I'm also interested to know interview/performance correlations, but I'm not aware of data on this and a cursory search wasn't very revealing!!
First, seems like it would be valuable to establish the reliability of an interview or system of interviews.
Medical schools, having more consistent experience with larger numbers of people, have been working on this for a while.
The 'latest and greatest' for the recent years has been the MMI (Multiple Mini-Interview) format for medical school admissions.
The foundation of the system is based on experience first at McMaster University, and there has been much subsequent research and discussion.
Here is a link to the paper,
"An admissions OSCE: the multiple mini-interview"
That's at least something to consider. There are discussions about this issue at the AAMC from a UME perspective, but for GME it's much more challenging due to the vast differences between different specialties and different programs.
The value of a single interview, as a data point to predict something about a person, is really interesting to think about and I'm pretty skeptical. Wonder what it would be like without them? Are other factors more reliable in predicting outcomes? Since interviews will continue to happen for the foreseeable future, are there ways to make them more reliable as predictors (ie., would a MMI for residency be useful?) Are there things that happen in psychiatry interviews that don't in other specialties? More questions than answers!