Survival Analysis

Modelling time until an event: churn, failure, conversion.

Also known as: survival analysis, time-to-event analysis, churn modelling

Survival analysis models time until something happens: how long customers stay, when machines fail, how quickly leads convert. Its defining problem is censoring — most subjects have not had the event yet when you look. A customer active today is not “retained forever”; they are retained so far, and throwing them out (or counting them as successes) biases everything.

customer A: churned month 3  (event observed)
customer B: active month 9   (censored: survived ≥ 9 months, future unknown)
wrong: drop B, or call B "retained" → both bias the curve

The survival curve — share surviving past each time — handles censoring honestly and reads directly: median lifetime, 12-month retention, the shape of risk over time. Comparing curves between cohorts or arms (with proper tests, not eyeballing) is the core churn/retention analysis.

The classic mistakes:

Dropping censored observations. Keeping only completed lifetimes selects for short ones — the dead tell you everyone dies young. This is survivorship bias wearing a lab coat.
Calling active users “retained”. Retention at month 12 can only be computed over users old enough to be 12 months in. Recent cohorts contribute only to early months — align by tenure (cohort analysis), never by calendar date.
Ignoring competing events. Users who are deleted for fraud did not “churn normally”; machines retired early did not “fail”. Lumping competing outcomes distorts the curve for the event you care about.
Proportional-hazards autopilot. The standard regression assumes each factor multiplies risk constantly over time. A feature whose effect fades (onboarding emails matter in week 1, not month 6) violates it — check, do not assume.
Reading causation off curves. The enterprise curve outlives self-serve — because of the segment or the sales process? Curves describe; causal inference explains.

When to use it: any duration question with incomplete follow-up — retention, tenure, lifetime value horizons, failure times. If every subject’s outcome is already known, ordinary regression suffices; survival machinery exists for the censored middle where most real data lives.