A study commissioned by the Michigan State Medical Society and released Monday said the state could be facing a shortage of about 6,000 physicians by 2020. The study, conducted by the Lansing-based research group Public Policy Associates, cites an increase in demand for physicians by aging baby boomers, along with doctors retiring and changing practice patterns, as the main reasons for the shortage. The society is also working with Wayne State University , Michigan State University and the University of Michigan to study physician counts and per capita ratios, as well as practice details such as specialties practiced, demand forecasts and training programs available.