Survival Analysis for Data Scientists

Part 4 of 6: Parametric Models, Accelerated Failure Time and the Value of Customers Beyond the Data. Six models fitted to a year of churn, four of which fit about equally well and disagree about the next four years; a covariate that stretches time instead of multiplying the hazard; and a decision rule for a number the data cannot yet pin down.

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

Part 1, Part 2 and Part 3 were careful never to say anything about time nobody had observed. Every customer value was a restricted mean: expected paid months up to a horizon inside the data. Business questions are rarely that polite. A finance team planning acquisition spend for a product launched a year ago wants the value of a customer over five years, and a valuation wants it over a lifetime. Neither number is in the data.

This part introduces the models that answer anyway: parametric survival models, which describe the whole retention curve with a few parameters and can therefore be evaluated at any time, observed or not. It also introduces the accelerated failure time model, a way of describing the effect of a characteristic that is often more natural than a hazard ratio. The application is the…