Using Proc Logistic to Improve Customer Retention Luke Furlong - - PDF document

10/28/2013 1

Using Proc Logistic to Improve Customer Retention

Luke Furlong Assurant Health

Reference

• SAS Course: Survival Data Mining: Predictive

Hazard Modeling for Customer History Data. Will Potts.

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The Problem

• Assurant Health has a product with higher

lapse than we would like.

• We would like to understand better the

characteristics of those lapsing.

• We would like to predict who is going to lapse.

Product Cycle

Policy issued Submit claim (office visit) Submit second claim (ER visit) Cancel Policy Call

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The model

• h(t) = F(f(t), β1Xit , β2Zi)
• h(t) = probability of lapse at time t
• f(t) = Duration – spline with spike at 12 months
• Zi= Time‐independent covariates

– Demographic variables, Policy details (add‐ons, billing type, etc.)

• Xit = Time‐dependent covariates

– Claims, calls, maxed out benefits, etc.

The model graphically

1 2 3 4 5 6 7 8 9 10 11 Lapse Rate Month Modeled lapse rates by Billing type

List Bill Direct Bill Other Billing Type

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Hazard Function can be flexible Code to create a spline

%LET KNOTS=2 3 5; DATA IM_HIST_RET; SET IM_HIST_RET; ARRAY K{3} _TEMPORARY_ (&KNOTS); CSB1=(T>K[1])*(T-K[1])**3-T**3+3*K[1]*T**2-3*K[1]**2*T; CSB2=(T>K[2])*(T-K[2])**3-T**3+3*K[2]*T**2-3*K[2]**2*T; CSB3=(T>K[3])*(T-K[3])**3-T**3+3*K[3]*T**2-3*K[3]**2*T; RUN;

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The Data

Policy Product type 1 Value 2 Value 3 Fundamentals 4 Enhanced Policy Call Type Call date 2 Admin 1/2/2012 2 Service 5/3/2011 3 Admin 3/9/2012 4 Service 4/23/2012 Policy Data Call Data

Create panel data set

Member Month Call Claim Lapse 1 1 1 $3000 1 2 1 3 1 1 4 1 2 1 1 $5000 2 2 3 1 $150 3 2 1 3 3 3 4 1

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Censoring and Truncation

• Censoring:
• End of study censoring:

no lapse event.

• Loss to follow‐up: can

censor at earlier dates

• Left truncation:

Introduces a length bias, needs correction.

• Don’t include rows from

before the truncation date.

Form of the model

• Logistic Regression
• Multinomial logit

– Allows for more than one outcome

• Example: Lapse, upgrade product, downgrade product.

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Predictive scoring

• Fitted model is applied to customers.
• Provides probability of lapse.
• Used to prioritize customers for intervention.

Code for model estimation and scoring

ODS OUTPUT PARAMETERESTIMATES=PE;/* use this output for plotting*/ /*Model Estimation*/ proc logistic data=HA_LAPS.IM_HIST_RET OUTMODEL=SASUSER.AHA_LAPS_MODEL_VAL; model DUR_LAPSE(event='1')= POL_DUR_MTH CSB1 CSB2 CSB3 LIST_BILL CREDIT_CARD COM T*COM T*LISTBILL T*CREDITCARD; RUN; /*Scoring*/ proc logistic inmodel=sasuser.AHA_LAPS_MODEL_VAL; score data=IM_HIST_RET out=Score_FUND; run;

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Forecasting

• Can be used to forecast lapse in next period.
• Can be used for multi‐period forecasting, if

time‐dependent covariates are known or assumed.

Visual display of fitted hazard function

1 2 3 4 5 6 7 8 9 10 11 Lapse Rate Month Modeled lapse rates by Billing type

List Bill Direct Bill Other Billing Type

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Code to write scoring code

DATA _NULL_; /*Creates a text file*/ FILE '\\Msp0wsasp001\prod5\AA\HA Lapse Drivers Luke 2012 Q4\model2.txt'; IF _N_=1 THEN DO; ARRAY K{3} _TEMPORARY_ (&KNOTS); put 'csb1=(t>' k[1] ')*(t-' k[1] ')**3-t**3+3*' k[1] '*t**2-3*' k[1] '**2*t;'; put 'csb2=(t>' k[2] ')*(t-' k[2] ')**3-t**3+3*' k[2] '*t**2-3*' k[2] '**2*t;'; put 'csb3=(t>' k[3] ')*(t-' k[3] ')**3-t**3+3*' k[3] '*t**2-3*' k[3] '**2*t;'; end; length variable2 $30 plus $10; set pe end=last; if variable='Intercept' then variable='eta'||'=1'; plus='+'; if last then plus=';'; variable2=variable; put variable2 '*' estimate best16. plus; if last then do; put 'shf1=exp(eta)/(1+exp(eta));'; end; run;

Plot the hazard function

data plt;/*create data for plotting*/ do t=0 to 16; AGE_18_24 = 0 ; CALL = 0 ; LIST_BILL = 0 ; . . . %include '\\Msp0wsasp001\prod5\AA\HA Lapse Drivers Luke 2012 Q4\model2.txt';

• utput;

end; run; goptions reset=global; proc gplot data=plt;/*plots data in SAS*/ symbol1 v=dot h=.5 i=join; axis1 order=(0 to 180) minor=none; plot(shf1)*t=call_TOTAL / vzero haxis=axis1; run; quit;

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Conclusion

• Predictive Hazard Modeling

– Provides flexible modeling choices. – Gives nice visualization of hazard function by independent variables – Can be used to score customers – Can be used for forecasting