Level of analysis and assumption of independence in Pearson Chi-square test

Question

I have survey data about injuries occurring to athletes over the span of their careers. Many of the athletes suffered multiple injuries (the most any athlete reported was five and this did not occur very often). While I can see that injuries within an athlete may be dependent on a previous injury, in the data, many within-athlete injuries involved different body parts with different mechanisms and types, occurring years apart.

My interest is in the characteristics of the injury itself not the athlete. I am looking to see if any one particular mechanism of injury was prevalent in the sport. And with that information, look at possible modifications to the equipment or rules to improve the safety.

I used a Pearson Chi square test to see if Anatomical site of injury was distributed evenly across mechanism of injury (e.g. contact with opponent, quick turn, etc.); and the type of injury (e.g., strain, sprain, etc.) across mechanism, too.

My original intent for this data was to present descriptives and some graphs contrasting the different mechanisms and the parts injured or the types of injury, however, I was asked by a reviewer to perform some statistical analyses to show that, for example, shoulder strains occurred more frequently than shoulder lacerations.

Now I have a concern about the independence of the observations. Since I'm looking at injury level variables and each injury is only included once in each analysis, I don't think I'm violating that assumption despite several athletes being in the analysis multiple times. Is this correct? Or do I have to worry about independence.

There are a number of pieces of equipment that can be modified and this will be the next project once "high risk" equipment is identified. With this project I was hoping to get evidence that would justify targeting those pieces of equipment with some data that reflect higher injury rates when using specific equipment and thus avoid altering equipment that did not have a high incidence of injury associated with it.

Thoughts and advice appreciated.

Answer 1

I think a problem like this is begging for a random effects model. If the same athletes are appearing in multiple times, it doesn't seem at all reasonable to assume independence between injuries. The exact form of the random effects might need a little expertise from someone in sports science, but for example, some athletes might just be more susceptible to injury than others, or specific types of injury. Furthermore, once you have been injured once there could be many ways this might affect later injuries (even to different sites/mechanisms - e.g. behavioral changes, such as being less aggressive).

Possibly the simplest thing to do though, is to split your data, so that you only take the first injury of each athlete. Perform the analysis on this, and then do the same on the 2nd+ injuries, and see if the results agree. This will sacrifice considerable statistical power (since you lose a lot of your dataset) but will sidestep almost all of the independence issues.

If you don't have enough data to support a multilevel model, then a possibly simpler model is simply to include extra factors for repeated injury. That is for each row in your data, add extra yes/no explanatory variables that indicate

• if that site has been injured before
• if that athlete has had that type of injury
• if that mechanism injured the athlete before
• if that athlete has been injured before at all

These four extra effects can then be fitted to your data an hopefully absorb the most obvious and largest non-independence effects. If you find that none of these flags are significant, then that should be a good indicator that independence is fine.

When drawing conclusions, one final point is to note that often categories are defined quite arbitrarily, and this can cause problems when asking "is X more common than Y". For example in cause of death statistics, Cardiovascular disease is a massive killer, while pancreatic cancer is not. But there are many types of cancer, and many types of Cardiovascular disease, so it isn't a meaningful comparison. A good way to create meaningful comparisons is to think about what the data will be used for. In your case you already know that you want to consider possible improvements to equipment etc. to prevent injury. It may be that some improvements affect more than 1 mechanism, so it is a good idea to group together the mechanisms by improvement that will affect them, at this stage of the analysis rather than later.