"Matching" with cross-sectional studies: are the samples dependent? I am comparing the prevalence of disease in participants of two separate cross-sectional surveys. One survey is from a group of prisoners and the other is from the general population.
To account for differences in age and sex, I randomly selected members of the general population survey from age and sex groups to match the prisoners.
To illustrate what I mean, imagine I was just matching by sex. The prisoner sample includes 900 men and 100 women. I would divide the general population sample into men and women, and then randomly select 9x the number from the male group as the female group at a certain ratio - e.g. 2700 men and 300 women if the ratio was 3:1.
I used this approach within all of the age/sex groups, maintaining the same ratio so that the two samples had the same age/sex profile.
I understand that for some matched or paired designs, it is necessary to account for the dependence of the samples in the analysis. Does this apply in this case?
Many thanks
 A: Matching creates complexity in analyses, which is why you see many researchers actually ignore the matching when the analysis is done.  Not good.  You can see from your question that matching creates the need to make a lot of arbitrary but far-reaching decisions.  Not good.  And any method that throws away valid observations is not very good from a purely statistical standpoint.  Lowering N lowers power and precision. Since you are adjusting for simple variables (not variables such as zip code) it will be far easier and more powerful to use a regression model.  A saturated smooth model (does not assume linearity in age or anything about age x sex interaction other than smoothness) would be to use a restricted cubic spline in age and a main effect for sex and an interaction between the two.   Or you can just start with ordinary linear terms which will likely work better than matching.  None of this requires complex adjustments that matching would create.  I've done into more detail about problems with matching in my BBR and RMS course notes.
BUT I'm not sure how valid an analysis is that does not adjust for socioeconomic status, in the context of comparing a general population with prisoners.
