I've written something up where I used tenure instead of the ranks. http://christopheraden.github.io/SickTime.html.
Here’s my concern with the original model, having slept on it: What does it actually buy you? In order to use the model, you must know the rank of sick time of the employee, relative to all other employees. In order to calculate this, you have to have the raw sick time numbers. At which point, what’s the point in making a regression with it—just work with the raw sick times to begin with!
Wouldn't sick time taken per year be a more interesting measure? Over time, wouldn't you expect that an employee of 30 years would've taken more sick time than an employee of six months? Aren't you really concerned about whether in a particular year older employees are not taking as much vacation as newer employees?