1
$\begingroup$

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?

$\endgroup$

1 Answer 1

0
$\begingroup$

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").

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.