By Matthew M. Hutmacher
Some of the most clinically meaningful and interpretable endpoints analyzed during drug development are based on the timing of an event. Notable examples are time until stroke or myocardial infarction, time until organ rejection, and overall survival (time to death) and progression free survival in oncology. Such data are not relegated to efficacy only. Adverse events such as time until bleeding, infection, edema, or even treatment discontinuation are often of critical interest to help define the therapeutic range.
One typical role for pharmacometricians is to quantify the exposure-response relationship for investigational therapies to help support dose recommendations and to identify subpopulations that could benefit potentially from different dosage regimens. Exposure such as dose (not a factor variable), or subject-specific measures such as average, trough, or maximum concentration can be linked to these time-to-event (TTE) data to identify patient factors and make predictions. Use of exposure as a predictor is even more important during latter stages of development, when the number of dose strengths studied is reduced, yet support of the dose level is required. In such trials, exposure can change over time, which induces some complexity.
It may be difficult to envision at the outset how to link exposure to TTE data. Such data are less biological and more statistical than those with which pharmacometricians work routinely. The data are not like results of a specific biomarker that is directly tied to the drug’s mechanism of action, such that pharmacokinetic and pharmacodynamic principles can be applied directly. For TTE data, how to link exposure with response is not as clear. Disease, drug effects, and patient risk factors influence when or whether the endpoint being studied occurs. As such, the pharmacometrician might consider linking exposure to the risk of having an event, but the model form for risk is more open-ended. Other statistical issues complicate TTE analyses as well. Subject withdrawal or study completion precludes observation of the event. Sometimes an event is only known to occur between two clinic visits. These have ramifications for the model.
Several methodologies exist in the literature for handling TTE data. Should the pharmacometrician ignore the baseline hazard and apply a Cox proportional hazards model and focus on relative risk? The form of the model is standard, and standard software and plotting routines make this attractive. What about absolute risk and the understanding of the baseline hazard, such as through parametric survival analysis? Is such a pursuit necessary to support dose recommendations?. The drug maybe known to have a delayed onset of effect (i.e., hysteresis); how would one accommodate such pharmacodynamic features? How does one assess model adequacy? There is not much guidance currently in the literature on such issues.
The AAPS webinar Time-to-Event Analysis for the Pharmacometrician: A Focus on Evaluation of the Hazard Function will provide an introductory look at applied methods and perspectives on many of the questions that pharmacometricians might have and issues they may face when undertaking such an endeavor. Register today!