# Joint (or multivariate) model to predict two correlated time-to-event outcomes

this is a general question.

Say you want to predict two time-to-event outcomes, the time until chronic heart disease, and time until diabetes. You think these outcomes are likely to be correlated, i.e. an individual at higher risk of one, may be at higher risk of the other. Therefore to get the joint risk, you somehow need to models the joint distribution, and the level of association between the two outcomes.

I have explored using copula models, marginal modelling approach and multistate models, and believe I have an understanding of them all. However I can't get my head round frailty models/joint models. It seems like a natural approach to have a shared random effect across the two marginal models, to allow some dependence on the hazard functions of the two outcomes. However no matter how much I look, I can only find joint models for "a longitudinal and time-to-event outcome". I feel like I am either missing something very obvious, or a large portion of the literature. Why is there nothing on a joint model for two time-to-event outcomes?

Many thanks for anybody who can help on this.

The frailtypack package in R provides something like what you seek. "Joint" frailty modeling with multiple baseline hazards is done by having the corresponding "shared" frailties be the same between baseline hazards except for an exponent that is estimated in the modeling. This page is a brief introduction.
That can be done in the context of longitudinal outcomes and a terminal event as you note, but frailtypack allows for joint modeling of up to 2 recurrent events and a terminal event, although perhaps with fewer options available than for simpler scenarios. In terms of the statistical issues, however, that approach to "joint" modeling (across baseline hazards) of "shared" frailties (within a baseline hazard) can presumably be implemented by anyone willing to write the necessary code. This article explains the details, and the package manual has more literature references.