Frame the problem as a time-to-event analysis where the event is rider cancellation and the time scale is wait time. Define S(t) and h(t), discuss right-censoring for rides that get matched, and propose a Cox proportional hazards model with time-varying covariates to capture how abandonment risk evolves with wait duration.
Pro tip: Emphasize that the baseline hazard itself is the key product insight—it shows how abandonment risk changes with wait time—and mention that you'd validate the proportional hazards assumption and consider time-varying effects if it fails.
Clarify that the event is rider cancellation and the time scale is the waiting time from request to cancellation or match. Explain that S(t) is the probability of still waiting at time t, and h(t) is the instantaneous cancellation rate given the rider has waited until t.
Discuss right-censoring: riders who get matched before cancelling are censored at their match time. Mention that censoring is likely non-informative but could be informative if, e.g., high-demand periods cause both longer waits and more matches.
List covariates that affect abandonment: rider history (past cancellations, loyalty), trip characteristics (distance, fare), real-time context (surge multiplier, ETA, time of day, weather), and supply-demand metrics (number of available drivers nearby).
Propose a Cox proportional hazards model with time-varying covariates (e.g., updated ETA) to estimate covariate effects while leaving the baseline hazard flexible. Alternatively, suggest a parametric model (e.g., Weibull) if a specific shape is expected, or a machine learning approach like random survival forests for prediction.
Mention checking the proportional hazards assumption (e.g., Schoenfeld residuals) and, if violated, using time-varying coefficients or stratified models. Interpret the baseline hazard to understand how abandonment risk changes with wait time and use the model to simulate interventions.
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Scaled Schoenfeld residuals plotted against time, plus log-log survival curves.
Start by explaining the importance of the proportional hazards (PH) assumption in Cox models, then describe both graphical and statistical methods to check it. Finally, discuss remedies if the assumption is violated, emphasizing practical trade-offs and business impact.
Pro tip: Mention that at scale, like at Uber, you often need to balance model complexity with interpretability, and sometimes stratified models or time-varying coefficients are preferred over abandoning the Cox framework entirely.
Briefly define that the hazard ratio between any two individuals is constant over time. Highlight that this is a key assumption of the Cox proportional hazards model.
Discuss log-minus-log survival plots and Schoenfeld residual plots. Explain how to interpret them: parallel curves for log-minus-log, and random scatter around zero for Schoenfeld residuals.
Mention the Schoenfeld residual test (e.g., correlation between residuals and time) and the global test. Note that these tests can be sensitive with large datasets.
List options: stratify by the violating variable, include time-varying coefficients, use accelerated failure time models, or switch to a different model like random survival forests.
Tie the choice of remedy to the business problem: interpretability, prediction accuracy, and computational constraints. Emphasize that the solution should align with stakeholder needs.
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Counting process formulation, splitting each rider's timeline into intervals where the covariate is constant.
Start by clarifying the survival model's structure and the nature of the time-varying covariate (quoted ETA). Then discuss appropriate methods like extended Cox models or joint modeling, and emphasize the importance of avoiding look-ahead bias and ensuring temporal validity.
Pro tip: Mention that you would validate the model using time-dependent AUC or concordance, and consider the practical implication: if ETA updates frequently, you might need to discretize time or use a landmark approach to keep the model tractable.
Confirm that the quoted ETA is updated at irregular intervals and that the event of interest (e.g., rider cancellation) can occur at any time. Identify whether the covariate is endogenous (affected by the event) or exogenous.
For exogenous time-varying covariates, use an extended Cox model with time-dependent covariates. For endogenous covariates, consider joint modeling of the longitudinal ETA process and the survival outcome.
Convert the data into a counting process format (start, stop, event) where each row represents an interval with a constant covariate value. Ensure that the risk set at each event time includes only subjects still at risk and with the correct covariate values.
Avoid look-ahead bias by only using covariate values available up to time t. Validate the model using time-dependent metrics like time-dependent AUC or Brier score, and check proportional hazards assumption for time-varying effects.
Discuss computational complexity and whether to discretize time or use a landmark analysis. Weigh the benefits of joint modeling against its complexity and interpretability for business insights.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.