A growing number of Americans are no longer getting health insurance directly from work as companies quit administering benefits, sending about 40 million people to shop for their own coverage by 2018, a new study estimates.

Instead of picking a companywide health plan, employers are increasingly giving workers financial support to choose their own from a menu of options. For 2015, 6 million workers selected coverage from markets run by private benefits administrators, according to a study from Accenture Plc.

That's double the previous year, when employees of Walgreens Boots Alliance Inc., Sears Holdings Corp. and Darden Restaurants Inc. all had to go shop on their own. By 2018, a quarter of employees who get insurance through work will pick a plan through the private markets, according to Accenture.