Universal Difference-in-Differences for Causal Inference in Epidemiology
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Difference-in-differences is without a doubt the most widely used method for evaluating the causal effect of a hypothetical intervention in the possible presence of confounding bias due to hidden factors. The approach is typically used when both pre- and post-exposure outcome measurements are available, and one can reasonably assume that the additive association of the unobserved confounder with the outcome is equal in the two exposure arms, and 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, and more generally, when the unmeasured 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, which states that confounding bias for the causal effect of interest, encoded by an association between treatment and the potential outcome under no-treatment can be identified with a well-specified generalized linear model relating the pre-exposure outcome and the exposure. As 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 maternal Zika virus infection on birth rate in Brazil.
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