spatial statistics: bivariate (cross) k-function vs k-function difference

#1
Dear list,

I want to assess if a series of cases (farms positive for a disease) are spatially clustered by comparing them to the general population (the total number of farms) in a given region. For that I would like to know if it is statistically correct to use the bivariate (also known as cross) k-function, considering cases as element 1 and general population (all farms, including the cases) as element 2. I am using splancs (k12hat function) in R. I know that you can do the difference of k-functions but I would like to know if the use of the bivariate k-function is correct.
If it is statistically correct, can I conclude that the positive farms are clustered/dispersed compared to the total population (using label permutation)?

Thanks in advance for your help

berto