PHILADELPHIA – John Sotos has a theory about why Abraham Lincoln was so tall, why he appeared to have lumps on his lips and even why he had gastrointestinal problems. The 16th president, he contends, had a rare genetic disorder — one that would likely have left him dead of cancer within a year had he not been assassinated. And his bid to prove his theory has posed an ethical and scientific dilemma for a small Philadelphia museum in the year that marks the 200th anniversary of Lincoln's birth.

Framed behind glass in the Grand Army of the Republic Civil War Museum and Library in northeast Philadelphia is a small piece of bloodstained pillowcase on which the head of the dying president rested after he was shot at Ford's Theater in Washington 144 years ago.

Sotos, a cardiologist and author, is hoping a DNA test of the strip will reveal whether Lincoln was afflicted with multiple endocrine neoplasia, type 2B...