Project 1 Q2: Survival Analysis for Telco Customer Churn

This post summarizes the survival-analysis part of Project 1. The goal is to analyze how long month-to-month internet customers remain active before churn, and to connect survival probabilities with customer lifetime value.

Dataset and Survival Setup

The analysis uses the IBM Telco Customer Churn dataset. Each row represents one customer. I used tenure as the duration variable and Churn as the event indicator.

Concept	Variable	Meaning
Duration	tenure	Customer lifetime in months
Event	Churn = Yes	Churn happened
Censoring	Churn = No	Customer has not churned yet
Population	Contract = Month-to-month and InternetService != No	Selected survival-analysis cohort

After filtering, the survival-analysis cohort contains 3351 customers. Among them, 1556 customers churned, giving a churn rate of 46.43%. The average tenure is 19.43 months.

Kaplan-Meier Survival Curve

The Kaplan-Meier estimator measures the probability that a customer survives beyond each month. It handles censored customers correctly, so active customers are not treated as churned.

Month	Survival probability
6	0.7803
12	0.6950
24	0.5753
36	0.4800
48	0.3872
60	0.2890

The median survival time is 34 months. This means that the estimated probability of a selected customer remaining active reaches about 50% around month 34.

Log-Rank Tests

I used log-rank tests to compare survival curves across customer attributes.

Feature	Minimum p-value	Interpretation
gender	0.153317	Not significant
seniorCitizen	0.723174	Not significant
partner	2.25e-31	Significant
dependents	3.24e-09	Significant
onlineSecurity	1.19e-32	Significant
onlineBackup	4.12e-43	Significant
techSupport	1.92e-21	Significant
paymentMethod	1.30e-21	Significant

The strongest differences appear in service and support variables such as online backup, online security, and tech support. These variables are more informative than gender or senior-citizen status for this survival task.

Cox Proportional Hazards Model

The Cox model estimates how each covariate changes churn hazard. Selected model results are:

Covariate	Coefficient	Hazard ratio	p-value
dependents_Yes	-0.3287	0.7199	< 0.001
internetService_DSL	-0.2173	0.8047	0.0002
onlineBackup_Yes	-0.7766	0.4600	< 0.001
techSupport_Yes	-0.6392	0.5277	< 0.001

The Cox concordance index is 0.6409. Online backup and tech support are associated with lower churn hazard. The proportional-hazards assumption check shows violations for several variables, so the Cox model should be interpreted carefully.

Accelerated Failure Time Model

I also fitted a log-logistic Accelerated Failure Time model. The AFT model achieved:

Metric	Value
Concordance index	0.7306
AIC	13698.72
Log-likelihood	-6838.36

Selected AFT coefficients:

Covariate	Coefficient	exp(coef)	p-value
onlineBackup_Yes	0.8128	2.2542	< 0.001
onlineSecurity_Yes	0.8616	2.3669	< 0.001
techSupport_Yes	0.6893	1.9923	< 0.001
partner_Yes	0.6768	1.9675	< 0.001
internetService_DSL	0.3837	1.4678	< 0.001

Positive AFT coefficients indicate longer expected time before churn. The AFT model had a higher concordance index than the Cox model in this analysis.

Customer Lifetime Value

Finally, I used survival probabilities to estimate customer lifetime value over a 72-month horizon.

Profile	72-month CLV
Baseline profile	895.03
Protected profile	2051.50

This step connects survival modeling with business value. The protected profile, which has stronger retention-related service features, has a much higher estimated CLV.

Conclusion

Survival analysis is useful for churn because it models not only whether customers churn, but when they are likely to churn. In this Telco dataset, support and service variables such as online backup, online security, and tech support are strongly related to longer customer survival. Kaplan-Meier curves provide interpretable survival probabilities, log-rank tests identify important group differences, Cox and AFT models quantify feature effects, and CLV converts survival probabilities into a business metric.