Studies that collect multi-outcome data such as tobacco and alcohol use are becoming increasingly common. In principle, multi-outcomes studies investigate the correlations between outcomes, including, causal links and/or joint distributions. Although there are many methods for studying multivariate outcomes, significant limitations regarding scale and interpretation persist. Here we introduce a model based on the exponential-family for discrete binary outcomes that provides a flexible framework for hypothesis testing of multiple binary outcomes in a computationally efficient fashion.

翻译：收集烟草和酒精使用等多种结果数据的研究越来越普遍。原则上,多种结果研究调查结果之间的相互关系,包括因果联系和/或联合分布。虽然研究多变结果的方法很多,但规模和解释方面的重大限制仍然存在。在这里,我们引入了一个基于指数-家庭的模式,用于独立二进制结果,为以高效计算的方式假设测试多重二进制结果提供一个灵活的框架。