Up for sale is a Dr. H. Jefferson O'Brien For Medical Examiner Vintage Pinback Button 1890's Pat.
The M. W. A. might stand for Modern Woodmen of America a fraternal benefit society founded in 1883. I found the name on this button in several newspaper articles. None of them mentioned running for medial examiner. There was an obituary for Dr. H. Jefferson O'Brien a graduate of The University of Minnesota in 1895, who came to Hollywood and was the Medical Director there until he passed away in 1942. I also see the same name as being appointed to the Soo Line Railroad in 1910 as their surgeon and physician.
This is one of the old style pinbacks, where the pin sticks past the button. The button measures 44mm in diameter or about 1 5/8".