Are you just comparing the count of the cases ? Or are you measuring something else and comparing these values for positive and negative cases ?

If you just want to judge the counts, is the question whether 3 | 802 different from a proportion of 0.5 | 0.5 ? That could be done with a binomial test, though the answer is pretty obvious.

Also with the counts, you could calculate e.g. Clopper-Pearson confidence intervals for the counts ( (3/805) and (802/805).

Another approach is to use a proxy variable. Let's say that some outcome of a blood test is known to be associated with this low prevalence disease and supposed there are good theories to say that is causally related, even necessary, for someone to get the disease (though others would not). You could try to predict the proxy. There are issues with this, but often you will see research that shows something lowers blood pressure with the argument that high blood pressure is related to things like heart attacks.

Thanks for your responses.

But the study planned to compare socioeconomics between positive and negative cases

Now I have 3 vs. 802 is that suitable for bivariate tests?

What kind of variables are your socioeconomic variables ? Are they nominal categorical, ordered categorical, or numeric ?

One issue is if you use the 3 and 802 variable is power. Suppose that the true prevalence is 3/805, and that there was an x variable that accounted for the probability of getting it, let's say this variable is uniform. If you use this to predict the outcome you would have low power. Attached is simple simulation showing this, and you can change things around to raise and lower the power, but it will remain low. And in reality there is unlikely to be an x variable with this large an effect. So, think about proxies!

Sal Mangiafico Sociodemographic includes both numeric continuous as age and categorical variables as educational status.

Daniel Wright thanks for your reply. And yes the power is my issue now. The problem is that it is a cross sectional study aiming to find the prevalence of a certain disease and a trivial data for each participant were collected I don't have a proxy to be used.

So, the best solution now is to do a descriptive tables for all participants and calculation of prevalence and 95% CI of it.

Probably if you want to conduct hypothesis tests on the demographic variables, a permutation test would be your best bet. But also, simply presenting the proportions or means with the confidence intervals would be a reasonable approach.