Using Cox regression to model customer time to churn in the wireless telecommunications industry

As markets mature and competitive pressure intensifies, companies can no longer ignore the importance of customer retention as their existing customer bases have become their precious assets.^{1, 2, 3} This is particularly true in the Canadian wireless telecommunications industry because the dominant barrier to switching, namely, the lack of wireless number portability,^{4, 5} was eliminated in 2007 and the government has started to bring competition to the wireless sector by allowing new entrants to bid and operate on the Advanced Wireless Services spectrum. ⁶ Furthermore, consumers in most metropolitan areas can choose wireless services from over 10 different brands. ⁷ With handset subsidy reaching over CDN$350 on average, customer acquisition has become an expensive yet challenging task for marketers in the wireless telecommunications industry. ⁸ This article aims to help wireless carriers address the churn issue by providing them with insights into the effects of customer demographic and behavior characteristics on churn rate through the use of a well-known statistical procedure called Cox regression.

Prior literature has shed some lights on the economic value of customer retention. Engel, Blackwell and Miniard ⁹ argue that having a low churn rate allows organizations to focus on their customers’ needs and hence reduces the need to approach new customers who may be risky from a financial perspective. Ganesh, Arnold and Reynolds ¹⁰ point out that loyal customers buy more in the long run and further contribute to the organization’s profitability. These long-term customers are expected to give positive word-of-mouth referrals if they are satisfied with the organization. It has also been suggested that organizations can serve existing customers in a less costly manner because of greater knowledge of their needs and consumption pattern. Athanassopoulos ¹ suggests that organizations would incur opportunity costs when customers churn away due to loss of sales. In addition, it has been widely argued that acquiring a new customer is several times more expensive than retaining one.^{11, 12, 13} Other benefits of having loyal customers include reduction of pricing and marketing sensitivity from competitive offerings.^{12, 14}

Extensive studies have been undertaken on customer retention strategies in the wireless telecommunications industry since the late 1990s, underlining the relevance of this topic in the industry.^{15, 16, 17, 18, 19, 20} Many of them, however, focus on specific European and Asian markets in which market conditions are not the same as they are in Canada. Thus, this research aims to contribute to the existing body of knowledge by exploring the issue of wireless customer churn from a Canadian perspective. Furthermore, this research takes into consideration an emerging database marketing strategy known as rate plan optimization in the analysis.^{21, 22}

Unlike previous customer retention studies that used surveys as the data collection method, this study tries to avoid sample selection bias by utilizing customer records extracted directly from the data warehouse of a Canadian wireless carrier. A total population of 4896 postpaid residential customers from a particular rate plan segment were selected for observation over a study period of 44 months, starting from their service activation month of May 2002 till the end of the observation period in December 2005.

Two major groups of independent variables were collected so that their impacts on the wireless churn rate could be analyzed. The first group considers demographic characteristics such as the customers’ age, residing location and the primary language that they use for communication. This research did not include some commonly used demographic variables such as income, gender and education level because such information is not available from the wireless carrier. The second group of variables explores the customers’ behavioral characteristics, including rate plan changing frequency, handset changing frequency, contract status and the suitability of wireless rate plan. Joo et al ²¹ and Wong ²² have argued that rate plan suitability can play an important role in influencing a customer’s intention to stay with the wireless carrier, and hence the modeling analysis also includes this factor. Figure 1 presents the conceptual framework of this research study.

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To gain a holistic view of the relationship between these independent variables and customer churn rate, the Cox regression model is adopted. Also known as proportional hazards regression analysis, it is a well-recognized statistical technique used to simultaneously investigate the effects of several explanatory variables on the survival of customers.^{23, 24} Cox regression is based on a modeling approach to the analysis of survival data, making it suitable for use in this type of research, which considers right-censored observations and time-varying covariates. ²¹

The hazard function measures the potential for the ‘event’ to happen at a particular time t, given that the event has not yet happened. A high hazard function value suggests that the event will likely happen. It is denoted by h(t) which can be estimated using the following Equation (1):

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In the context of data mining in the telecommunications industry, ‘survival’ refers to customer retention whereas the ‘hazard function’ can be viewed as the probability that a customer will churn away from the wireless carrier. Incorporating the various demographic and behavioral characteristics variables, we can express the risk of customer churn at time t as in Equation (2):

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where h₀(t) is the baseline hazard at time t which corresponds to the probability of customer churn when all the explanatory variables are zero. The baseline hazard determines the shape of the hazard function over time. The regression coefficients, b_age to b_suitability, give the proportional adjustment that can be expected in the hazard, given the changes in the explanatory variables. In other words, the hazard function value is equal to the product of the baseline hazard and a covariate effect; the latter helps to determine the overall magnitude of the function. The use of Cox regression allows this research to precisely estimate the effects of customers’ demographic and behavioral characteristics on their churn intention. PAWS Statistics 17.0.2 software from SPSS Inc. is used to run Cox regression and other statistical procedures in this research study.

The Canadian wireless telecommunications industry is facing rapid changes as the government brings competition to the market by implementing wireless number portability and allowing new entrants to bid and operate on the Advanced Wireless Services spectrum. Faced with high customer acquisition costs and a fast maturing market, wireless carriers are urged to shift their marketing focus from customer acquisition to retention activities. Through the use of Cox regression, this article presents a model that marketers can use to identify customer segments that are sensitive to churning behavior. On the basis of the research results, extra retention efforts should be directed to younger customers and those who are residing in the Eastern Canada region. Moreover, wireless carriers should consider giving incentives to encourage existing customers to switch rate plans and upgrade their mobile handsets as these activities are shown to be effective in reducing churn.

This article also confirms prior research findings that about half of all customers are subscribing to rate plans that are not financially optimized, and that they are churning significantly faster than those with optimal ones. To better retain these customers, wireless carriers should proactively monitor their rate plan suitability and make necessary adjustments as part of their customer relationship management initiatives.

Although this study contributes to the knowledge on customer retention in the context of the wireless telecommunications industry, some limitations and opportunities for further research deserve to be mentioned. First of all, this research only analyses data provided by a Canadian wireless carrier, so there is a geographical bias. This may be a first step towards assessing customer retention in the wireless telecommunications industry in North America or some other region. Second, this research focuses on the postpaid wireless service. Future studies can explore the prepaid market and develop explanatory variables that are applicable to such customer segment. Another limitation of this research is that only data from residential customers are used for analysis. Researchers can develop a more sophisticated model to cover the business customers as well.

In summary, the findings of this article may help researchers and practitioners in the wireless telecommunications industry adopt a holistic perspective and make informed decisions about the opportunities and challenges that churn management would present.