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Mobile health studies can leverage longitudinal sensor data from smartphonesto guide the application of personalized medical interventions. In this paper,we propose that adoption of an instrumental variable approach for randomizedtrials with imperfect compliance provides a natural framework for personalizedcausal inference of medication response in mobile health studies. Randomizedtreatment suggestions can be easily delivered to the study participants viaelectronic messages popping up on the smart-phone screen. Under quite generalassumptions we can identify the causal effect of the actual treatment on theresponse in the presence of unobserved confounders. We implement a personalizedrandomization test of the null hypothesis of no causal effect of treatment onresponse, and evaluate its performance in a large scale simulation studyencompassing data generated from linear and non-linear time series models underseveral simulation conditions. In particular, we evaluate the empirical powerof the proposed test under varying degrees of compliance between the suggestedand actual treatment adopted by the participant. Our investigations provideencouraging results in terms of power and control of type I error rates.Finally, we compare the proposed instrumental variable approach to a simpleintent-to-treat strategy, and develop randomization confidence intervals forthe causal effects.

Towards personalized causal inference of medication response in mobile  health: an instrumental variable approach for randomized trials with  imperfect compliance