> The mental health of the remaining 1963 students who did not take the survey is very likely to be in worse shape than of those who did. In discussion the authors say "Moreover, we want to emphasize the likely sample bias in our data. We recruited participants mainly via mailing lists and our project therefore probably has especially appealed to people who are already interested in health or aware of mental health issues."

I would counter that it may go in the other direction too. The other group of people who have little interest in the topic of mental health are those who are already doing really well. It's a non-problem for them, so why would they engage?