Exploring Customer Retention with Survival Analysis
Introduction
Customer retention is an increasingly pressing issue in today’s ever-competitive commercial arena. Companies are eager to develop a customer retention focus and initiatives to maximise long-term customer value. Specifically, the importance of customer retention; conceptualises an integrated customer value/retention model; and explains how usage segmentation can assist in relationship-building, retention strategy and profit planning. I am proposing a solution that integrates various techniques of customer data analysis, modelling and mining multiple concept-level associations to form an intuitive and novel approach to gauging customer loyalty and predicting their likelihood of defection. Immediate action triggered by these “early-warnings’’ resulting this could be the key to eventual customer retention
Unveiling Customer Retention for Lifetime Value
At the core of every contractual or subscription-based business model lies the concept of the retention rate. A crucial managerial responsibility involves utilizing past retention data for a specific customer group to forecast future outcomes accurately, including customer tenure and lifetime value. Consequently, Customer Lifetime Value (LTV) stands as a fundamental pillar of database marketing. LTV is commonly defined as the total net income a company can anticipate from a customer (Novo 2001). The precise mathematical definition and calculation methodology depend on various factors, such as whether customers are “subscribers” (typical for most online subscription products) or “visitors” (pertaining to indirect marketing or e-business).
Decoding Customer Lifetime Value: Insights for Business Intelligence
This article delves into the calculation and practical utilization of Customer Lifetime Value (LTV). The Business Intelligence Unit of CRM companies customizes analytical solutions to address crucial business challenges such as churn and retention analysis, fraud analysis, campaign management, credit and collection, risk management, and more. LTV assumes a pivotal role in various applications, particularly in churn analysis and retention campaign management. When analyzing churn, understanding the LTV of customers or segments serves as essential complementary information to churn probability, providing insights into the actual value lost due to churn and guiding efforts aimed at mitigating churn risks. In the context of retention campaigns, the key concern lies in establishing the relationship between the resources invested in retention efforts and the resulting impact on the LTV of targeted segments.
Disentangling Customer Lifetime Value: Modeling Essentials & Insights
In the realm of lifetime value (LTV) modelling, three primary components come into play: the customer’s value over time, the duration of their service, and a discounting factor. These components can be computed or approximated individually or through a combined modelling approach. When applying LTV modelling to retention campaigns, an additional consideration arises — calculating a customer’s LTV before and after the retention efforts. This entails computing multiple LTV values for each customer or segment, corresponding to various potential retention campaigns or suggested incentives. The ability to estimate these distinct LTV values is fundamental to the effectiveness and practicality of LTV applications.
Exploring Customer Tenure: Insights from Survival Analysis
In addressing the question of average subscription length and customer tenure, we encounter challenges related to the dynamic nature of the data. The inclusion of both active and inactive customers in the calculation raises questions about the validity of the average derived from the entire CRM database. Furthermore, the average subscription length can vary significantly when calculated at different time points, making it an elusive moving target. Alternatively, focusing solely on inactive customers does not provide a comprehensive solution, as the dataset is biased towards those who have already cancelled.
These limitations highlight the need for a different approach that acknowledges the unobserved endpoint and refrains from relying on a simplistic average calculation. Survival analysis emerges as a powerful tool to address these challenges and provide more meaningful insights.
Survival Analysis In Action
Survival analysis offers a valuable tool for addressing the aforementioned challenge of estimating event times in a population when complete event data is not available. Although survival analysis has a long history in statistics, its application extends beyond medical statistics. In the context of customer analysis, we are particularly interested in understanding the duration between customer sign-up, transitioning from a free trial to a paid subscription, and their anticipated usage duration. This information directly contributes to the assessment of customer lifetime value.
Uncovering the Essence of Concepts and Definitions
To gain a conceptual understanding of survival analysis, let us delve into key definitions. Firstly, we consider capital T, which represents the time until a customer’s subscription ends. This quantity is greater than zero and can be infinite if the customer never churns. Our focus lies in understanding customer lifetime value, which relates to the probability that a customer remains active until any future day T. This probability is a non-decreasing function over time. Additionally, we examine the hazard function, which represents the probability that a customer churns precisely on a given day T, neither a day earlier nor a day later. These two aspects, the survival function and the hazard function, are intricately related, and through elementary probability reasoning, we can establish a relatively simple relationship between them.
Package Options for Survival Analysis
In the realm of Python, there are two prominent packages for survival analysis: lifelines and sci-kit-survival. Lifelines is a well-established package known for its lightweight nature and impressive visualization capabilities. On the other hand, the scikit-survival package is built upon the robust foundation of scikit-learn. Both packages can be seamlessly integrated into pipelines, following the familiar usage pattern of scikit-learn.
Dataset Selection
For our demonstration, we have chosen a customer churn dataset. This dataset serves as an illustrative example, allowing us to guide readers through the complete cycle of customer retention from a data science perspective. Our aim is to leverage the available dataset to uncover valuable insights and construct a predictive model that can be applied to future data.
Power of Feature Engineering in Survival Analysis
In our dataset, we encounter a significant amount of categorical data, including features such as partner status, dependent status, and contract type. To handle these categorical variables, a standard approach known as one-hot encoding is often employed. This process transforms each category into a binary feature, resulting in either n or n-1 new binary features, depending on the chosen encoding scheme. In the context of the Cox model, this approach allows for the estimation of separate coefficients for each category, enabling a precise assessment of the impact of individual categories on the survival outcome. However, it is important to note that this encoding scheme can lead to a substantial increase in the dimensionality of the dataset, known as the curse of dimensionality.
Unravelling the Kaplan-Meijer Estimate and Cox Proportional Hazards Regression
- Extract Kaplan-Meijer Estimate Of The Survival Function
- Cox Proportional Hazards Regression Analysis
The Kaplan-Meijer Estimate of the Survival Function The Kaplan-Meijer estimate provides valuable insights into the probability of a customer remaining active and not churning until a specific point in time, denoted as “t.” In contrast, the cumulative hazard function quantifies the cumulative risk or probability of churn up to time “t.” Our focus lies in understanding the survival function, which represents the probability of a customer still being active at day “T.” Due to limitations in data availability, estimating this function requires employing the Kaplan-Meijer estimate. This estimate is computed by multiplying the ratios of customers who have reached each point in time.
The Cox Proportional Hazards Regression Analysis
The hazard rate, also known as the force of mortality or instantaneous event rate, characterizes the risk of an event occurring in a small time interval around “t,” assuming the event has not yet happened. Estimating the true form of the survival function is a critical aspect of survival analysis. The Kaplan-Meijer estimator considers the number of customers who have churned and the “number at risk,” which refers to customers who are still under contract but may churn in the future.
Upon executing the provided code, a graph is generated, illustrating the survival curve with closely aligned confidence intervals. This indicates that our model effectively approximates the true survival curve within the dataset. Consequently, we can determine the average subscription length by identifying the median time at which customers are expected to remain active, corresponding to the 50% probability threshold. This measure provides insights into the expected duration of customer engagement within the survival curve.
By leveraging this analysis, we gain a deeper understanding of customer longevity, thereby influencing customer lifetime value. Furthermore, an extension of this approach involves constructing a regression model that incorporates various customer factors, enabling us to estimate the survival function more comprehensively.
Survival Regression Analysis for Modeling Customer Lifetime Value
The Cox proportional hazards model is widely employed to examine the relationship between multiple risk factors and survival time in customer lifetime value analysis. This model measures the hazard rate, representing the risk of an event occurring given that the customer has survived up to a specific time. The proportional hazards assumption implies that the hazard ratio between any two customers remains constant over time. The baseline hazard function, denoted as lambda zero, captures the time-varying changes, while the customer features, such as contract type and streaming preferences, influence the hazard rate.
However, it is important to note that the Cox model assumes that all impacts on survival are constant over time, which may not always hold true. Factors such as varying refund amounts over time could introduce time-varying effects on survival. Therefore, careful consideration is required when applying the Cox model in customer lifetime value analysis to accurately model the duration of customer relationships.
Model Training and Coefficient Analysis in Survival Regression
The Cox proportional hazards model is fitted in a straightforward manner, providing summary results that reveal the coefficients and their corresponding exponents. These coefficients play a crucial role in determining the impact of each feature on the hazard rate and the overall survival function. Examining the coefficients allows us to assess the significance of each feature and the model’s confidence in capturing their effects accurately.
For instance, let’s consider the coefficient for the feature “OnlineSecurity,” which has an exponent of 0.67. The further the exponent deviates from one, the greater the impact of the corresponding coefficient on the survival function. A lower coefficient indicates a reduced hazard rate and suggests that the customer is more likely to remain a customer for an extended period. Conversely, if a coefficient is close to one, it implies minimal impact, and the model may struggle to determine the precise influence of that feature. In such cases, it is advisable to exclude variables with coefficients close to one from the model, as they contribute little meaningful information and introduce noise.
Validation of Survival Model: Concordance Index
In the process of developing a predictive survival model, it is crucial to assess its performance using appropriate measures. Among the various proposed performance metrics, we have utilized the concordance index in our evaluation. This index quantifies the degree to which the model successfully orders pairs of observations within the dataset.
To illustrate, we consider all data points and their corresponding predicted times until a customer churns, which are expected to be greater than zero. The concordance index is computed in a similar manner to the area under the curve (AUC) score. It ranges between 0.5 and 1, where 0.5 signifies random ordering and 1 represents a perfect ordering of all individuals based on their expected survival times. The closer the concordance index is to 1, the higher the accuracy of the model’s predictions.
Customer Level Survival Predictions
Having developed a Cox proportional-hazards model, we have generated survival predictions for a random 1% sample of the data. Each line in the predictions represents a distinct customer’s survival curve.
An important observation is that none of the survival curves intersect. This adherence to the proportional hazards assumption indicates that the shape of each curve is determined by the baseline hazard function, which is then adjusted based on the associated features.
Moreover, these predictions provide insights into what constitutes a satisfied customer versus an unsatisfied one. By analyzing the patterns and trends within the survival curves, we can discern the factors that contribute to customer satisfaction and identify areas where customers may exhibit low engagement with our service. This understanding enables us to enhance customer retention, improve our service offerings, and gain deeper insights into customer retention and lifetime value.
Leveraging Python and Data Analysis for Actionable Insights
Understanding customer churn, the termination of a customer’s relationship with a business is crucial for determining a business’s revenue. It is imperative for businesses to identify loyal customers and those at risk of churn, as well as understand the underlying factors influencing these decisions from the customer’s perspective. This blog post delves into the intricacies of customer retention beyond a simple classification problem and employs a survival analysis approach to predict customer churn risk. By leveraging survival analysis techniques, this blog uncovers insights and actionable findings that can guide targeted marketing strategies for improved customer retention.
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References:
Blattberg, R. C., Kim, B. D., & Neslin, S. A. (2008). Database Marketing: Analyzing and Managing Customers. Springer.
Rooset, J., & Kumar, V. (2002). Customer Lifetime Value Modeling and Its Use for Customer Retention Planning.
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