Survival Analysis & Customer Lifetime Value

Survival Analysis & Customer Lifetime Value#

“Because not all customers live forever — some churn, some ghost, and a few keep buying like it’s therapy.” 💸

💡 What This Chapter Is About#

Welcome to the world of time-to-event modeling — where instead of predicting who will buy, we predict how long they’ll stay alive (business-alive, not medically 👀).

In this chapter, we’ll learn:

  • How to measure churn risk over time ⏳

  • How to use Kaplan–Meier curves to estimate survival probability 📉

  • How to apply Cox models to understand the why behind customer loss 🔍

  • And finally, how to estimate Customer Lifetime Value (CLV) 💰 — a metric so beloved by marketers, it determines ad budgets, retention plans, and who gets the fancy CRM seats.

🧠 Business Motivation#

Think about a streaming company:

Some customers binge-watch for years. Others vanish right after the free trial ends (hi, commitment issues 👋).

Survival analysis helps us answer:

  • “What’s the probability this customer will still be around in 3 months?”

  • “Which features (discounts, subscriptions, engagement) help people not churn?”

  • “How much is this customer worth — over their lifetime?”

That last question? That’s where CLV comes in — the holy grail of marketing finance meets data science. 🏆

📈 Analogy Time#

Concept

In Medicine

In Business

Event

Death 💀

Churn 🏃‍♀️

Survival Time

Days until death

Days until churn

Censoring

Patient still alive

Customer still active

Hazard Function

Risk of death

Risk of leaving

Kaplan–Meier Curve

Survival curve

Retention curve

So yes — you’re basically doing customer epidemiology. The diagnosis? “Mild churn anxiety.” 😅

🧰 You’ll Learn#

  • ⏳ Survival Analysis Basics: What’s “time-to-event” and why does censoring matter?

  • 📊 Kaplan–Meier Estimator: How to visualize churn curves over time.

  • 📈 Cox Proportional Hazards Model: How to estimate churn risk given multiple features.

  • 💵 CLV Models: How to translate survival probabilities into customer value.

  • 🧪 Lab: Predicting and valuing churned customers for a subscription business.

🐍 Python Heads-Up#

You’ll soon meet: lifelines, pandas, matplotlib, and a sprinkle of numpy for survival calculations. If your Python skills are barely surviving, revive them with 👉 Programming for Business

🧮 Real-Life Applications#

Industry

Use Case

SaaS

Predict subscription churn and upsell timing

Banking

Model loan default risk over time

E-commerce

Estimate how long buyers stay active

Telecom

Forecast churn probability per customer

Insurance

Policy lapse prediction and renewal value

Marketing

Segment customers by lifetime value (CLV)

☕ Quick Example#

Imagine 100 customers who subscribed this month. After 6 months, some left, others stayed.

Survival analysis gives you:

  • A curve showing retention decline

  • A hazard rate showing when customers are most likely to leave

  • A CLV estimate = (Average Revenue) × (Expected Survival Time)

Boom — now your retention strategy is backed by math and drama. 🎭

🧾 TL;DR#

Concept

TL;DR

Survival Analysis

Predicts how long until something happens

Kaplan–Meier

Plots retention over time

Cox Model

Explains why churn happens

CLV

Puts 💵 value on customer lifetime

Big Idea

Combine stats + business sense = retention superpowers

“Survival analysis teaches you patience — because waiting for churn to happen is also a kind of churn.” 😅

# Your code here
Contents