Abstract Causal inference on multiple non-independent outcomes raises serious challenges, because multivariate techniques that properly account for the outcome’s dependence structure need to be considered. We focus on the case of binary outcomes framing our discussion in the potential outcome approach to causal inference. We define causal effects of treatment on joint outcomes introducing the notion of product outcomes. We also discuss a decomposition of the causal effect on product outcomes into marginal and joint causal effects, which respectively provide information on treatment effect on the marginal (product) structure of the product outcomes and on the outcomes’ dependence structure. We propose to model the distribution of the potential outcomes conditional on pre-treatment variables using the class of log-mean linear regression models, which is particularly appealing because all the causal estimands of interest and the decomposition into marginal and joint causal effects can be easily derived by model parameters. The method is illustrated in two randomized experiments concerning ( i ) the effect of the administration of oral pre-surgery morphine on pain intensity after surgery; and ( i i ) the effect of honey on nocturnal cough and sleep difficulty associated with childhood upper respiratory tract infections.

中文翻译：

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二元非独立结果的联合和边际因果效应

摘要 对多个非独立结果的因果推断提出了严峻的挑战，因为需要考虑正确解释结果依赖结构的多元技术。我们专注于二元结果的情况，在因果推断的潜在结果方法中进行讨论。我们定义了治疗对联合结果的因果影响，引入了产品结果的概念。我们还讨论了对产品结果的因果效应分解为边际和联合因果效应，它们分别提供了对产品结果的边际（产品）结构和结果的依赖结构的处理效果的信息。我们建议使用对数均值线性回归模型类对以预处理变量为条件的潜在结果的分布进行建模，这特别有吸引力，因为所有感兴趣的因果估计以及分解为边际和联合因果效应都可以通过模型参数轻松导出。该方法在关于 (i) 术前口服吗啡对手术后疼痛强度的影响的两个随机实验中得到说明；(ii) 蜂蜜对与儿童上呼吸道感染相关的夜间咳嗽和睡眠困难的影响。