Survival Analysis for Data Scientists

Part 5 of 6: Competing Risks, Recurrent Events and the Price of a Service Contract. How to count events when a unit can leave in more than one way, why one minus Kaplan-Meier overstates the risk, what a hazard ratio does and does not say about how often something happens, and how to count events that repeat.

Until now, every customer in this series could leave in only one way. Most real processes are less tidy. A machine can break down, or be retired before it gets the chance. An employee can resign, or be promoted out of the role. A loan can default, or be repaid early. Each of these alternatives removes the unit from the risk of the event of interest, permanently, and the methods so far do not know what to do with that.

This part covers two extensions. Competing risks deal with several ways of leaving, of which only one can happen. Recurrent events deal with events that happen again and again to the same unit, such as repairs. The application combines both: a manufacturer of industrial pumps prices a five-year service contract, which pays for every repair and for a breakdown, and ends when the pump leaves service for any reason. Getting the price right needs both ideas, and the two most natural shortcuts err in opposite directions.

The fleet