Assessing the Impact of Confounded Time-Averaged Exposure in Logistic Regression Exposure-Response Analyses

Objectives: Exposure-response (ER) analyses are an integral part of model-informed drug development, playing a key role in evaluating the risk-to-benefit ratio for dose selection, justification, and confirmation. In the context of logistic regression analyses with binary endpoints (such as objective response rate for efficacy or treatment-emergent adverse events [TEAEs] for safety), the selection and derivation of the exposure metric are critical. Various metrics are chosen based on physiological plausibility and include: maximum concentration, minimum concentration, area under the curve (AUC) after the first dose or at steady-state (SS), average concentration at SS (Cavg,ss), and average concentration to event (CavgTE). CavgTE incorporates the effects of dose interruptions, modifications, and reductions. However, its derivation demands meticulous attention in a logistic regression framework, especially for time-invariant ER analysis. This study focuses on evaluating different methods to define CavgTE for subjects without events (censored) by the end of treatment (EoT). Additionally, it examines the impact of these methods on the modeled ER relationships.

Methods: Standard ER analysis methods were used to derive exposure metrics using individual empirical Bayes estimates from a developed population PK model. CavgTE was computed as average exposure over time, where time was the time at which the first event occurred. In subjects that did not experience an event, time was censored, and CavgTE was calculated up to the EoT, or follow-up.

To demonstrate the impact of using a specific time for censored subjects, a virtual population (n = 50, 100 and 200) was simulated according to a one-compartment model and AE proportional odds model with Markov components. For subjects without an event, five scenarios were explored to obtain CavgTE: EoT, EoT+7 days, +14 days, +21 days, +28 days of follow up. The result of a logistic regression analysis using either of the five different CavgTE and endpoints were then compared with ER models that used Cavg,ss as the exposure metric. All simulations and logistic regression were performed in R (v4.1.0).

Results: The analysis demonstrated a decrease in the p-value for the slope (exposure) when longer follow-up periods were added to the EoT time in calculating CavgTE for censored patients. This observation suggests that the statistical significance of ER relationships (e.g., using a threshold of p<0.05) may vary depending on the duration selected for deriving CavgTE for censored events. A similar pattern was observed when altering the size of the drug effect and sample size.

Conclusions: The selection of an appropriate exposure metric is crucial in assessing logistic ER relationships, as it significantly affects subsequent event projection, dose selection, and Go/No-Go decisions. The choice of exposure metric, especially for subjects who do not experience an event, needs to be carefully considered to prevent the risk of false positive or negative conclusions. This is particularly important in cases where ER relationships with alternative exposure metrics do not exhibit statistically significant trends.