  Health policy researchers often have questions about the effects of a policy
implemented at some cluster-level unit, e.g., states, counties, hospitals, etc.
on individual-level outcomes collected over multiple time periods. Stacked
difference-in-differences is an increasingly popular way to estimate these
effects. This approach involves estimating treatment effects for each
policy-implementing unit, then, if scientifically appropriate, aggregating them
to an average effect estimate. However, when individual-level data are
available and non-implementing units are used as comparators for multiple
policy-implementing units, data from untreated individuals may be used across
multiple analyses, thereby inducing correlation between effect estimates.
Existing methods do not quantify or account for this sharing of controls. Here,
we describe a stacked difference-in-differences study investigating the effects
of state medical cannabis laws on treatment for chronic pain management that
motivated this work, discuss a framework for estimating and managing this
correlation due to shared control individuals, and show how accounting for it
affects the substantive results.
