The increase in the use of mobile and wearable devices now allows dense assessment of mediating processes over time. For example, a pharmacological intervention may have an effect on smoking cessation via reductions in momentary withdrawal symptoms. We define and identify the causal direct and indirect effects in terms of potential outcomes on the mean difference and odds ratio scales, and present a method for estimating and testing the indirect effect of a randomized treatment on a distal binary variable as mediated by the nonparametric trajectory of an intensively measured longitudinal variable (e.g., from ecological momentary assessment). Coverage of a bootstrap test for the indirect effect is demonstrated via simulation. An empirical example is presented based on estimating later smoking abstinence from patterns of craving during smoking cessation treatment. We provide an R package, funmediation, available on CRAN, to conveniently apply this technique. We conclude by discussing possible extensions to multiple mediators and directions for future research.

翻译：移动和可磨损装置的使用增加,现在可以对一段时间的调解过程进行密集评估。例如,药物干预可以通过减少暂时戒烟症状对戒烟产生影响。我们界定和确定平均差价和差价比率尺度潜在结果的因果关系直接和间接影响,并提出一种方法来估计和测试随机处理对悬殊二进制变量的间接影响,这种变化是由密集测量的纵向变量(例如,从生态瞬间评估得出的)的非参数轨迹所调节的。通过模拟可以显示间接影响的靴套试验的覆盖范围。一个经验性的例子是根据对以后吸烟与戒烟治疗期间的消毒模式的禁欲程度的估计而提出的。我们提供了一套R包、在CRAN上可以使用的迷幻剂,以方便地应用这一技术。我们最后通过讨论可能扩大多个调解员和今后研究的方向。