Censoring in ufc fights

Hi all,

I want to apply survival analysis on UFC fights. Basically, I want to describe fighters as diseases. So I am exploring my dataset and have some questions.

A standard UFC fight consists of three five-minute rounds. Title fights, however, are extended to five five-minute fights. We assume that an event / death time for opponent o exists an can be denoted T * Next, we have T ; the observed event or censoring time. The measurement of this variable is in seconds.

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In the case of a knock-out, o is uncensored and T * = T When o survives until the end the of the match and wins based on the decision of the jury, o is right-censored and T * > T

Question: how should we deal with the event of a loss for o by decision of the jury? Literally, the event of a loss / death occurs. So, is o uncensored in this case? The chart below shows that the majority of the outcomes is determined by jury. How can we model this is in a parametric way?

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Thank you for your time

Morning,

Are you looking to code this up in rstanarm, brms, or Stan? If so, do you have a model already in mind? If you are looking for broader advice on modeling https://stats.stackexchange might be a better place to ask.

Ara is right the we try to keep the scope here to models fitted with packages from the Stan ecosystem, but I’ll just assume you are planning to this as this looks like a neat little puzzle.

I have almost no understanding of fighting sports, but I would actually expect that what leads to a knockout is only indirectly related to jury decisions - there would be shared factors, but I wouldn’t expect the jury decisions to be reasonably interpretable as estimates of who would be knocked-out. So I would probably start by modelling the outcome (knockout vs. jury decision) and knockout times - conditional on knockout happening separately and then try to build a shared model which would assume either some correlation of predictors or a similar structure.

I also think you are missing an important piece of the structure in that this is a competitive thing between two fighters, so I think it would make sense to model the full set of four outcomes - potentially as an oridnal model - and have predictors for both fighters. I think there are some football case studies out there that might serve as inspiration.

Finally, there seems to be some additional structure in the knockout times within each round, so one might probably want to model this as well.

Best of luck with the model!