Can you include negative results when doing statistics of antibody titers?

#1
I need to analyse some antibody titers. Depending on factors they are divided into two (eg. male and female) or more groups. I have to compare the groups. Example:
male
1/2
neg
neg
neg
1/8
female
neg
1/4
1/16
1/2
1/4
For the descriptive part, if I got it right, I calculate the prevalence and use only the positive ones to calculate the mean. So, it would be in the male group the prevalence is 40% and mean titer X and in the female the prevalence is 80% and mean titer Y. The mean is or the geometric mean of the reciprocals or the arithmetic mean of the reciprocal logs (and then antilog it) - it gives the same number.
When I want to compare the two groups, how do I do that? What do I do with the negatives? Do I use all of them and use the negatives as 1/1 (but log is 0), do I use only the positive ones and how do I explain it then, or what do I do?
Maybe it is common knowledge, but I cannot find the answer. Wherever I'm looking/googling/epidemiology books, I find the above explanation for the means, but the examples I find are on groups that are all positive and they just compare the titers.

Thank you for your time!