As presented in the paper, for competing risks, the accuracy in time answers the question "Does my model accurately predict which event will occur first to individuals at a given horizon?".
It differentiates from the C-index which answers an alternative question: "Does my model accurately rank individuals by their incidence probability for a specific event of interest?
A model with good accuracy in time is useful for the physicist to determine where to focus the treatment for a given individual. A model with a good C-index on the other hand is useful to allocate treatment resources to individuals that need it the most.
In the paper, we introduced the accuracy in time as:
where
is the most probable event at time horizon $\zeta$,
is the event (or censoring) observed at $\zeta$, and $n_{nc}$ represents the number of individuals uncensored at $\zeta$.
As presented in the paper, for competing risks, the accuracy in time answers the question "Does my model accurately predict which event will occur first to individuals at a given horizon?".
It differentiates from the C-index which answers an alternative question: "Does my model accurately rank individuals by their incidence probability for a specific event of interest?
A model with good accuracy in time is useful for the physicist to determine where to focus the treatment for a given individual. A model with a good C-index on the other hand is useful to allocate treatment resources to individuals that need it the most.
In the paper, we introduced the accuracy in time as:
where
is the most probable event at time horizon $\zeta$,
is the event (or censoring) observed at $\zeta$, and $n_{nc}$ represents the number of individuals uncensored at $\zeta$.