Concepts in cancer survival analysis: Research questions, data, and models

Survival functions for slowly increasing risk. The hazard ratio (HR) is 0.2.

Survival functions for rapidly increasing risk. The hazard ratio (HR) is 0.2.

Multistate model describing the possible course of a patient after being disease free, e.g., after surgery with curative intent. The arrows indicate transition probabilities, which depend on time. a(t) and c(t) indicated transition probabilities from disease-free to relapse and dead respectively, while b(t) indicates the transition probability from disease-free to dead. With this model, we can e.g., compare the probability of dying in the initial state (disease-free) to the probability of dying in the relapse state, hypothesizing that b(t) > c(t).