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

33

Model 1 - Time to Next Purchase

Survival Discrete Model

44

5

Survival Analysis Node

5

Enterprise Miner 13.2

66

1.1 - Model 1 - Time to Next Purchase

Survival Discrete Model

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

88

1.2 - Model 1 - Time to Next Purchase

99

1.2 - Model 1 - Time to Next Purchase

1010

1.2 - Model 1 - Time to Next Purchase

1111

Final Model - Hazard Function

1212

Final Model - Benefit graph

1313

Final Model

1414

1515

1.2 - Model 1 - Time to Next Purchase

16

PROC ARIMA / PROC AUTOREG

16

SAS/ETS – Econometrics Time Series

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

19

PROC ARIMA / PROC AUTOREG

19

SAS/ETS – Econometrics Time Series

20

Simulation Studio 13.2

20

SAS/OR – Operational Research

21

Simulation Studio 13.2

21

2222

2 - Model 2 - Call Centre Demand

Call Centre Demand Model

2323

2.1 - Model 2 – Call Centre

Wait Time Goal = 30

Wait Time Max = 90

2424

2.2 - Model 2 – Call Centre

Wait Time Goal = 30

Wait Time Max = 90

2525

2.3 - Model 2 – Call Centre

Wait Time Goal = 30

Wait Time Max = 90

2626

2.4 - Model 2 – Call Centre

Wait Time Goal = 30

Wait Time Max = 90

2727

2.5 - Model 2 – Call Centre

2828

3.1 - Model 3 – Stress Test and Scenario Analysis

2929

3030

62 days for data preparation

6 days for modelling

31

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;

42

Forecast under Scenario

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

4545

Go Further – Books

4646

Go Further – Books

47

Questions

47

www.modellingtraining.com

info@modellingtraining.com

- SAS code

- Results

- PDF

Email:

Web page:

Tel: 01943 430241

07880 474564