of E-R models are impacted by (1) inter-individual variability (IIV) in PK parameters, (2) correlation among exposure metrics, (3) shape of the E-R curve (e.g. the Hill coefficient of the sigmoid Emax model), and (4) random variability in response values.
For each scenario, rich PK profiles were generated for 300 subjects for a series of doses using a two-compartment model; Cavg, Ctrough, and Cmax were calculated for each subject. Response values were generated based on a “true” sigmoid Emax model with a “true” exposure metric. For each simulated dataset, E-R models were fitted using all 3 exposure metrics. Using each of these models, optimal dose was derived as the lowest dose that achieves 90% of the Emax. Additionally, the model with the lowest Akaike Information Criterion (AIC) was identified. This process was repeated 1000 times.
Simulation summaries included (1) sensitivity/specificity associated with the selection of the exposure metric, (2) root mean squared error (RMSE) of E-R model parameters, and (3) the probability of choosing the correct dose.
Results:
In general, IIV in PK parameters had a significant impact on the correlation among exposure metrics. For example, when IIVs in CL and Ka were high (>50%), correlation between Cavg and Cmax was lower compared to the scenario when IIVs in CL and Ka were low (<20%).
The impact of the choice of the exposure metric on the performance of the E-R model varied depending on the random variability in response and the shape of the E-R curve. Overall, as the random variability in response increased, the model performance was worse. Furthermore, when Hill coefficient was high (e.g. 5), the probability of selecting both the correct exposure metric and the correct dose was high. Additionally, E-R model parameters were estimated with high accuracy and precision (low RMSE). On the other hand, when the Hill coefficient was low (e.g. 0.5), the probability of choosing the right dose was low regardless of the exposure metric used. The selection of correct exposure metric was critical for dose selection when the Hill coefficient was close to 1. In this case, when correlation among exposure metrics was low, the AIC-based selection approach achieved high sensitivity and specificity in identifying the “true” exposure metric. In the small proportion of cases when the wrong metric was chosen, the probability of identifying the correct dose was low. When the correlation was high (e.g. correlation coefficient > 0.95), the AIC-based exposure metric selection method could not differentiate among the exposure metrics with sufficient sensitivity and specificity, but because of the strong correlation, the final dose selection was not affected even if a wrong metric was chosen.
Conclusions:
Choice of the exposure metric and the performance of the E-R model depend on the correlation among exposure metrics, shape of the E-R curve, and the random variability in PK and response. For a sigmoid Emax model, the choice of exposure metric was particularly critical when the Hill coefficient was close to 1.
If the correlation coefficients among plausible exposure metrics are >0.95, any of those metrics can be used. Otherwise, exposure metric can be selected based on AIC; this approach has robust operating characteristics.
Reference: PAGE 32 (2024) Abstr 11091 [www.page-meeting.org/?abstract=11091]
Poster: Methodology - Other topics