I have two groups (group 1: $n=100$, and group 2: $n=200$), and multiple proportions for each group (where the number represents the proportion of individuals in the group with each disease). Example:
group1 group2 high cholesterol 0.20 0.28 high blood pressure 0.18 0.16 cardiovascular disease 0.13 0.20 diabetes 0.25 0.20 vitamin d deficiency 0.05 0.15
I want to calculate whether there is a significant difference between the two groups, overall, across the disease categories. Since this data is not a contingency table, I clearly cannot use a chi-squared test or a Fisher's Exact Test. I know how to compare single proportions across two groups, but is there a way to compare multiple proportions across the two groups simultaneously and get a single p-value? Of course, I could test each disease individually with a two-proportion z-test and then adjust for multiple comparisons, but can I test everything at once (in the flavor of a Fisher Exact Test)?
UPDATE: The categories are not disjoint as an individual can have 0 diseases or $>1$ diseases (seen by the fact that the proportions for either group do not add up to 1), which is why we cannot use the usual strategies that are used for a contingency table. In essence, instead of comparing the proportions $A$ and $B$ across two groups, I am trying to compare the vectors of proportions, $A = [a_1, a_2, a_3, a_4, a_5]$ and $B = [b_1, b_2, b_3, b_4, b_5]$ across two groups.