Should I use cox regression for this?

Question

Should I be using cox regression for this?

I am analyzing the performance of a tennis player. I want to understand how long on average his performance starts to drop during a match.

I indicate an optimal performance when the tennis player makes a good number X of aces a number Y of double fouls etc .. (and other predictors variables)

When, on the other hand, double fouls and batting errors begin to rise, the performance gradually becomes poor. And I want to indicate this poor performance with a 3-level categorical variable:

level 0 bad performance (number of double fouls = 6 per game) ...

level 1 bad performance: number of double fouls 4 per game

level 2 poor performance: 2 double fouls per game I would like to identify the point in time when the tennis player's performance begins to decline.

Should I use cox regression for this purpose or am I overcomplicating things?

Answer 1

This is a complicated question. Cox proportional hazards regression is used when the outcome is a binary failure (yes/no) at a given time for multiple objects (ball bearing sets, research animals, human subjects, etc). You have three possible outcomes as a function of time. You could use each level of your categorical outcome (0,1,2) as a yes/no failure as a function of time, and run failure analysis (Cox PH) on each outcome separately -- otherwise, you are throwing everything into a hopper and saying that you want to analyze everything in one step.

The time interval has to be uniform, so say, for each 5-minute window for your level=0 outcome (number of double fouls = 6 per game), you code the result as a 1-failure (it did happen) or it didn't (code 0), and log the time at which the failure occurred. You also need a list of essentially all the e.g. 5-minute intervals and a yes/no for failure. Then input the 2 outcomes (failure (y/n) and time) into Cox PH.

There are some concerns that you are only looking at 1 research subject, since this can affect correlation assumptions for Cox PH.

Overall, I would suggest talking with a sports medicine researcher at at local university -- since they would know how to do this more specifically. Thus, your question is a sports medicine question that only focuses on one subject, not a generic "textbook" statistical analysis question which commonly is based on a sample of athletes.

Better yet, if you had multiple athletes, you could model failure and adjust for within-subject correlation of outcomes over time via a random effect for subject, using generalized estimating equations (GEE) models. All the popular packages run GEE. (in economics, this is called "panel data analysis").