Abstract
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.
Highlights
Mobile health refers to the use of mobile phones and other wireless devices to improve health outcomes, often by providing individuals with support for health-related behavior change
We provide an additional assumption under which valid estimates of the effect of the time-varying treatment, estimates of the variance components, and person-specific predictions of these treatment effects can be obtained through standard linear mixed models (LMM) software, even if some covariates are endogenous
We argued that the fundamental issue in LMM with endogenous covariates is that the fixed effects, including the treatment effect, will only have a conditional-on-the-random-effect interpretation, and the marginal interpretation is no longer valid
Summary
Mobile health (mHealth) refers to the use of mobile phones and other wireless devices to improve health outcomes, often by providing individuals with support for health-related behavior change. Micro-randomized trials (MRTs) provide an experimental design for developing mHealth interventions These trials provide longitudinal data to assess whether there is an effect of a time-varying. Despite losing the marginal interpretation, the conditional interpretation of the parameters is consistent with scientific interest in the prediction of person-specific effects in MRTs. Here we propose to interpret treatment effects as conditional on the random effect in LMM with possibly endogenous covariates. We provide an additional assumption under which valid estimates of the effect (conditional on the random effect) of the time-varying treatment, estimates of the variance components, and person-specific predictions of these treatment effects can be obtained through standard LMM software, even if some covariates are endogenous.
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