Survival Analysis with Python for Forecasting Customer Lifetime

Survival analysis is an important area of statistics used to predict the time it takes for a specific event to occur. Originally developed in the medical and biological sciences, this method has become widely applied in business, especially with the rise of interest in Data Science. In this article, we will explore how survival analysis can be utilized to forecast customer lifetime, including calculating probabilities and hazard rates for telecommunications subscribers.

Survival analysis allows for estimating how long a specific event will last while accounting for the fact that some events may not have occurred by the time data is collected. Examples of applications include the time until a machine fails, the time until a customer cancels a subscription, and the time until a repeat purchase. However, standard regression models like OLS or logistic regression are not suitable for survival analysis, as they are designed to handle completed events.

Key concepts of survival analysis include the notions of 'birth' and 'death' of data points. Birth refers to the moment we start measuring that data point, such as the day a patient is diagnosed. Death occurs at the moment of the event of interest, such as when an employee leaves a company. It is important to note that observation can end before the event occurs, leading to the concept of censored data.

The survival function S(t) expresses the probability of the event not occurring as a function of time. It will naturally decrease as time passes, as more individuals will experience the event. Conversely, the hazard function indicates the probability of the event occurring at a given point in time, allowing for assessing the risk of customer churn based on data from those who have not yet left the company.

There are two main models used for performing survival analysis: the Kaplan-Meier model and the Cox proportional hazards model. The Kaplan-Meier model is simpler to use but does not account for the effect of additional predictors, while the Cox model is the industry standard as it is more mathematically stable and can incorporate various variables.