A Frailty Model for Semi-competing Risk Data with Applications to Colon Cancer

In semi-competing risks (which generalizes the competing risks scenario), a subject may experience both terminal and non-terminal events, usually dependent, where the event time to the intermediate non-terminal event (say, tumor recurrence in cancer studies) is subject to censoring by the terminal event (say, death), but not vice-versa. As an alternative to the latent failure time formulation of semi-competing risks with joint survival functions, here, we consider an illness-death (multistate) shared frailty framework, where the dependency between the terminal and non-terminal failure times is incorporated via the power variance frailty between the conditional transition rates that are assumed Markov. Inference is conducted via maximum likelihood. A simulation study is conducted to evaluate the finite sample performance of the model parameters. Finally, we compare and contrast our power variance frailty proposal to known alternatives via application to a colon cancer dataset. Relevant code for implementation of our model is available in GitHub.