Survival analysis allows insurance companies like AXA Belgium to better understand customer behavior over time. By modeling how long customers remain with the company, survival analysis can identify moments when customers are at higher risk of churn. This provides valuable insights for direct marketing campaigns to improve customer retention and lifetime value. Survival analysis uses the entire customer population, including censored customers, to create a more accurate picture of longevity. Statistical models like the Cox proportional hazards model account for covariates to predict churn risk while considering the time dimension, which traditional regression ignores.

1. Uncovering the true Customer Value by using
Survival Analysis
Marie Willo
Customer Intelligence and Rewarding Manager – AXA Belgium
Chloé Van Vreckem
Customer Insights Consultant – 4C Consulting

2. accessible
everywhere
loves
(to know)
their customers
connected
when needed
highly
profitable
engages
in every
interaction
we build customer companies

3. 3
No
global
view of
the client

4. No
Time
Dimension

5. 5
No
golden
standard
to serve

6. CUSTOMER
MARGIN
Current
customer
revenue
CUSTOMER
RETENTION
Customer
tenure
CUSTOMER
EXPANSION
Future
customer
revenue
CLV is based on 3 building blocks

7. Customer
Value
Management
at
AXA Belgium

8. CUSTOMER
MARGIN
Current
customer
revenue
CUSTOMER
RETENTION
Customer
tenure
CUSTOMER
EXPANSION
Future
customer
revenue
CLV is based on 3 building blocks

9. The origin

10. Medicine
‘Time is Crucial’
Business
‘Time is Money’

11. Why
considering
Survival Analysis?

12. Based on 1 model
a global picture can
be created of
customer behaviour
throughout time
1

13. Evaluation campaign on arbitrary points in time
Churn
Classic
marketing
program
30% stays
New
marketing
program
50% staysAFTER 12 MONTHS

14. Evaluation campaign on arbitrary points in time
Churn
Classic
marketing
program
20% stays
New
marketing
program
21% staysAFTER 16 MONTHS

15. Highlight moments in time where customers are at higher
‘risk’ to leave the company
New marketing program
Classic marketing program
Event = churn
Time (months)
Survival
probability

16. More
technical…

17. Probability to survive at any point in time:
St =
ni – di
ni
Total probability of survival till that time:
𝑆𝑡= 𝑡𝑖
≤𝑡
ni – di
ni
ni: # ‘survivors’ just prior time ti
di: # ‘deaths’ at time ti

18. We can
use the
entire
population
2

19. 
Customers ‘out of risk’

20. By censoring
customers
(out of risk),
all available
information
is used

21. 3
Model variables give
valuable customer
insights for direct
marketing campaigns
3

22. Which
Statistical models?

23. Cox proportional hazard model
Most common used model for survival data (*)
• Flexible choice of covariates
• Fairly easy to model
• Standard software exists
• Well developed elegant mathematical theory
Few distributional assumptions
• Non informative censoring
• Proportional hazards
• Independence
(*)Goetghebeur E and Van Rompaye B. Survival analysis edition 2011

24. 0%
20%
40%
60%
80%
100%
0 1 2 3 4 5 6 7 8 9 10 11 12
S(t)=Survival curve F(t)=Cumulative Incidence
Time (months)
Definitions

25. 0%
5%
10%
15%
20%
25%
30%
0 1 2 3 4 5 6 7 8 9 10 11
Incidence Hazard
Definitions
Time (months)

26. Time Survival Curve
Cumulative
incidence Incidence Hazard
0 100% 0% 20% 20%
1 80% 20% 20% 25%
2 60% 40% 10% 17%
3 50% 50%
Definitions

27. Time Survival Curve
Cumulative
incidence Incidence Hazard
0 100% 0% 20% 20%
1 80% 20% 20% 25%
2 60% 40% 10% 17%
3 50% 50%
Definitions

28. Hazard
𝜆(𝑡) =
𝑓(𝑡)
𝑆(𝑡)
𝑆(𝑡) = exp( −
0
𝑡
𝜆 𝑢 𝑑𝑢 )

29. 𝜆 𝑡, 𝒁 = 𝜆0 𝑡 𝑒𝑥𝑝 𝛽1 𝑍1 + 𝛽2 𝑍2+…+𝛽 𝑝 𝑍 𝑝
𝜆0=baseline hazard
𝑍1, 𝑍2,… , 𝑍 𝑝= covariates
Cox proportional hazard model

30. 𝜆 𝑡, 𝒁 = 𝜆0 𝑡 𝑒𝑥𝑝(𝛽1 𝑍1)
𝜆0=baseline hazard
𝑍1 =
0 = 𝑓𝑒𝑚𝑎𝑙𝑒
1 = 𝑚𝑎𝑙𝑒
𝛽1=-0.7  exp(𝛽1)=0.5
The hazard of men
leaving the company
is half of the hazard
for women.
Cox proportional hazard model

31. Classic regression ignores time – time is crucial
Solution: survival analysis
Advantages
Use of entire sample
Instantaneous risk estimation
Conditions
Non informative censoring
Proportional hazards
Independence
In summary…

32. CUSTOMER
MARGIN
Current
customer
revenue
CUSTOMER
RETENTION
Customer
tenure
CUSTOMER
EXPANSION
Future
customer
revenue
Value of the client?

33. Target
customers
with the
highest
Customer
Lifetime
Value

34. Increasing
Business
Revenue