Disentangling personalized treatment effects from "time-of-the-day" confounding in mobile health studies

Ideally, a patient's response to medication can be monitored by measuring changes in performance of some activity. In observational studies, however, any detected association between treatment ("on-medication" vs "off-medication") and the outcome (performance in the activity) might be due to confounders. In particular, causal inferences at the personalized level are especially vulnerable to confounding effects that arise in a cyclic fashion. For quick acting medications, effects can be confounded by circadian rhythms and daily routines. Using the time-of-the-day as a surrogate for these confounders and the performance measurements as captured on a smartphone, we propose a personalized statistical approach to disentangle putative treatment and "time-of-the-day" effects, that leverages conditional independence relations spanned by causal graphical models involving the treatment, time-of-the-day, and outcome variables. Our approach is based on conditional independence tests implemented via standard and temporal linear regression models. Using synthetic data, we investigate when and how residual autocorrelation can affect the standard tests, and how time series modeling (namely, ARIMA and robust regression via HAC covariance matrix estimators) can remedy these issues. In particular, our simulations illustrate that when patients perform their activities in a paired fashion, positive autocorrelation can lead to conservative results for the standard regression approach (i.e., lead to deflated true positive detection), whereas negative autocorrelation can lead to anticonservative behavior (i.e., lead to inflated false positive detection). The adoption of time series methods, on the other hand, leads to well controlled type I error rates. We illustrate the application of our methodology with data from a Parkinson's disease mobile health study.