Peng Man 1, Han Liu 1, Lena E. Friberg 1, Martin Bergstrand 2
1 Uppsala Universtiy (Uppsala, Sweden), 2 Pharmetheus (Uppsala, Sweden)
Background
Pharmacometric time-to-event (TTE) analysis commonly applies parametric survival models and often assumes a homogeneous population hazard after covariate effects are accounted for, meaning that individuals with identical covariate values share the same hazard function. However, baseline hazard heterogeneity stemming from unknown sources of inter-individual variability (IIV) can induce an apparent time dependence at the population level. In single-event TTE models, random effects are rarely included to capture this latent hazard heterogeneity, largely due to concerns regarding limited parameter identifiability and η-shrinkage when only one observation is available per individual [1].
Objectives
This study aimed to demonstrate how unobserved baseline hazard heterogeneity can induce apparent time dependence mimicking a Weibull distribution, and to evaluate the ability of different modeling approaches to account for this heterogeneity while its source was assumed unknown. The impact of these modeling approaches on the identification of true covariate effects was also assessed.
Methods
Single-event TTE data were simulated using exponential or Weibull baseline hazard models. Hazard heterogeneity was introduced via IIV on the baseline hazard or through covariate effects (e.g., age, sex) sampled from the 2017-2020 NHANES database [2]. Each scenario comprised 200 replicated datasets with 200 individuals followed weekly for one year. Two modeling strategies were compared: a conventional Weibull modeling approach and an exponential modeling approach incorporating a log-normally distributed random effect on the baseline hazard (exponential + IIV). Model performance was evaluated based on the ability to identify an adequate model (true or exchangeable model), and the ability to identify true covariate effects.
Results
In simulations of constant hazard models with baseline heterogeneity, averaging the individual hazards of event-free subjects over time resulted in an apparent time-dependent decline at the population level, closely mimicking a Weibull-like time dependence. When the source of heterogeneity was assumed unknown, the Weibull model attributed this apparent time dependence to genuine time dependence in 55.5% to 98.5% of simulation runs. In contrast, the exponential + IIV model successfully captured the unobserved heterogeneity in 95.5% to 100% of runs, outperforming the pure exponential model and fully accommodating the apparent time-dependent reduction. When no hazard heterogeneity existed, erroneous inclusion of IIV was uncommon (2.5% of runs), compared with a higher tendency to include the Weibull shape parameter (10%) in the same setting. Both approaches showed a comparable ability to identify true covariate effects, but the exponential + IIV approach exhibited fewer false inclusions and demonstrated that the magnitude of IIV for baseline hazard remained identifiable despite the sparsity of single-event data.
Conclusion
Apparent time dependence in TTE data can arise naturally from unaccounted-for baseline hazard heterogeneity due to unobserved or omitted covariates. Incorporating random effects into exponential models provides an effective, conceptually aligned framework for capturing latent hazard heterogeneity while avoiding misinterpretation of population-level patterns as homogeneous time dependence. The exponential model with IIV maintains low false-inclusion rates and serves as a practical starting point for single-event TTE analyses, particularly when a decreasing marginal hazard plausibly reflects unmeasured risk factors rather than a true time-varying individual hazard.
References:
[1] Savic RM, Karlsson MO. Importance of Shrinkage in Empirical Bayes Estimates for Diagnostics: Problems and Solutions. AAPS J. 2009 Sept;11(3):558–69.
[2] National Health and Nutrition Examination Survey, Questionnaires, Datasets, and Related Documentation, 2017-March 2020 Pre-Pandemic Data. Centers for Disease Control and Prevention.
Reference: PAGE 34 (2026) Abstr 12111 [www.page-meeting.org/?abstract=12111]
Poster: Methodology - New Modelling Approaches