I have evaluated the prevalence (proportion) of a disease in men and women, in different studies available in the literature. So I have sample sizes for men and women (in different studies) and also know the number of the affected people in each gender. So I can calculate standard errors for each prevalence.
However, the more interesting finding is the ratio of the prevalence (proportion) of disease in males divided by its prevalence (proportion) in females (male:female ratio). I have calculated these too. However I need the SE for those "ratios of proportions" in order to draw a funnel plot.
I couldn't find a proper way to calculate SE for those ratios. Do you think it is possible? If not, how am I supposed to draw funnel plots for my male:female ratios?