  Temporally dense single-person "small data" have become widely available
thanks to mobile apps and wearable sensors. Many caregivers and self-trackers
want to use these data to help a specific person change their behavior to
achieve desired health outcomes. Ideally, this involves discerning possible
causes from correlations using that person's own observational time series
data. In this paper, we estimate within-individual average treatment effects of
physical activity on sleep duration, and vice-versa. We introduce the model
twin randomization (MoTR; "motor") method for analyzing an individual's
intensive longitudinal data. Formally, MoTR is an application of the g-formula
(i.e., standardization, back-door adjustment) under serial interference. It
estimates stable recurring effects, as is done in n-of-1 trials and single case
experimental designs. We compare our approach to standard methods (with
possible confounding) to show how to use causal inference to make better
personalized recommendations for health behavior change, and analyze 222 days
of Fitbit sleep and steps data for one of the authors.
