Survival Analysis for Data Scientists

Part 3 of 6: The Cox Model, Checking Proportional Hazards and Pricing Customer Segments, How the partial likelihood estimates the effect of customer characteristics without modelling the baseline, how to check its central assumption, and how to turn hazard ratios into the euros a marketing budget is set in.

Diogo Ribeiro is a mathematician, researcher and lecturer at the Faculdade de Media Artes e Design, Universidade Técnica do Porto.

Part 1 estimated a single retention curve and Part 2 compared two. A real customer table has many characteristics at once: where the customer came from, how large they are, what they signed up for. Each split of the table into groups leaves fewer customers per group, and a team that wants to know how churn depends on five characteristics cannot draw a retention curve for every combination of them.

This part introduces the model that is used for this more than any other, the Cox proportional hazards model. It describes how characteristics multiply the hazard, and it can be estimated without saying anything about the shape of the hazard itself. The application is a marketing decision: the most the business should pay for a new customer from each lead segment. Along the way, the model’s central assumption fails for one variable, and the failure is visible in the…