This document discusses survival analysis and its application to analyzing the departure dynamics of Wikipedia editors. It begins by defining survival analysis and its goal of modeling time-to-event data using techniques that account for censoring. A case study is presented on analyzing data from 110,000 Wikipedia editors to determine who is likely to stop editing, how long they will continue editing, and why they stop. Statistical techniques like the Kaplan-Meier estimator, Cox proportional hazards models, and adjusted survival curves are used to analyze editing durations and identify covariates that impact the hazard rate of editors stopping contributions.

1. “Survival” Analysis of
Web Users
Dell Zhang
DCSIS, Birkbeck, University of London
1

2. Outline
• What Is It
• Why Is It Useful
• Case Study
– The Departure Dynamics of Wikipedia Editors
2

3. What Is It
3

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

9. 9

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

13. Why Is It Useful
for Online Marketing etc.
13

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

17. 17

18. 18

19. Predict whether a new question asked on Stack Overflow will be closed
when
19

20. Case Study
The Departure Dynamics of
Wikipedia Editors
20

21. About 90,000 regularly active volunteer editors around the world21

22. 22

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

24. Who are likely to “die”?
(WikiChallenge)
24

25. 25

26. 2001-01-01 2010-04-01 2010-09-01
2001-06-01 2010-09-01 2011-02-01
26

27. 27

28. Behavioural Dynamics Features
Exponential Steps
months
Web Search (SIGIR-2009),
Social Tagging (WWW-2009),
Language Modelling (ICTIR-2009)
28

29. 29

30. 30

31. 31

32. Gradient Boosted Trees (GBT)
32
© 2008-2012 ~maniraptora

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

34. 34

35. 35

36. 36

37. 37

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

39. How soon will they “die”?
39

40. 110,000 random samples birth & death
January 2001
The evolution of Wikipedia editors' community.
40

41. 110,000 random samples active editors
January 2001
The evolution of Wikipedia editors' community.
41

42. Survival Function
What is the fraction of a population which
will survive past a certain time?
42

43. Occasional Editors Customary Editors
The histogram of Wikipedia editors' lifetime. 43

44. Kaplan-Meier Estimator
44

45. 45

46. The empirical survival function. 46

47. Normal Distribution
47
Probability Plot

48. Extreme Value Distribution
48
Probability Plot

49. Rayleigh Distribution
49
Probability Plot

50. Exponential Distribution
50
Probability Plot

51. Lognormal Distribution
51
Probability Plot

52. Weibull Distribution
52
Probability Plot

53. The survival function. 53

54. Weibull distribution
54

55. Expected Future Lifetime
median lifetime: 53 days
55

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

57. Bathtub Curve
http://en.wikipedia.org/wiki/Bathtub_curve 57

58. The hazard function. 58

59. The hazard function. 59

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.
60

61. Why do they “die”?
61

62. Covariates
Last
Edit
62

63. 63

64. 64

65. Cox Proportional Hazards Model
65

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

67. Cox PH vs. Logistic
67

68. Maximum Likelihood Estimation
68

69. Cox Proportional Hazards Model
β se z p
X1:
-0.1095 0.0172 -6.3664 0.1935e-9
namespace==Main
X2:
-0.0688 0.0036 -19.2474 0.0000e-9
log(1+cur_size)
69

70. Hazard Ratio
70

71. Adjusted Survival Curves
71

72. 72

73. Next Step
73

74. Cartoon: Ron Hipschman
Data: David Hand 74

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.
75

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
78

79. ?
79

80. 80