  Despite the common occurrence of interference in Difference-in-Differences
(DiD) applications, standard DiD methods rely on an assumption that
interference is absent, and comparatively little work has considered how to
accommodate and learn about spillover effects within a DiD framework. Here, we
extend the so-called `DiD-SNMMs' of Shahn et al (2022) to accommodate
interference in a time-varying DiD setting. Doing so enables estimation of a
richer set of effects than previous DiD approaches. For example, DiD-SNMMs do
not assume the absence of spillover effects after direct exposures and can
model how effects of direct or indirect (i.e. spillover) exposures depend on
past and concurrent (direct or indirect) exposure and covariate history. We
consider both cluster and network interference structures an illustrate the
methodology in simulations.
