The Economist Blog : http://www.economist.com/blogs/economist-explains/2013/09/economist-explains-6

Twitter has taken advantage of a provision in America’s Jumpstart Our Business Start-ups Act—or JOBS act for short—that allows “emerging growth companies” to kick off the IPO process confidentially. The firm hopes that by keeping its financial performance under wraps for a while, and then heading swiftly to a listing, it can avoid the kind of hype that surrounded Facebook’s IPO in 2012. The JOBS Act also lets emerging growth firms talk to big investors privately to gauge the appetite for their shares.
According to JOBS act 2012, this usual way can be used by companies with annual income lower than 100 million dollars. Though this way, Twitter can keep their financial situation confidential and protect their own privacy. They still get chance to get IPO.
reference: http://www.cnetnews.com.cn/2013/0923/2990683.shtml