Model waiting-time abandonment via survival
Overview
This question evaluates proficiency in survival analysis and time-to-event modeling, including defining survival and hazard functions, handling right-censoring and left-truncation, encoding time-varying covariates, and interpreting hazard ratios from Cox PH versus Weibull AFT models.
Uber
Oct 13, 2025, 9:49 PM
Data Scientist
Onsite
Statistics & Math
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Survival Modeling of Rider Abandonment During Pickup Waits
Context
You are modeling when a rider cancels (abandons) while waiting for pickup. Let time origin t = 0 be the ride request time. The event of interest is rider cancellation before pickup. If the rider is picked up before canceling, the observation is right-censored at pickup time.
Assume you have covariates including quoted ETA, surge multiplier, time-of-day, and location. Some covariates (e.g., quoted ETA, surge) may change over time.
Tasks
- Define survival S(t) and hazard h(t) in this setting and relate them.
- List key covariates and how to encode them (quoted ETA, surge multiplier, time-of-day, location).
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Explain how to handle:
- Right-censoring (completed rides/pickups)
- Left-truncation (delayed entry, e.g., analysis begins at driver assignment)
- Time-varying covariates
- Specify and compare a Cox proportional-hazards (PH) model vs. a Weibull accelerated failure time (AFT) model. Interpret hazard ratios for the covariates.
- Compute the median additional wait a rider will tolerate under median covariates, for both models.
- Describe diagnostics for PH assumptions and how violations would change your specification.
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