Can taking Baths in Bleach Reduce Eczema? Part 2

This is a followup to an earlier post. In the June issue of Pediatrics, a study was published examining the benefit of baths on diluted bleach. First, let's discuss the rationale for this study. Eczema or atopic dermatitis produces a deficit of antibodies to a bacteria called Staphylococcus aureus, Staph aureus for short. This bacteria can invade the skin and cause a secondary infection, so there's more itching, scratching, and skin destruction. Bleach is known to kill bacteria, including Staph aureus. Now on to the specifics. The study was randomized and investigator-blind, placebo controlled, but small. Only 31 patients, all of whom had "moderate to severe eczema with signs of a bacterial infection. The control arm got water baths and plain petroleum ointment for the nose. The treatment arm got diluted bleach baths (how this was made was not stated in the abstract) plus Muciprocin (an antibiotic) ointment to place in the nose. Over the next 3 months, the amount of active eczema was scored at visits for each patient. Less eczema was found in the treatment arm, although no comment was made as to statistical significance. This is not a good sign, because if present, this surely would have been stated.
I do not recommend baths in dilute bleach for two reasons. First, lack of definitive benefit. Second, potential for harm to good skin and risk of damage to mucous membranes (eyes, mouth, genitals).