  Objective. To provide step-by-step guidance and STATA and R code for using
propensity score (PS) weighting to estimate moderation effects. Research
Design. Tutorial illustrating the key steps for estimating and testing
moderation using observational data. Steps include (1) examining covariate
overlap across treatment groups within levels of the moderator, (2) estimating
the PS weights, (3) evaluating whether PS weights improved covariate balance,
(4) estimating moderated treatment effects, and (5) assessing sensitivity of
findings to unobserved confounding. Our illustrative case study uses data from
41,832 adults from the 2019 National Survey on Drug Use and Health to examine
if gender moderates the association between sexual minority status (e.g.,
lesbian, gay, or bisexual [LGB] identity) and adult smoking prevalence.
Results. For our case study, there were no noted concerns about covariate
overlap and we were able to successfully estimate the PS weights within each
level of the moderator. Moreover, balance criteria indicated that PS weights
successfully achieved covariate balance for both moderator groups. PS weighted
results indicated there was significant evidence of moderation for the case
study and sensitivity analyses demonstrated that results were highly robust for
one level of the moderator but not the other. Conclusions. When conducting
moderation analyses, covariate imbalances across levels of the moderator can
cause biased estimates. As demonstrated in this tutorial, PS weighting within
each level of the moderator can improve the estimated moderation effects by
minimizing bias from imbalance within the moderator subgroups.
