I will remove the old existing tiles and underneath mud bed in my bathroom. Right now
the floor in the bathroom is a few inches higher
than the adjacent room. To make both floors even
I will need to install a 1/4 inch Duroc concrete board over the subflooring instead of a 1/2 inch
recommended. Before doing so I want to be sure that the 1/4 inch will be strong enough and prevent any cracking grout and tiles. Any advice?

Hi Jean
Cement board doesn't add strength to your floor so it doesn't matter which you use. The 1/4" will work just as good as the thicker sizes, but just make sure to set the board into a fresh bed of mortar as the manufacturer recommends.

Make sure that your floor is solid before any membrane such as cement board or Ditra is applied so that you don't have problems in the future. Tell us what is on the floor now including your joists sizes and spacing so we can more accurately help you.

just to clarify Jean, and I hope harry can back me up on this is that 1/2 cament board is used mainly on walls so for example if you were doing a shower, you cement wall would be flush with the surrounding drywall.