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11
Survival Data Mining using Enterprise Miner
and Proportional Hazard Cox Model
25th June 2015Manchester – UK
Professor Jorge Ribeiro Patrick Ribeiro
2
Survival Analysis Node
2
Enterprise Miner 13.2
Simulation Studio 13.2
SAS/OR Operational Research
SAS/ETSEconometrics
Time Series
PROC ARIMA
PROC AUTOREG
77
1.2 - Model 1 - Time to Next Purchase
“People are much more
likely to get on a bus if
they know where it is
going”.
Steps Plan
1717
SAS/ETS – Econometrics Time SeriesThe Cross-Correlation Function
tt HL 4
Jan
tt HL 1
tt HL 2
Oct
Nov
Dec
Jan
Feb
Lag
Apr
Dec
Jan
Feb
Mar
Dec
18
PROC ARIMA / PROC AUTOREG
18
SAS/ETS – Econometrics Time Series
Primary Event Variables
Royal Wedding
Bank Holiday
Price
Marketing Campaign
Point/Pulse
Step
Ramp
tevent
32
Step 1 – Economic variables
Economic Variables
Unemployment
GDP
Inflation
Cash rate
Credit availability
House prices
Commercial property prices
Commodity prices
Swap rates
Equity prices
33
Cox Proportional Hazards Model
1 1
0
{ ... }( )( ) i k ikX X
ih t eh t
Baseline Hazard function - involves time but not predictor variables
Linear function of a set of predictor variables - does not involve time
...
34
Step 3 – Model
PROC PHREG DATA = MODEL COVSANDWICH(AGGREGATE);
CLASS Risk ;
MODEL (START,END)*DEFAULT(0) = Risk P1GDP UNEMPLOYMENT;
ID CUSTOMER_ID;
HAZARDRATIO Risk / DIFF=REF;
HAZARDRATIO P1GDP / UNITS = 1 2 3 5;
HAZARDRATIOUNEMPLOYMENT / UNITS = 1 2 3 5;
RUN;
PD_Band Risk
1 to 5 1
6 to 11 5
12 to 16 09
17 to 18 12
19 to 20 15
35
SAS ResultsFor each 1 unit increase in the GDP,
the Hazard of Default goes down by an
estimated 16.7 %.
0.18257e 0.833
100*(0.833 1) 16.7%
36
SAS Results For each 1 unit increase in the
Unemployment, the Hazard of Default
increases by an estimated 25.5 %.
0.22684e 1.255 100*(1.255 1) 25.5%
Risk
37
SAS Results A customer in the Band 01 has a ONLY 8.7%
the risk of Default (or - 91.3%) compared to a
customer in the Band 15 (the reference Band).
2.44279e 0.087 100*(0.087 1) 91.3%
HAZARD RATIO (BAND 01)0.087
HAZARD RATIO (BAND 15)
38
100*(0.087 1) 91.3%
HAZARD RATIO (BAND 01)0.087
HAZARD RATIO (BAND 15)
HAZARDRATIO Risk / DIFF=REF;
SAS Results A customer in the Band 01 has a ONLY 8.7%
the risk of Default (or - 91.3%) compared to a
customer in the Band 15 (the reference Band).
Risk
39
SAS Results
Output 7
PROC PHREG DATA = MODEL COVSANDWICH(AGGREGATE);
CLASS Risk (PARAM=REF REF='15') ;
MODEL (START,END)*DEFAULT(0) = Risk P1GDP UNEMPLOYMENT;
ID CUSTOMER_ID;
HAZARDRATIO P1GDP / UNITS = 1 2 3 5;
HAZARDRATIOUNEMPLOYMENT / UNITS = 1 2 3 5;
RUN;
100*(0.694 1) 30.6%
100*(0.578 1) 42.2%
100*(0.401 1) 59.9%
40
SAS Results
Output 8
PROC PHREG DATA = MODEL COVSANDWICH(AGGREGATE);
CLASS Risk (PARAM=REF REF='15');
MODEL (START,END)* DEFAULT(0) = Risk P1GDP UNEMPLOYMENT;
ID CUSTOMER_ID;
HAZARDRATIO P1GDP / UNITS = 1 2 3 5;
HAZARDRATIO UNEMPLOYMENT / UNITS = 1 2 3 5;
RUN;
100*(1.574 1) 57.4%
100*(1.975 1) 97.5%
100*(3.109 1) 210.9%
41
Survival Function
Scenario Analysis 1
P1GDP=1.1;
Unemployment=6;
Scenario Analysis 2
P1GDP=0.8;
Unemployment=10;
4343
Go Further Introduction to Survival
Analysis using PH Cox ModelsApplying Survival
Analysis for Business
4444
Go Further Survival Data Mining
Programming ApproachSurvival Data Mining
Using Enterprise Miner
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