Mechanistic Multi-Task Logistic Regression as an Alternative to Parametric Hazard Models in Joint Time-to-Event Analysis

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 continuous parametric hazard family. Methods: A 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. Results: Longitudinal 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. Conclusions: Mechanistic 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.