Confounding Impact of Event-Driven Exposure Phenomenon on Summary Exposure Metrics in Time-to-Event Exposure Response Analyses
Authors: Johnson Jordon , Chaturvedula Ayyappa , Agoram Balaji 
Published: February 2025

Objectives: An important consideration of exposure-response (ER) modeling is the selection of an exposure metric. Time varying exposure metrics are regarded as superior compared to static first dose exposure metrics or a time-aggregated approach. The analysis objective was to evaluate the performance of various exposure metrics in a time-to-event (TTE) ER analysis. Methods: Simulation, graphical, and model evaluations were conducted using NONMEM (v7.5) and R (v4.2.3). Exposures for an oral drug with a long half-life (~16 days) dosed every 3 weeks were simulated for 2000 subjects with 30% between subject variability on clearance. Four exposure metrics - average exposure until the event (Cavg,TE), time varying average exposure (Cavg,TV), time varying period corrected average exposure (Cavg,TV-PC), and average exposure over the first dose cycle (Cavg,C1) - were calculated. A TTE model with Weibull hazard was used to simulate a distribution of event times [overall or progression-free survival (OS or PFS)].Four event scenarios were simulated: 1. majority of OS occurred within the first dose cycle (short TTE) without causal dependence (CD) on exposure,2. majority of OS occurred after the first dose cycle (long TTE) without CD on exposure,3. PFS correlated (R2=0.5) with an OS endpoint without CD on exposure, where dosing ended at PFS,4. OS with direct CD on exposure where 50% of subjects had single or multiple dose reductions and 12.5% discontinued the drug. The true TTE model with and without exposure metric was fit to the simulated datasets. Significant exposure metrics were evaluated using objective function values (OFV) at α=0.001. Exposure metric performance was judged by whether the true ER relationship was detected in the estimation process.Results: Short TTE distributions without CD on exposure resulted in spurious ER relationships using Cavg,TE and Cavg,TV, but Cavg,C1 and Cavg,TV-PC correctly concluded the lack of ER relationship. For long TTE distributions without CD on exposure none of the exposure metrics detected a spurious ER relationship, however, Cavg,TE was nearly significant indicating a few events can skew the OFV. The scenario where PFS was correlated to OS, Cavg,TE, Cavg,TV, and CavgTV-PC resulted in a spurious ER relationship, but Cavg,C1 concluded the truth. Lastly, the scenario of a TTE distribution with a direct CD on exposure with multiple dose reductions, Cavg,C1 failed to detect the truth, however, Cavg,TV-PC detected the true ER relationship.Conclusions: Selection of an exposure metric for a TTE ER analysis should be based on the endpoint distribution and potential confounding between dosing and events. The widely accepted Cavg,TV can provide spurious ER relationships when the majority of events occur within the first dose cycle or when endpoint correlated events determine the length of dosing. Cavg,C1 and Cavg,TV-PC both performed well in specific use cases, with Cavg,C1 being resilient to spurious ER relationships. Citations: [1] Wiens MR, French JL, Rogers JA. Confounded exposure metrics. CPT Pharmacom & Syst Pharma. 2024;13(2):187-191.