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this is my first time developing a survival analysis model so bare with me if the nomenclature is not on point.

Basically, I'm running a Cox PH model for the length a contract is active, where 1 is terminated and 0 not.

That in itself is a pretty standard survival problem if I'm not mistaken, but there is a characteristic in my data that I'm not sure how to clean for this model.

To explain, here are some stats: 67% of cases were terminated, while 33% were not. Here is the histogram of the length of the contract for each group:

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As you can see, most terminated contracts do so before 100 days, while not terminated contracts tend to last longer (the median is 187 days).

What I want to do is truncate the number of days so, let's say if the value is 300, any observation with more than 300 days will be rewritten as 300 days. This is because I am more interested in the terminated case, and if I leave the data as it is, the predicted time to event is not very precise. I found that if I truncate the time (I tried it with 100 days but I believe it is too little given the not truncated distribution) the estimated time to event is better.

To sum up, my question is, is there a way I can find the best value to truncate the length of the contracts to? Maybe the median time for not terminated contracts?

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You certainly can choose to censor* cases beyond some time of interest. If there are cases with event times beyond that cut-off, those will have to be annotated as censored as of that time. Even if they later have an event, they hadn't as of the end of your analysis period.

Do be careful, however, to base your choice of that cut-off time on your knowledge of the subject matter rather than on repeated trials to see what works "best" on your data set. Trying out different end points in time is a type of data dredging that will tend to overfit your particular data set and not generalize well to new cases.

*There's a subtle but important distinction in terminology between "truncation" and "censoring" in survival analysis. What you would be doing is right-censoring, when the information provided to your analysis is just that the time-to-event is longer than the last observation time.

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