Up-and-coming private hospitals in China's overburdened public healthcare system are trying to cure a shortage of doctors, which could dent the country's reform drive just as private investors are getting interested.

The healthcare sector is set to more than double by the end of the decade to $600 billion, according to consultancy firm Bain & Co.

Part of the shortage problem is that, across most of China, doctors need permission from the State-owned hospitals where they are employed before they can accept work in the private sector.