Survival Analysis & Time-to-Event Modeling
Churn timing, failures and defaults when half your data is still censored
Model how long something lasts when many of your observations are not finished yet: right, left and interval censoring versus truncation, what a 'churned by day 30' label throws away (a 20,000-user simulation where the naive label under-states 90-day churn by 11 points and an events-only analysis puts the median at 19 days instead of 46), and immortal-time bias (a feature with no effect that looks like a 76 percent hazard cut). Then the core functions (survival, hazard, cumulative hazard, restricted mean), the Kaplan-Meier estimator with Greenwood variance and log-log intervals, Nelson-Aalen and the log-rank test (including crossing curves where it has no power), Cox proportional hazards (partial likelihood, hazard-ratio interpretation, ties, Schoenfeld residual tests, stratification, time-varying covariates and effects), parametric and accelerated-failure-time models (Weibull, log-normal, log-logistic, and extrapolation that goes badly wrong when the family is wrong), competing risks (1-KM overstating cumulative incidence 61 percent versus 46, cause-specific versus Fine-Gray), recurrent events, machine learning for survival (random survival forests, boosted Cox, DeepSurv and DeepHit, and discrete-time survival as classification on person-period data, the practical workhorse), evaluation under censoring (Harrell and Uno concordance, time-dependent AUC, IPCW Brier score and IBS, calibration at a horizon), and applications from expected lifetime and LTV to credit default and readmission. The worked example computes Kaplan-Meier by hand for 10 users, interprets a Cox table fitted on 4,000 simulated subscribers, and converts survival curves into expected lifetime and LTV. Every number comes from code that was run.
Practice questions (6)
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Compute a Kaplan-Meier Curve and Median by Hand for Eight Trial Users
Intermediate · Free -
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Interpret a Cox Table, Then Find Its Leakage and Its Proportional-Hazards Failure
Advanced · Free -
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Design a Discrete-Time Weekly Churn Model on Person-Period Data
Advanced -
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Choose a Model for Loan Default When Prepayment Is a Competing Risk
Advanced -
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Plan the Evaluation of a Censored Time-to-Churn Model Before Launch
Advanced