  A basic descriptive question in statistics often asks whether there are
differences in mean outcomes between groups based on levels of a discrete
covariate (e.g., racial disparities in health outcomes). However, when this
categorical covariate of interest is correlated with other factors related to
the outcome, direct comparisons may lead to biased estimates and invalid
inferential conclusions without appropriate adjustment. Propensity score
methods are broadly employed with observational data as a tool to achieve
covariate balance, but how to implement them in complex surveys is less studied
- in particular, when the survey weights depend on the group variable under
comparison. In this work, we focus on a specific example when sample selection
depends on race. We propose identification formulas to properly estimate the
average controlled difference (ACD) in outcomes between Black and White
individuals, with appropriate weighting for covariate imbalance across the two
racial groups and generalizability. Via extensive simulation, we show that our
proposed methods outperform traditional analytic approaches in terms of bias,
mean squared error, and coverage. We are motivated by the interplay between
race and social determinants of health when estimating racial differences in
telomere length using data from the National Health and Nutrition Examination
Survey. We build a propensity for race to properly adjust for other social
determinants while characterizing the controlled effect of race on telomere
length. We find that evidence of racial differences in telomere length between
Black and White individuals attenuates after accounting for confounding by
socioeconomic factors and after utilizing appropriate propensity score and
survey weighting techniques. Software to implement these methods can be found
in the R package svycdiff at https://github.com/salernos/svycdiff.
