Survival Analysis
a practical application

structure of the talk
• Me
• Tails.com
• Lifetime value and retention
• Survival analysis - motivation and theory
• A survival regression model
• Outputs and accuracy measures
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University of York: Maths MMath
University of Bristol: PhD Random Matrix Theory
Department for Education: Operations Research
Analyst, Post-16 Education and Funding
ASI Data Science: Data Science Internship
Tails.com: Data Scientist
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about me

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Our proposition is based on a one-to-one relationship with each owner and their dog
Changing the world of pet food for good
Our proposition is based on a one-to-one relationship with each owner and their dog
customer visits tails.com
and enters dog’s details
perfect product blended to
meet pet’s individual
requirements as a one-off
Packaging personalised
with dog’s name & their
unique blend details
Delivered to customer
left in a safe place if
necessary
feeding plan automatically
updates as dog ages or
after optional owner
feedback
auto-replenishment
so the owner never runs
out, or has too much
free adjustable, personalised
feeding scoop making it easy
to feed the right amount every
day

over 85,000 dogs UK wide
deliver 4 million meals every month
average monthly order costs £24
3 treat varieties, 15 wet food varieties
over 1 million blends searched in 0.1s to find the optimal blend for your dog
expect sales of well over £20m this year
around 100 employees...
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tails.com in numbers

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… and around 25 office dogs

customer retention and
lifetime value

Lifetime Value helps us make smart decisions on…
...product giveaways
...customer refunds
...marketing spend
...project prioritisation
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why do we care about lifetime value?

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retention and lifetime value
Retention
(how long you will
be a customer)
Frequency
(how often you
will order)
Order Value
(how much we make
from your orders)
Lifetime Value
(total profit
attributed to you)

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retention and lifetime value
Retention
(how long you will
be a customer)
Frequency
(how often you
will order)
Order Value
(how much we make
from your orders)
Lifetime Value
(total profit
attributed to you)

survival analysis

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motivation
What is the average subscription length?
Censored data - not
observed end event yet

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survival analysis in action

The time to a subscription end for a randomly
chosen customer (time the customer churned)
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survival analysis definitions
Hazard function: probability that the customer
will churn at time t
And are related by:
T ≥ 0
Survival Function: probability that the
customer hasn’t churned by time t

package options

Lifelines
Lightweight, good visualisations. Limited model
selection
Cameron Davidson Pilon
github.com/CamDavidsonPilon
scikit-survival
Bigger selection of linear and nonlinear model
options
Sebastian Pölsterl - PyCon UK 2017
github.com/sebp/scikit-survival
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model choices
Survival, KMSurv, OISurv:
Decent model selection, lots of tutorials and lectures
on the subject use these packages.
Generally slower to train, and less intuitive to use
than Python options

modelling

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Kaplan-Meier estimate of the survival function
Using lifelines package:

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Time since subscription start
Probabilitystillacustomer
Probability
customer still
active = 50%
Expected time
active
Kaplan-Meier estimate of the survival function

Key Assumption: Impact of a factor on survival is multiplicative, and impact is constant over time
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survival regression
Input Features x: Everything we know about...
- Your dog
- You
- Your actions in trial
Cox Proportional Hazards model

Dealing with categorical data
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feature engineering
pet_id breed
1 Jack Russell
2 Labrador
3 Dalmatian
pet_id jack_russell labrador dalmatian
1 1 0 0
2 0 1 0
3 0 0 1
One hot
encoding
Category with n
options converted
to n - 1 binary
features
Assign
sensible
ordering
pet_id breed
1 Jack Russell
2 Labrador
3 Dalmatian
pet_id breed_median_days_active
1 xxx
2 yyy
3 zzz
Logical ordering given
instead of category -
estimate median time active
based on population
Better clarity on
impact of each
individual category
Generally more accurate
prediction

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training the model
…..

evaluation

Measure accuracy by successful ordering of pairs of customers
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concordance index
Mowgli
Predicted time a customer will be active
0
Mr. Patch

Measure accuracy by successful ordering of pairs of customers
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concordance index
Mowgli:
Active for 12 months
Mr. Patch:
Active for 18 months
Predict Mowgli active for longer
wrong!
Predict Mr Patch active for longer
correct!
Concordance Index between 0 and 1
1: Perfect ordering of pets
0.5: As good as random ordering
0: Perfect anti-ordering

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qA
pet level survival predictions
Time since subscription start
Probabilitystillacustomer
Lines don’t intersect - due to underlying
proportional hazard assumption
Happy customer,
active for a long
time
Uninterested
customer,
churns quickly

python, data and dogs
your kind of thing?

lorna@tails.com
https://tails.com/careers
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