CLV & Cohort Analysis

Survival Analysis for Tenure Prediction

Use survival analysis to estimate churn-free tenure when some customers are still active. Learn how hazards, censoring, and model choices change your retention insights.

Which method estimates retention while properly handling right-censored customers?

Principal component analysis

ARIMA

K-means clustering

Kaplan–Meier estimator

Kaplan–Meier computes stepwise survival probabilities and accommodates customers still active at cutoff. Alternatives listed are not survival estimators.

In a churn context, the hazard rate at time t represents ______.

average tenure across the cohort

the instantaneous risk of churn at time t given survival until t

the lifetime probability of ever churning

instantaneous revenue per user

Hazard is a conditional rate describing failure risk among those still retained at t. It is not a lifetime probability or an outcome like revenue.

The key assumption of a Cox proportional hazards model is that ______.

there is no censoring in the data

all covariates are time-invariant by definition

covariate effects multiply the hazard and remain proportional over time

survival times are normally distributed

Cox PH assumes proportional hazards, not normal survival times. It handles right-censoring and can include time-varying covariates.

To incorporate monthly activity that changes over time, you should use ______.

simple linear regression on tenure

a Cox model with time-varying covariates or a piecewise approach

naive Bayes on churn labels

Kaplan–Meier with static strata only

Time-varying covariates let effects evolve with time. KM stratification is static, and non-survival classifiers ignore censoring structure.

The median tenure from a survival curve is defined as ______.

the time when the estimated survival falls to 0.5

the mean of uncensored durations only

the mode of the hazard function

the first time hazard equals 0.5

The survival median is the 50% survival time. It is not a mean of observed durations or a property of the hazard peak.

Right-censoring occurs when ______.

event time is known to lie within an interval

a subject has not churned by the end of observation

entry time is unknown (left-censoring)

observations are truncated before entry

Right-censoring marks incomplete events at study end. Left-censoring and interval-censoring describe different partial information settings.

Restricted mean survival time (RMST) is best used to ______.

remove the need for censoring adjustments

summarize expected tenure up to a fixed horizon

test the proportional hazards assumption directly

estimate instantaneous churn risk

RMST integrates survival to a time tau, giving expected time retained within that window. It does not test PH or eliminate censoring challenges.

If churn can happen via distinct, exclusive causes (e.g., voluntary vs. involuntary), an appropriate framework is ______.

standard Cox PH without cause indicators

binary logistic regression only

KM ignoring cause information

a competing risks model (e.g., cause-specific hazards or Fine–Gray)

Competing risks separates causes to avoid biased incidence estimates. Ignoring causes conflates event types and can mislead planning.

Accelerated failure time (AFT) models are typically interpreted via ______.

time ratios describing multiplicative effects on survival time

odds ratios of churn at any time

differences in mean tenure only

p-values of Schoenfeld residuals

AFT coefficients scale time to event, often on a log-time scale. They are not odds ratios and are distinct from PH diagnostics.

Schoenfeld residual checks are commonly used to ______.

decide between right- and left-censoring

estimate the baseline hazard function

assess violations of the proportional hazards assumption

compute RMST directly

Schoenfeld residuals help diagnose time-varying effects that break PH. They do not estimate baselines or censoring types.

Starter

You know the basics of retention curves and censoring.

Solid

Good grasp of hazards and when to use different survival models.

Expert!

You can choose, diagnose, and explain survival models to stakeholders.

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