SHANGHAI—Big Pharma is investing billions of dollars to tackle deadly diseases prevalent in China, developing new drugs to combat a lineup of top killers that differ from those in the West.

Swiss drugmaker Novartis AG is testing a molecule to combat a rare head and neck cancer widespread in southern China. American rival Johnson & Johnson is creating innovative drugs to tackle lung cancer and hepatitis B, endemic in China. And France’s Sanofi SA is researching a new way to treat liver cancer—one of the most common forms...