  Difference-in-differences is undoubtedly one of the most widely used methods
for evaluating the causal effect of an intervention in observational (i.e.,
nonrandomized) settings. The approach is typically used when pre- and
post-exposure outcome measurements are available, and one can reasonably assume
that the association of the unobserved confounder with the outcome has the same
absolute magnitude in the two exposure arms, and is constant over time; a
so-called parallel trends assumption. The parallel trends assumption may not be
credible in many practical settings, including if the outcome is binary, a
count, or polytomous, as well as when an uncontrolled confounder exhibits
non-additive effects on the distribution of the outcome, even if such effects
are constant over time. We introduce an alternative approach that replaces the
parallel trends assumption with an odds ratio equi-confounding assumption under
which an association between treatment and the potential outcome under
no-treatment is identified with a well-specified generalized linear model
relating the pre-exposure outcome and the exposure. Because the proposed method
identifies any causal effect that is conceivably identified in the absence of
confounding bias, including nonlinear effects such as quantile treatment
effects, the approach is aptly called Universal Difference-in-differences
(UDiD). Both fully parametric and more robust semiparametric UDiD estimators
are described and illustrated in a real-world application concerning the causal
effects of a Zika virus outbreak on birth rate in Brazil.

Methodology