4. Time-To-Event Data
• Survival Analysis is a branch of statistics which
deals with the modelling of time-to-event data
– The outcome variable of interest is time until an
event occurs.
• death, disease, failure
• recovery, marriage
– It is called reliability theory/analysis in
engineering, and duration analysis/modelling in
economics or sociology.
4
5. Y X
How to build
a probabilistic model of Y ?
5
6. Y X
How to build
a probabilistic model of Y ?
How to build
a probabilistic model of Y given X ?
6
7. Y X
How to build
a probabilistic model of Y ?
How to build
a probabilistic model of Y given X ?
7
8. Censoring
• A key problem in survival analysis
– It occurs when we have some information about
individual survival time, but we don’t know the
survival time exactly.
8
10. Y X
Options:
1) Wait for those patients to die?
2) Discard the censored data?
3) Use the censored data as if they were
not censored?
4) ……
10
11. Goals
• Survival Analysis attempts to answer
questions such as
– What is the fraction of a population which will
survive past a certain time? Of those that survive,
at what rate will they die?
– Can multiple causes of death be taken into
account?
– How do particular circumstances or characteristics
increase or decrease the odds of survival?
11
12. • Censoring of data
• Comparing groups
– (1 treatment vs. 2 placebo)
• Confounding or Interaction
factors
– Log WBC
12
14. The Data Are There
• Events meaningful to online marketing
– Time to Clicking the Ad
– Informational: Time to Finding the Wanted Info
– Transactional: Time to Buying the Product
– Social: Time to Joining/Leaving the Community
– ……
Time Matters!
14
15. Evidence-Based Marketing
• Let’s work as (real) doctors
– Users = Patients
– Advertisement (Marketing) = Treatment
Survival Analysis brings
the time dimension
back to the centre stage.
15
23. Departure Dynamics
• Who are likely to “die”?
• How soon will they “die”?
• Why do they “die”?
“live”= stay in the editors’ community
= keep editing
“die” = leave the editors’ community
= stop editing (for 5 months)
23
33. Gradient Boosted Trees (GBT)
• The success of GBT in our task is probably
attributable to
– its ability to capture the complex nonlinear
relationship between the target variable and the
features,
– its insensitivity to different feature value ranges as
well as outliers, and
– its resistance to overfitting via regularisation
mechanisms such as shrinkage and subsampling
(Friedman 1999a; 1999b).
• GBT vs RF
33
38. Final Result
• The 2nd best valid algorithm in the
WikiChallenge
– RMSLE = 0.862582: 41.7% improvement over
WMF’s in-house solution
– Much simpler model than the top performing
system : 21 behavioural dynamics features vs. 206
features
– WMF is now implementing this algorithm
permanently and looks forward to using it in the
production environment.
38
56. Hazard Function
Of those that survive, at what rate will they die?
The instantaneous potential per unit time for the event to occur,
given that the individual has survived t.
56
60. Conclusions
• For customary Wikipedia editors,
– the survival function can be well described by a
Weibull distribution (with the median lifetime of
about 53 days);
– there are two critical phases (0-2 weeks and 8-20
weeks) when the hazard rate of becoming inactive
increases;
– more active editors tend to keep active in editing
for longer time.
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66. Semi-Parametric
• The semi-parametric property of the Cox
model => its popularity
– The baseline hazard is unspecified
– Robust: it will closely approximate the correct
parametric model
– Using a minimum of assumptions
66
75. Lightning Does Strike Twice!
• Roy Sullivan, a former park ranger from Virginia
– He was struck by lightning 7 times
• 1942 (lost big-toe nail)
• 1969 (lost eyebrows)
• 1970 (left shoulder seared)
• 1972 (hair set on fire)
• 1973 (hair set on fire & legs seared)
• 1976 (ankle injured)
• 1977 (chest & stomach burned)
– He committed suicide in September 1983.
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76. A Lot More To Do
• Multiple Occurrences of “Death”
– Recurrent Event Survival Analysis (e.g., based on
Counting Process)
• Multiple Types of “Death”
– Competing Risks Survival Analysis
76
77. Software Tools
• R
– The ‘survival’ package
• Matlab
– The ‘statistics’ toolbox
• Python
– The ‘statsmodels’ module?
77
78. References
• David G. Kleinbaum and Mitchel Klein. Survival Analysis: A Self-Learning
Text. Springer, 3rd edition, 2011. http://goo.gl/wFtta
• John Wallace. How Big Data is Changing Retail Marketing Analytics.
Webinar, Apr 2005. http://goo.gl/OlMmi
• Dell Zhang, Karl Prior, and Mark Levene. How Long Do Wikipedia Editors
Keep Active? In Proceedings of the 8th International Symposium on Wikis
and Open Collaboration (WikiSym), Linz, Austria, Aug 2012.
http://goo.gl/On3qr
• Dell Zhang. Wikipedia Edit Number Prediction based on Temporal
Dynamics. The Computing Research Repository (CoRR) abs/1110.5051. Oct
2011. http://goo.gl/s2Dex
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