Considerations when deriving time-averaged exposure for censored subjects for logistic regression exposure-response analyses
Anna Largajolli (1)*, Yu-Wei Lin (2)*, A. Yin Edwards (1), S. Y. Amy Cheung (1), Kashyap Patel (2)+, Stefanie Hennig (2)+
1 Certara Inc., Princeton, New Jersey, USA ; 2 Certara Inc., Melbourne, Australia.
Objectives: 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 (e.g. objective response rate for efficacy or treatment-emergent adverse events [AEs] for safety), the choice and derivation of exposure metric is crucial as it could influence key ER modeling decisions. Typically, several exposure metrics are investigated, based also on physiological plausibility, including maximum concentration, minimum concentration, AUC after the first dose or steady-state (SS), average concentration at SS (Cavg,ss) and average concentration to event (CavgTE). CavgTE is more frequently requested by regulatory reviewers, as it accounts for dose interruptions, modifications, and reductions. However, its derivation requires careful consideration in a logistic regression framework for time-invariant ER analysis. This study evaluated different approaches to define CavgTE for subjects without events (censored) by the end of treatment (EoT) and their impact 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 using the actual observed dosing history, 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, two examples were used for illustration. Firstly, based on a real dataset example with an established ER relationship, a virtual population (n>100) with various study designs was simulated according to a one-compartment model and AE proportional odds model with Markov components. The simulated dataset was based on examples of real data for several endpoints in which the distribution of event times was different. 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. Furthermore, the impact of varying drug half-life was also investigated for each of the five different CavgTE scenarios on logistic ER models. Secondly, to ensure replication of the above motivating example, 100 sets of virtual population (n= 100 subjects) were simulated using a simple one-compartment with transit absorption PK model to derive individual exposures. The events were generated using a ‘known’ linear logistic regression model based on CavgTE as the predictor with varying strengths of ER relationships (weak, moderate, or strong), which varied the number of events per dataset. Further, either a weekly or every other day dosing regimen was used. The simulated data was then used to quantify ER where varying EoT (as above) were used for censored subjects. All simulations and logistic regression were performed in R
Results: For the motivational real dataset example, it was found that the tested ER relationships presented a lower p-value on slope (exposure), with increasing follow-up times added to the EoT time when calculating CavgTE for censored patients. In contrast, the relationship between Cavg,ss and response endpoint was less defined and not significant.
For the simulated data example, two contrasting trends were found depending on study design (ie, dosing frequency, accumulation). When dosing was less frequent, tested ER relationships presented a lower p-value with increasing follow-up times added to the EoT time. In contrast, when dosing was more frequent, a higher p-value was observed with increasing follow-up times added to the EoT time. The same relationships were seen when varying the drug effect size.
Conclusions: The choice of exposure metric can have significant impact on the evaluation of logistic ER relationships that influence subsequent event projection, dose selection and Go/No-Go decisions. Therefore, CavgTE for subjects without an event must be carefully derived to avoid potentially making a false positive or negative conclusion and particular care should be taken when ER relationships with other exposure metrics don’t show statistically significant trends.
* joined first author, + joined senior author