Survival analysis - baseball pitcher Is it appropriate to use a Cox Proportional Hazard model to determine when to remove a starting pitcher from a game?
Censoring should not be a problem because there is a predefined start time and an end time. Are there any concerns that there is always an event (e.g. the pitcher always is removed from the game because it either ends or a relief pitcher is brought in)? 
I’m trying to understand why a pitcher might be removed (fatigue due to number of pitches, number or runs given up in the inning, etc). Also, predict when a pitcher should be removed in-game. 
Is a survival analysis the best method to try or are there better alternatives?
 A: Survival models are applicable even if there is no censoring. (Though, at first thought, the game ending with the pitcher still playing is a censored event, no?)
Your dataset is going to be time-varying though, since the pitcher accumulates "wear & tear" over the game, and this determines when they exit. Something like:
id time  cumulative_throws  cumulative_fast_balls  relieved
1   0     0                  0                      0
1   1     7                  4                      0
1   2     20                 16                     1
...

(I don't watch much baseball, so I'm guessing at what the dataset might look like)
Anyways, Cox models can handle time-varying datasets, and they will provide you estimates of the effect of each variable in the dataset in the context of the other variables!
One trouble with time-varying models is that prediction isn't easy. (Why? To predict, you need to extrapolate your time-varying dataset into the future, which a) is very difficult, statistically b) if you extrapolate, you are assuming they continue living!). With time-varying models, you can still provide a hazard at each time point, and either a) extrapolate this, b) base a decision rule on the latest hazard.
Alternatively, you could also a model the binary decision "remove pitcher?" after each inning. This would involve training something like a logistic model on data from the end of each inning to predict if the pitcher is removed in the next inning. This model has the advantage of more straight-forward prediction, but interpretation is much more difficult because there is within-subject correlations in the dataset that isn't being modelled.
