Using ACS data as denominators for incidence/mortality rates


I am trying to figure out how to take into account the inherent sampling errors that are in the ACS when using it to calculate rates and their confidence intervals. I have health data counts as numerator and trying to use ACS data as denominator. I’m not using census data as census data doesn’t have the birthplace variable that the ACS does.

Thank you!

Since your estimates are coming from two separate data sources, the rate you are calculating will be a ratio of two independent random variables. There is no simple formula for calculating the distribution of this rate (see this Wikipedia article for more info on this), but there are methods for estimating it. Some statistical packages will estimate means and variances of nonlinear combinations of random variables, such as the command -nlcom- in Stata. The formulas for ratios of independent normal random variables may be appropriate if you have appropriately large sample sizes for both numerator and denominator. This pdf gives a nice explanation of estimating mean and variance of a ratio using Taylor series approximations. You may also want to read the Census Bureau’s guidance on these types of calculations: