At my institution, initial invitations to interview are provided largely by the PD after reviewing applications. I believe the APDs also review applications given that we receive a very large number of applications - something like 1000-1500 - in a fairly short amount of time. However, this initial review is strictly qualitative.
When it comes to reviewing applicants after they've interviewed and creating the final ROL, we use a rubric scoring system. We look at a variety of factors, each of which is associated with a certain number of points. Some of these things are relatively black and white - e.g., this amount of research productivity results in X amount of points for the "research" section - but some things are qualitative. In our system, the most important things by far are interview evaluations, clinical performance, and, to a lesser degree, pre-clinical performance. There are several other criteria that we use, but each individual criterion is weighted much less compared to these factors. At the end of the interview season, applicants are entered into the program's ROL by order of overall score. The PD will rarely make a small correction to the score if he feels that the rubric doesn't adequately capture his overall gestalt impression of the applicant, but he is quite open about this and the correction is comparatively small. Rarely does it result in a meaningful difference in the overall outcome.