survival data mining

Survival Data MiningGordon S. Linoff

FounderData Miners, Inc.

[email protected]

©2004 Data Miners, Inc.http://www.data-miners.com 2

What to Expect from this Talk

Background on survival analysis from a data miner’s perspectiveIntroduction to key ideas in survival analysis– hazards– survival– competing risks

Lots of examples– Stratification– Quantifying Loyalty Effort– Voluntary and Involuntary Churn– Forecasting– Time to Reactivation and Re-purchase


Who Am I?

I am not a statisticianAdept with databases and advanced algorithmsFounded Data Miners with Michael Berry in 1998We have written three books on data miningHave become very interested in survival analysis for mining customer data – survival data mining


What Does Data Mining Really Do?

Provides ways to quantitatively measure what business users know or should know qualitatively

Connects data to business practices

Used to understand customers

Occasionally, produces interesting predictive models


Prospect NewCustomer

EstablishedCustomer

FormerCustomer

Customer Relationship Lifetime

Events • Initial Purchase•Sign-Up

•2nd Purchase•Usage

•Failure to Pay•Voluntary Churn

Customers Evolve Over Time

Data Mining Is About Customers


The State of the Customer Relationship Changes Over Time

Starts P1

P1 P2

STOP

P2 P1STOP

Starts P1P1 P2

Starts P1

P1 P3

P3 P1


Traditional Approach to Data Mining Uses Predictive Modeling

4 3 2 1 +1

Jan Feb Mar Apr May Jun Jul Aug Sep

Model Set

Score Set 4 3 2 1 +1Data to build the model comes from the pastPredictions for some fixed period in the futurePresent when new data is scoredModels built with decision trees, neural networks, logistic regression, regression, and so on


Survival Data Mining Adds the Element of When Things Happen

Time-to-event analysis

Terminology comes from the medical world– which patients survive a treatment, which patients do not

Can measure effects of variables (initial covariates or time-dependent covariates) on survival time

Natural for understanding customers

Can be used to quantify marketing efforts


Example Results (Made Up)

99.9% of Life bulbs will last 2000 hoursMean-time-to-failure for hard disk is 500,000 hours“A recent study published in the American Journal of Public Health found that ‘life expectancy’ among smokers who quit at age 35 exceeded that of continuing smokers by 6.9 to 8.5 years for men and 6.1 to 7.7 years for women.” [www.med.upenn.edu/tturc/pdf/benefits.pdf ]– Example of initial covariate

Stopping smoking before age 50 increases lifespan by one year for every decade before 50


Original Statistics

Life table methods used by actuaries for a long, long time– These the are the methods we will be focused on

Applied with vigor to medicine in the mid-20th CenturyApplied with vigor to manufacturing during 20th Century as wellTook off with Sir David Cox’s Proportion Hazards Models in 1972 that provide effects of initial covariates


Survival for Marketing Has Some Differences

We are happy with discrete time (probability vs rate)– Traditional survival analysis uses continuous time

Marketers have hundreds of thousands or millions of examples– Traditional survival analysis might be done on dozens or

hundreds of participants

We have the benefit of a wealth of data– Traditional survival analysis looks at factors incorporated

into the study

We have to deal with “window” effects due to business practices and database reality– Traditional survival ignores left truncation


To Understand the Calculation, Let’s Focus on the End of the Relationship

Challenge defining beginning of customer relationship

Challenge defining end of customer relationship

Challenge finding either in customer databases

START STOPtenure is the duration of the relationship


How Long Will A Customer Survive?

Survival always starts at 100% and declines over time

If everyone in the model set stopped, then survival goes to 0; otherwise it is always greater than 0

Survival is useful for comparing different groups

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Key Idea: Data is Censored

time

Known Customer

Start

Known tenure when customers stop

Unknown tenure for active customers

(censored)


Use Censored Data to Calculate Hazard Probabilities

Hazard, h(t), at time t is the probability that a customer who has survived to time t will not survive to time t+1

h(t) =

Value of hazard depends on units of time – days, weeks, months, yearsDiffers from traditional definition because time is discrete – hazard probability not hazard rate

# customers who stop at exactly time t# customers at risk of stopping at time t


Bathtub Hazard(Risk of Dying by Age)

Bathtub hazard starts high, goes down, and then increases again

Example from US mortality tables shows probability of dying at a given age

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Hazards Are Like An X-Ray Into Customers

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Haz

ard

(Dai

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isk

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hurn

)

Peak here is for non-payment and end of

initial promotion

Bumpiness is due to within week variation


Hazards Can Show Interesting Features of the Customer Lifecycle

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Peak here is for non-payment after one year

Peak here is for non-payment after two years


How Long Will A Customer Survive?

Survival analysis answers the question by rephrasing it slightly:– What proportion of customers survive to time t?

Survival at time t, S(t), is the probability that a customer will survive exactly to time tCalculation:– S(t) = S(t – 1) * (1 – h(t – 1))– S(0) = 100%

Given a set of hazards by time, survival can be easily calculated in SAS or a spreadsheet


Survival is Similar to Retention

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Tenure (Weeks)

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rviv

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Retention is jagged.It is calculated on customers who started exactly w weeks ago.

Survival is smooth.It is calculated using customers who started up to w weeks ago.


Why Survival is Useful

Compare hazards for different groups of customers Calculate median time to event– How long does it take for half the customers to

leave?

Calculate truncated mean tenure– What is the average customer tenure for the first

year after starting? For the first two years?– Can be used to quantify effects


Median Lifetime is the Tenure Where Survival = 50%

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Average Tenure Is The Area Under The Curves

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average 10-year tenurehigh end customers =73 months (6.1 years)

average 10-year tenureregular customers =

44 months (3.7 years)


Survival to Quantify Marketing Efforts

A company has a loyalty marketing effort designed to keep customers

This effort costs money

What is the value of the effort as measured in increased customer lifetimes?

SOLUTION: survival analysis– How much longer to customers survive after accepting the

offer?– How to quantify this in dollars and cents?


Loyalty Offers is an Example of a Time-Dependent Covariate

time

Time = 0 Time = n Time c

Open Circle indicates that customer has

stopped before (or on) the analysis

date

Non-Responders have no “loyalty” date

Responders have a “loyalty” date


We Can Use Area to Quantify Results

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Months After Intervention

Perc

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etai

ned

Group 1 Group 2

How much is this

difference worth?

Chart shows survival after loyalty offer acceptance compared to similar group not given offer


We Can Use Area to Quantify Results

Increase in survival is given by the area between the curves.For the first year, area of triangle is a good enough estimate

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Months After Intervention

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Group 1 Group 2

93.4%

85.6%

Note: there are easy ways to calculate the exact value


Loyalty-Responsive Customers Are Doing Better Than Others

Survival for first year after loyalty intervention– Group 1: 93.4%– Group 2: 85.6%– Increase for Group 1: 7.8%

Average increase in lifetime for first year is 3.9% (assuming the 7.8% would have stayed, on average, 6 months)Assuming revenue of $400/year, loyalty responsive contribute an additional revenue of $15.60 during the first yearThis actually compares favorably to cost of loyalty program


Competing Risks: Customers May Leave for Many Reasons

Customers may cancel– Voluntarily– Involuntarily– Migration

Survival Analysis Can Show Competing Risks– overall S(t) is the product of Sr(t) for all risks

We’ll walk through an example– Overall survival– Competing risks survival– Competing risks hazards– Stratified competing risks survival


Overall Survival for a Group of Customers

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OverallSharp drop during this period, otherwise

smooth


Competing Risks for Voluntary and Involuntary Churn

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Involuntary

Voluntary

Overall

Steep drop is associated with

involuntary churn

Survival for each risk is always greater than

overall survival


What the Hazards Look Like

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Involuntary

Voluntary

As expected, steep drop has a very high

hazard


Most Involuntary Churn is fromNon Credit Card Payers

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Involuntary-CC

Voluntary-CC

Involuntary-Other

Voluntary-Other

Steep drop associated only with non-credit card

payers


Time to Reactivation

When a customer stops, often they come back –this is winback or reactivation

In this case, the “initial condition” is the stop

The “final condition” is the restart

Not all customers restart


Survival Can Be Applied to Other Events: Reactivation

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("Risk" of Reactivating)


Time to Next Order

In retailing type businesses, customers make multiple purchases

Survival analysis can be applied here, too

The question is: how long to the next purchase?

Initial state is: date of purchase

Final state is: date of next purchase

It is better to look at 1 – survival rather than survival


Time to Next Purchase, Stratified by Number of Previous Purchases

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Customer-Centric Forecasting Using Survival Analysis

Forecasting customer numbers is important in many businessesSurvival analysis makes it possible to do the forecasts at the finest level of granularity – the customer levelSurvival analysis makes it possible to incorporate customer-specific factorsCan be used to estimate restarts as well as stops


Using Survival for Customer Centric Forecasting

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Number Actual Predicted


ExistingCustomer

Base

New StartForecast

Do Existing BaseForecast (EBF)

Do New StartForecast (NSF)

Do Existing BaseChurn Forecast

(EBCF)

Do New Start ChurnForecast (NSCF)

Existing CustomerBase Forecast

New StartForecast

ChurnForecast

ChurnActuals

Compare

The Forecasting Solution is a Bit Complicated


Survival Data Mining Connects Data to Business Needs

Provides ways to quantitatively measure what business users know or should know qualitativelyConnects data to business practicesTechniques such as survival analysis provide new ways of looking at customersTechniques such as customer-centric forecasting integrate data mining with business processes such as forecasting

survival data mining

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