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Americans have been fascinated with successful entrepreneurs since the days of Horatio Alger. In recent years, Silicon Valley billionaires like Apple's Steve Jobs, Google's Larry Page and Sergey Brin and Facebook's Mark Zuckerberg have become icons. Elizabeth Holmes looked to be next. Claiming she was transforming medicine with her blood-testing company, Theranos Inc., the 31-year-old Stanford University dropout became a celebrity. The New Yorker and Fortune published admiring profiles. Time named her one of the 100 Most Influential People in the World. Harvard's medical school appointed her to its prestigious board of fellows. President Obama named her a U.S. ambassador for global entrepreneurship. Theranos became the nation's largest private health-care startup, with Ms. Holmes's stake valued at more than $4.5 billion.