Mechanistic Multi-Task Logistic Regression: An Alternative to Parametric Hazard Models in Pharmacometric Joint Time-to-Event Analysis
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Background
Parametric time-to-event models require specification of a baseline hazard function, which may influence prediction when the underlying hazard shape is uncertain. This study compared conventional joint longitudinal–time-to-event models with mechanistic Multi-Task Logistic Regression, which directly models the survival distribution without selecting a parametric hazard family.
Methods
Two complementary analyses were conducted. First, a simulated dataset of 100 individuals with longitudinal sum of longest diameters and event outcomes was analyzed using a shared mechanistic tumour shrinkage-regrowth model. Second, the same event-model families were applied to a clinical progression-free survival dataset containing 453 patients and 1,346 longitudinal SLD observations. Event submodels comprised exponential, Gompertz, Weibull, log- normal, log-logistic, and periodic or circadian hazards, mechanistic MTLR, and a hybrid neural- mechanistic extension. The simulated analysis used five-fold cross-validation, dynamic discrimination, Brier scores, integrated Brier score, calibration, and event-interval log score. The clinical case study used joint-estimation diagnostics and model-specific simulation-based longitudinal and PFS visual predictive checks.
Results
In the simulated dataset, longitudinal parameter estimates were comparable across models. The log-normal hazard achieved the lowest overall integrated Brier score (0.1928), whereas mechanistic MTLR achieved the highest later-landmark discrimination (AUC 0.867 versus 0.798 for all hazard models) and the lowest mean event-interval negative log score (2.362). In the clinical dataset, all eight models met numerical convergence criteria. The SLD-event association was positive across all event formulations. The periodic hazard had the lowest AIC among continuous-time hazard models but estimated a period of approximately 58 days, consistent with scheduled progression assessment. Mechanistic and hybrid MTLR showed the strongest descriptive PFS VPC calibration, with 93.4% and 95.9% coverage of the observed Kaplan-Meier curve, respectively. The hybrid nonlinear weight was small and imprecise.
Conclusions
The simulated and clinical analyses jointly support mechanistic MTLR as a practical complementary approach to conventional joint hazard models. Parametric hazards can provide strong probabilistic accuracy when the hazard family is well chosen, whereas mechanistic MTLR avoids continuous baseline hazard-family selection and can provide competitive discrimination and event-time distribution prediction.
