Abstract
Customer lifetime value (LTV, see e.g. Bauer et al. 2005 and Rosset et al. 2003), which measures the profit generating potential, or value, of a customer, is increasingly being considered a touchstone for administering the CRM (Customer relationship management) process. This in order to provide attractive benefits and retain high-value customers, while maximizing profits from a business standpoint. Robust and accurate techniques for modelling LTV are essential in order to facilitate CRM via LTV. A customer LTV model needs to be explained and understood to a large degree before it can be adopted to facilitate CRM. LTV is usually considered to be composed of two independent components: tenure and value. Though modelling the value (or equivalently, profit) component of LTV, (which takes into account revenue, fixed and variable costs), is a challenge in itself, our experience has revealed that finance departments, to a large degree, well manage this aspect. Therefore, in this paper, our focus will mainly be on modelling tenure rather than value.
TopBackground
A variety of statistical techniques arising from medical survival analysis can be applied to tenure modelling (i.e. semi-parametric predictive models, proportional hazard models, see e.g. Cox 1972). We look at tenure prediction using classical survival analysis and compare it with data mining techniques that use decision tree and logistic regression. In our business problem the survival analysis approach performs better with respect to a classical data mining predictive model for churn reduction (e.g. based on regression or tree models). In fact, the key challenge of LTV prediction is the production of segment-specific estimated tenures, for each customer with a given service supplier, based on the usage, revenue, and sales profiles contained in company databases. The tenure prediction models we have developed generate, for a given customer i, a hazard curve or a hazard function, that indicates the probability hi(t) of cancellation at a given time t in the future. A hazard curve can be converted to a survival curve or to a survival function which plots the probability Si(t) of “survival” (non-cancellation) at any time t, given that customer i was “alive” (active) at time (t-1), i.e., Si(t)=Si(t-1) x [1-hi(t)] with Si(1)=1. Once a survival curve for a customer is available, LTV for that specific customer i can be computed as:LTV = 
, (1) where vi(t) is the expected value of customer i at time t and T is the maximum time period under consideration. The approach to LTV (see e.g. Berger et. Al. 1998) computation provides customer specific estimates (as opposed to average estimates) of the total expected future (as opposed to past) profit based on customer behaviour and usage patterns. In the realm of CRM, modelling customer LTV has a wide range of applications including:
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Evaluating the returns of the investments in special offers and services.
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Targeting and managing unprofitable customers.
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Designing marketing campaigns and promotional efforts
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Sizing and planning for future market opportunities
Some of these applications would use a single LTV score computed for every customer. Other applications require a separation of the tenure and value component for effective implementation, while even others would use either the tenure or value and ignore the other component. In almost all cases, business analysts who use LTV are most comfortable when the predicted LTV score and/or hazard can be explained in intuitive terms.