The previous chapter demonstrated the value of survival analysis for understanding customers and their stop behaviors. It introduced a powerful method for calculating hazards, called the empirical hazards method, where separate hazard probabilities are calculated for all tenures. And, it included several examples and extensions showing how to apply survival analysis to some business problems, including forecasting the number of active customers in the future.
This chapter builds on this foundation, by introducing three extensions of basic survival analysis. These extensions solve some common problems faced when applying survival analysis in the real world. They also make it possible to understand the effects of other factors besides tenure on survival.
The first extension focuses on the factors that are most important for determining who survives and who does not. A big complication here is that the effect of these factors depends on tenure. For instance, consider the effect of market on survival. Customers in Gotham and Metropolis have about the same survival for the first year. Around the one‐year anniversary, Gotham customers start leaving at a much faster rate. In other words, the effect of market on survival varies by tenure.
The most prominent statistical technique in this area, Cox proportional hazards regression, assumes that such effects do not change over time. Although this method is outside the scope ...