具有内生协变量的线性混合模型:对序贯治疗效果建模及其在移动健康研究中的应用
Linear mixed models with endogenous covariates: modeling sequential treatment effects with application to a mobile health study.
作者信息
Qian Tianchen, Klasnja Predrag, Murphy Susan A
机构信息
Department of Statistics, Harvard University, Cambridge, MA 02138.
School of Information, University of Michigan, Ann Arbor, MI 48109.
出版信息
Stat Sci. 2020;35(3):375-390. doi: 10.1214/19-sts720. Epub 2020 Sep 11.
Mobile health is a rapidly developing field in which behavioral treatments are delivered to individuals via wearables or smartphones to facilitate health-related behavior change. Micro-randomized trials (MRT) are an experimental design for developing mobile health interventions. In an MRT the treatments are randomized numerous times for each individual over course of the trial. Along with assessing treatment effects, behavioral scientists aim to understand between-person heterogeneity in the treatment effect. A natural approach is the familiar linear mixed model. However, directly applying linear mixed models is problematic because potential moderators of the treatment effect are frequently endogenous-that is, may depend on prior treatment. We discuss model interpretation and biases that arise in the absence of additional assumptions when endogenous covariates are included in a linear mixed model. In particular, when there are endogenous covariates, the coefficients no longer have the customary marginal interpretation. However, these coefficients still have a conditional-on-the-random-effect interpretation. We provide an additional assumption that, if true, allows scientists to use standard software to fit linear mixed model with endogenous covariates, and person-specific predictions of effects can be provided. As an illustration, we assess the effect of activity suggestion in the HeartSteps MRT and analyze the between-person treatment effect heterogeneity.
移动健康是一个快速发展的领域,在这个领域中,行为治疗通过可穿戴设备或智能手机提供给个人,以促进与健康相关的行为改变。微随机试验(MRT)是一种用于开发移动健康干预措施的实验设计。在微随机试验中,治疗在试验过程中针对每个个体进行多次随机分配。除了评估治疗效果外,行为科学家还旨在了解治疗效果在个体间的异质性。一种自然的方法是熟悉的线性混合模型。然而,直接应用线性混合模型存在问题,因为治疗效果的潜在调节因素通常是内生的,也就是说,可能取决于先前的治疗。我们讨论了在线性混合模型中包含内生协变量时,在没有额外假设的情况下出现的模型解释和偏差。特别是,当存在内生协变量时,系数不再具有惯常的边际解释。然而,这些系数仍然具有基于随机效应的条件解释。我们提供了一个额外的假设,如果该假设成立,科学家可以使用标准软件来拟合带有内生协变量的线性混合模型,并提供个体特异性的效果预测。作为一个例子,我们评估了“心脏步数”微随机试验中活动建议的效果,并分析了个体间治疗效果的异质性。