Genetic test-kit company 23andMe Inc. has for years used saliva to tell millions of consumers how closely related they are to Neanderthals or whether they are likely to develop diseases like diabetes or Alzheimer’s. Now, it’s fulfilling a bigger ambition: drug development.

For the past year, 23andMe has been sharing its huge trove of genetic data with drug giant GlaxoSmithKline PLC GSK, +1.12% , which took a $300 million stake last summer. That collaboration has so far produced six potential drug targets, and the companies expect to start human trials on at least one candidate drug next year. But it also raises ethical questions about using people’s genetic data to create profitable drugs.