Attrition Model and Remaining Lifetime

Author: Melinda Richmond Date: May 6, 2009 Attrition Model and Mean Remaining Lifetime Disclaimer: Dummy Data

What is Survival Analysis?
Survival analysis is a set of statistical methods for time-dependent outcomes. It is typically used when a research question centers around whether or when an event occurs, such as when does a customer attrite?
Life Table and Empirical Hazard
The life table looks at a lifetime implication of customers whose risk of attriting is depended on tenure and the hazard provides a graphical representation.
Flexible Hazard Modeling Methodology
The hazard model based on logistic regression was built using discrete time survival data and the model possess a simple parametric form.
How the Model was Used
The model was scored which provides predictive scores of a customer attriting. The mean residual life was calculated which provides an estimate of the mean remaining lifetime of a customer.
Future Considerations
Competing Risk such as mutually exclusive reasons for attriting, time-independent variables such as attrition risk, and incorporating seasonality into the model should be considered for the future.
Executive Summary

Research question: Whether a customer with COMPANY ABC has attrited, and if so, when did the customer attrite?
Let’s consider two COMPANY ABC customers, Customers A and B. Customer A, attrited during the study period having thirty-nine years of tenure. Customer B, did not attrite during the study period, so the event time of this customer attriting is unknown.
Customer A, represents a customer with a time-dependent outcome (attrited) which depends on a discrete event time, T=thirty-nine years of tenure. Customer B, represents a customer with a time-dependent outcome (not attrited) which depends on an unknown discrete event time, i.e., tenure of when the customer attrites is unknown. This is known as right-censoring. We have the answer to the research question. We know whether or not the customer attrited and when the customer attrited during observable time (the study period, see page 4).
In addition to knowing the outcome and event time, whether time is known or censored, we need to know what other variables help to explain why a customer attrites. These are known as time-dependent covariates. For example: What was the age of the customer who attrited after thirty-nine years of tenure? Was this customer who attrited after thirty-nine years of tenure in a paid up status?
When the values of the covariates change in time, then the data for each customer consists of many individual time series.
What is Survival Analysis?

Window of Opportunity for Survival Analysis Data Jan 2006 Dec 2006 STUDY PERIOD PRIOR AFTER Account Opened Attrited Right-Censored Attrited

Life Table All customers have had a tenure (t) = 0 years, 3.1 million. 500 (0.0161%) new customers attrited and 160,000 new customers did not attrite by end of study period, i.e., right-censored. 2.9 million customers have had a tenure (t) = 1 years. 650 (0.0221%) first year customers attrited and 161,000 first year customers did not attrite by end of study period, i.e., right-censored.

Empirical Hazard The increasing part of the curve indicates that customers are more likely to leave COMPANY ABC , and the decreasing part of the curve indicates that customers are less likely to leave COMPANY ABC .

Logistic Regression Model

Scored the hazard estimates from the model on 2007 data. The score measures the likelihood of a customer attriting. A graph is presented on page 10, which compares the actual number of attritors to the predicted number of attritors.
The average remaining lifetime of a customer is computed by scoring future time intervals with the hazard model. A graph is presented on page 11, displaying the average remaining lifetime.
conditional probability of the customer attriting at time t given that the customer has not attrited yet
How the Model was Used

Fitted Model for Number of Attritors

Fitted Model for Restricted Mean Residual Lifetime

This write-up does not consider the reason for a customer attriting. However, if one knows mutually exclusive reasons for a person attriting one could model on competing risk (mutually exclusive reasons of attriting) using a multinomial logistic approach as opposed to a logistic approach.
Identify attrition risk by large, medium, or small. These are variables independent of time. One could build three separate models obtaining an equation for each risk.
This write-up does not consider seasonality. However, we know that with certain observations there maybe a seasonality effect.
Future Considerations

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Attrition Model and Remaining Lifetime

by Melinda Richmond

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