A decade earlier, only 13 therapies were recognized as orphan treatments. Worldwide sales of orphan drugs amounted to less than $20 billion in 2000, but by 2020 are forecast to cost $176 billion, according to EvaluatePharma, a market research firm. By that year, the money spent on orphan drugs will account for about 19 percent of the world’s total drug expense. Orphan drugs treat diseases that affect fewer than 200,000 people in the United States and cost an average of $137,000 a year. And treatments for so-called ultra-rare diseases, like the disorder that Synageva targets, generally cost much more.