Mechanistic Multi-Task Logistic Regression: An Alternative to Parametric Hazard Models in Pharmacometric Joint Time-to-Event Analysis

BackgroundParametric 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 continuous parametric hazard family. MethodsA simulated dataset of 100 individuals with longitudinal sum of longest diameters and event outcomes was analyzed using a shared mechanistic tumor shrinkage-regrowth model. Event submodels comprised exponential, Gompertz, Weibull, log-normal, log-logistic, and circadian hazards, mechanistic Multi-Task Logistic Regression, and a hybrid neural- mechanistic extension. All models were estimated jointly using shared patient-specific random effects and longitudinal data. Models were evaluated using longitudinal goodness-of-fit, visual predictive checks, five-fold cross-validated inverse-probability-of-censoring-weighted dynamic area under the curve and Brier scores, integrated Brier score, calibration, and event-interval negative log score. ResultsLongitudinal parameter estimates and diagnostics were comparable across models. All conventional hazard models produced identical dynamic area under the curve values within prediction windows, although probabilistic accuracy differed. The log-normal hazard achieved the lowest overall integrated Brier score (0.1928). Mechanistic Multi-Task Logistic Regression achieved the highest later-landmark discrimination (area under the curve 0.867 versus 0.798 for all hazard models) and the lowest mean event-interval negative log score (2.362). The hybrid model improved intermediate-landmark discrimination but not overall probabilistic accuracy. ConclusionsMechanistic Multi-Task Logistic Regression provided competitive joint time-to-event prediction while avoiding baseline hazard-family selection. It represents a practical complementary alternative to parametric hazard modeling, particularly when hazard shape is uncertain and dynamic discrimination is important.