Impact of using time-averaged exposure metrics on binary endpoints in exposure-response analyses

Exposure-response (ER) analyses are routinely performed as part of model-informed drug development to evaluate the risk-to-benefit ratio for dose selection, justification, and confirmation. For logistic regression analyses with binary endpoints, several exposure metrics are investigated, based on pharmacological plausibility, including time-averaged concentration to event (C_avTE). C_avTE is informative because it accounts for dose interruptions, modifications, and reductions and is therefore often compared against ER relationships identified using steady-state exposures. However, its derivation requires consideration in a logistic regression framework for time-invariant ER analysis because it has the potential to introduce bias. This study evaluated different approaches to derive C_avTE for subjects whom did not have an event by the end of treatment (EoT) and assessed their impact on the ER relationship. Here we used a modified model based on a real data example for simulating exposures and events (safety) in different virtual population sizes (n = 50, 100, or 200) and drug effect magnitudes (0.5, 0.75, or 1). Events were generated using a proportional odds model with Markov components. For subjects whom did not experience an event, C_avTE was derived at EoT, EoT+7 days, +14 days, +21 days, +28 days. The derivation of C_avTE at different time points demonstrated significant impact on trends detected in logistic ER relationships that could bias subsequent event projection, dose selection and Go/No-Go decisions. C_avTE in censored subjects must therefore be carefully derived to avoid potentially making false positive or negative conclusions. Overall, C_avTE can be a useful exposure metrics in an ER analysis, when considered along with physiological or biological plausibility, the drug's pharmacokinetic, and mechanism of action. Biological plausibility and different analysis factors (e.g., the time of the events with respect to observational period, the level of dose reduction/interruption) should be considered in the choice of the exposure metric. It is recognized that although time-invariant logistic regression is relatively fast and efficient, it overlooks recurring events and does not take into account the exposure and response time course with the potential drawback of ignoring important elements of the analysis like onset or duration of the effect. Care should be taken when ER relationships with other exposure metrics do not identify any statistically significant trends.