This week, NPR posted an article about a group of scientist doing just that. Using Twitter data they are comparing vaccine estimates published by the CDC to look at patterns between perception of vaccines and whether or not people are getting sick. In fact there is an increasing number of scientists using twitter information in research.
According to the article, the use of twitter is particularly interesting because "You can observe how people feel about certain things in a real-world context". It is a huge amount of data and one challenge is to sort out the misinformation and false alarms and bias from the good information. The scientists using it feel that it is a helpful tool in their work.
The article can be found at: http://www.npr.org/blogs/health/2011/10/14/141335492/what-twitter-knows-about-flu-vaccines