The Effect of Cold Showering on Health and Work
pubmed.ncbi.nlm.nih.gov
pubmed.ncbi.nlm.nih.gov
So increase in sickness?
"Self reported" is just the way the data was obtained, which makes sense in the context of the country this study was performed as most short sickness absences do not have to be justified and are self reported. You can read that sentence as "reduction of sickness absence" which matches with the other sentence in the results section "A negative binomial regression model showed a 29% reduction in sickness absence for (hot-to-) cold shower regimen compared to the control group"
"Sickness absence" can be read as "absence of sickness (thus being healthy)" or "absence (from work) due to sickness".
A reduction of sickness absence can be interpreted as a reduction of "not being sick", i.e. an increase in sickness.
But the original reply was perhaps just being pedantic in jest.