There's no real system.
The information from our applications is sent in one packet of information with 25 pages that the program directors have to literally sift through. And it changes every year so they have to sift through it every year. And they get 350 of these applications.
And all they have to do is say yes or no.
At some of my interviews where I knew it just wasn't going to happen or I wasn't interested, I used my "so do you have any questions for us" to ask what was on my application that scored me an interview.
There's no system and it depends on the day and the mood and the other applications they've looked at that day.
This is a great post in some ways. Think of a program director with tons of applications and 50 interview slots for 5 residents. If you have 350 applications, probably 50-100 are easier to say no to. Maybe you get it to 80-100 applications that you REALLY like for 50 slots. There is no doubt there is some arbitrariness (is that a word?) when getting it down to those who you invite in the end. Here are some things that come into play that you might not think of. Program directors may consider:
1. Historical performance of applicants from your school
2. Diversity of interview pool (race, gender, life experiences, geographic location, dental school represented, etc.)
3. How many applicants have you already invited from school X?
4. Schools you would like to recruit more (i.e. maybe you're looking for applicants from school Y so you can have them come and at least SEE your program. It's an investment).
5. Quality of the letters of recommendation. These are all over the board. Some are helpful and some are really not great.
6. Letters coming from an OMS? Did you have letters all from perio and prosth and your dean and maybe one from OMS? Not the best choice.
7. Research (YMMV with this, and importance is way different per program, or even between attendings in a program).
8. Quality of personal statement (again, YMMV. Some PDs won't read this, some really do).
9. CBSE score. Importance of this is variable. I would suggest some use this as a cutoff just because it is challenging to wade through so many applications. It's also relative to the other applicants.
10. Did you extern there? BIG deal. Maybe you didn't, and they will interview people they already know with lower CBSE scores. Happens all the time and totally makes sense.
Bottom line, it is complicated and every program has their method of choosing. And yes, sometimes the PD will miss something or just decide arbitrarily, but they have to make a call at some point. If you didn't get an interview someplace but have great credentials, it could be any number of these issues, and it probably isn't that you are a bad candidate. Be grateful for the interviews you did receive and make the most of it. All it takes is one (although obviously, more is better odds, I know). If you didn't match and felt you had good credentials, give some of these factors consideration.