To assess the impact of interventions on observational studies, several approaches have been proposed for identification of causal effects. They include propensity score matching, regression discontinuity, instrumental variables and causal graphs. In this paper, we focus on the Differences-in-Differences. We review the subject, discuss its scope and limitations, and extend it to a class of nonlinear models, inducing more appropriate causal measures in relation to the type of response variable and the corresponding statistical model. More specifically, we extend the usual causal effect identification procedure for more general setups, particularly Generalized Linear Models, presenting the necessary assumptions. We call such methodology Generalized Difference-in-Difference method. To illustrate, we analyze novel data from three relevant health issues in Brazil: the demographic impact of the Zika virus outbreak on birth rates, and the impact of two distinct interventions in primary health care, namely the Family Health Program and the More Doctors Program, on hospitalizations rate. Such analyzes, besides original and referring to important topics, complement and extend previous studies. Finally, we argue, in the methodological and application sections, that the use of the Generalized Difference-in-Difference will help us to avoid errors and fallacies arising from the misapplication of the usual Difference-in-Difference method at different scales.

中文翻译：

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使用非线性模型的广义差分方法的因果测量

为了评估干预措施对观察性研究的影响，已经提出了几种确定因果关系的方法。它们包括倾向得分匹配、回归不连续性、工具变量和因果图。在本文中，我们关注差异中的差异。我们回顾了这个主题，讨论了它的范围和局限性，并将其扩展到一类非线性模型，从而针对响应变量的类型和相应的统计模型引入更合适的因果度量。更具体地说，我们为更一般的设置，特别是广义线性模型，扩展了通常的因果效应识别程序，提出了必要的假设。我们称这种方法为广义差分法。为了显示，我们分析了巴西三个相关健康问题的新数据：寨卡病毒爆发对出生率的人口影响，以及初级卫生保健中两种不同干预措施（即家庭健康计划和更多医生计划）对住院率的影响. 这些分析，除了原创和提及重要主题外，还补充和扩展了以前的研究。最后，我们在方法和应用部分争论说，使用广义差分差分将帮助我们避免由于在不同尺度上误用常用差分差分方法而引起的错误和谬误。即关于住院率的家庭健康计划和更多医生计划。这些分析，除了原创和提及重要主题外，还补充和扩展了以前的研究。最后，我们在方法和应用部分争论说，使用广义差分差分将帮助我们避免由于在不同尺度上误用常用差分差分方法而引起的错误和谬误。即关于住院率的家庭健康计划和更多医生计划。这些分析，除了原创和提及重要主题外，还补充和扩展了以前的研究。最后，我们在方法和应用部分争论说，使用广义差分差分将帮助我们避免由于在不同尺度上误用常用差分差分方法而引起的错误和谬误。