Dr., on the other hand, is an honorific. Like Mr. , Mrs. , or Prof. , it isn't meant to be used as a noun at all. To answer more directly, there is no proper way to use the abbreviated form to indicate possesion, as it isn't a noun. More @Wikipedia
Hover over any link to get a description of the article. Please note that search keywords are sometimes hidden within the full article and don't appear in the description or title.