Uber is betting big on health care. What began as an experiment to deliver flu vaccines to people's offices is now a real and growing business for the company in non-emergency medical transportation, which involves helping people get to the doctor's office on time.

To help lead the company into its next phase of growth, it has hired Aaron Crowell, a longtime health consultant, as the head of its health business. It has also added Dan Trigub, a regional vice president of healthcare, from arch-rival Lyft's health care team.

Both companies have honed in on a specific use case in health: Helping people who can't drive or don't have a car get to their medical appointments. An estimated 3.6 million Americans miss their health care appointments every year because they lack reliable transportation options, according to the JAMA Internal Medicine.

In many cases, the cost of the ride will be covered by an insurer, including Medicare and Medicaid plans. As people are getting older, sicker and richer in many developed countries, that presents a big growth opportunity. The size of the medical transportation services market is projected by researchers to reach $42 billion by 2024. Non-emergency medical transportation, where Uber and Lyft are starting out, is a $3 billion market alone.

Uber can provide a window into the ride experience for health system partners, which appealed to Crowell, who comes from a traditional health transportation background.

"I joined Uber because I saw it as having a very unique position," said Crowell, in an interview at Uber's headquarters in San Francisco. "We have a GPS technology for tracking rides that is quite missing from the industry."

Crowell said he sees an opportunity for the service to go international, as there's a need outside of the United States. To get into health care, the company had to comply with federal privacy rules and regulations, known as HIPAA, as well as tweak its product so that patients don't need a smartphone to use it.

Lyft, Uber's main ride-sharing rival, is also staffing up in health care. It brought on former McKesson executive Megan Callahan to its team this month to help it expand its own health transportation offering.

Trigub says he jumped ship because he was impressed by Uber's "passion, commitment and dedication to the product," he said. "Our aging, at-risk and low-income populations, among others, deserve greater access to transportation during the times they need it most."