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.

翻译：差异中的差异法无疑是评估假设干预在可能存在隐藏因素导致的混杂偏倚时因果效应的最广泛使用的方法。该方法通常适用于可获得暴露前后结局测量值的情况，且可合理假设未观测混杂因子与结局的加性关联在两个暴露组中相等且随时间恒定——即所谓的平行趋势假设。然而，在许多实际场景中，平行趋势假设可能不可信，包括结局为二分类、计数或多分类变量时，以及更普遍的情况：即使未测量混杂因子对结局分布的影响随时间恒定，其效应仍可能呈现非加性。我们提出一种替代方法，用比值比等混杂假设替代平行趋势假设。该假设表明，目标因果效应的混杂偏倚（以治疗与未治疗时潜在结局之间的关联编码）可通过一个将暴露前结局与暴露关联的特定广义线性模型识别。由于该方法可识别任何理论上在无混杂偏倚时可识别的因果效应（包括分位数治疗效果等非线性效应），故被称为通用差异中的差异法。本文描述了全参数化及更稳健的半参数UDiD估计量，并通过巴西孕妇寨卡病毒感染对出生率因果效应的实际案例加以说明。