Potential Bias Evaluation of Conventional Exposure-Response Analysis Methods: A Small Molecule Cancer Drug Example
Authors: Yin Xuefen , Xiong Ye , Bi Youwei , Zhao Hong , Fletcher Elimika , Madabushi Rajanikanth , Zhu Hao , Schmidt Stephan , Liu Jiang 
Published: February 2025

Objectives: Conventional Exposure Response (ER) analyses may generate bias relationships when evaluating a single dose level, particularly for cancer drugs where response is an event and dose modifications are common. This study aims to investigate potential bias in such analyses, and their relationships with drug pharmacokinetic (PK) properties, dose modification patterns, and event onset timing. Subsequently, we sought to propose solutions that enable robust ER evaluations for dose optimization. Methods: Our study utilized a simulation-based approach to assess various ER scenarios: 1) no-relationship, where drug exposure does not affect response; 2) positive-relationship, where exposure increases event likelihood; 3) inverse-relationship, where exposure reduces event likelihood. PK datasets were generated using a two-compartment model, designed to accommodate both constant and variable dosing history. The initial PK parameters, sourced from actual data, were adjusted to reflect different PK characteristics exhibiting different time to steady state and accumulation ratios. For the no ER relationship scenario, we generate a time-to-event (TTE) dataset, with 75% events from a Weibull distribution and 25% censored observations randomly selected from the follow-up period. This TTE data was joined with sampled subjects from the PK dataset, where the end time point for each individual was set to either censoring/event time or the last dosing time, whichever occurred first. ER relationships were assessed using Kaplan-Meier plots, Cox proportional-hazards models, and logistic regression. In scenario 1, a false ER relationship was indicated if statistical significance was observed in at least 10% of the 1000 replicated simulations. Results: Results for scenario 1 are presented here. For the dosing scenario of “no dose modification”, a false negative ER slope is likely to be observed using average concentration till event/censor (CavgTE). The biased relationship becomes more evident if the event onset is early relative to the PK accumulation. In contrast, with significant dose modification, using CavgTE will result in a false positive ER slope. The ER analysis using exposure metrics from the first dosing cycle avoids bias, as they are unaffected by subsequent accumulation or dose modification. In cases of later event onset, ER analysis based on logistic regression tends to be less impacted than that based on TTE analysis. Conclusions: Our study revealed potential bias in conventional ER analysis in some scenarios for cancer drugs where the response is an event. This bias could lead to misinterpretation of causal relationships and subsequently incorrect dose selection. A thorough evaluation of exposure metrics and their temporal relationship to the event can uncover bias sources and guide the analysis choice. In cases of high uncertainty, causal effects inferred from ER analysis should be validated through a randomized trial studying multiple dose levels.Citations: N/A