Model waiting-time abandonment via survival

Treat rider abandonment as depending on how long the rider has already waited. Within a survival-analysis framework, define $S(t)$ (the survival function), $h(t)$ (the hazard function), and the main covariates: quoted ETA, surge multiplier, time of day, and location. Explain how to account for right-censoring from completed rides, left-truncation, and time-varying covariates; contrast a Cox proportional-hazards model with a Weibull AFT model, explain the meaning of hazard ratios, and calculate the median additional wait a rider will tolerate at median covariate values. Describe how to diagnose the proportional-hazards assumption and how violations would alter the model specification.

Overview: This question tests skill in survival analysis and time-to-event modeling, including defining survival and hazard functions, dealing with right-censoring and left-truncation, encoding time-varying covariates, and interpreting hazard ratios from Cox PH versus Weibull AFT models.