For each record in my datasets I have the following information
$$ (X_1 \ , \dots \ , X_m \ , \delta \ , T \ )$$
where $X_i$ are features, $\delta$ is 1 if the target event occurs and 0 otherwise, and $T$ is the timestamp of the occurred event. In particular, $T$ might be missing if there was no event or set to time the follow-up ended.
I want to compute a risk index for each record in my dataset.
I was thinking to go for a classification model that uses features $X_i$ to predict the class $\delta$. However, $T$ is important: if the event $\delta$ is likely to occur soon the risk should be higher.
That is why a survival analysis should be suited for this problem. I don't need the full estimation of the $S(t) = P(T>t)$ but just a single index that represents the risk for a single record.
The mean survival time, that can be computed for each record, seems a nice risk index - the lower the higher the risk is.
My question are:
- Is the survival analysis suited for my purposes?
- How can I evaluate the performance of my model?
About question (2): I am keen to use the Harrell's $c$-index for example, but I am not sure about which predicted outcome is used to compute it. From Harrell's book Regression Modeling Strategies page 247:
The $c$ index [...] is computed by taking all possible pairs of subjects such that one subject responded and the other did not. The index is the proportion of such pairs with the responder having a higher predicted probability of response than the non responder.
If the survival analysis turns out to be a right choice I think it should be easy to use some standard method to introduce time varying covariates $X_i(t)$.