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

Mobile health studies can leverage longitudinal sensor data from smartphones to guide the application of personalized medical interventions. In this paper, we propose that adoption of an instrumental variable approach for randomized trials with imperfect compliance provides a natural framework for personalized causal inference of medication response in mobile health studies. Randomized treatment suggestions can be easily delivered to the study participants via electronic messages popping up on the smart-phone screen. Under quite general assumptions we can identify the causal effect of the actual treatment on the response in the presence of unobserved confounders. We implement a personalized randomization test of the null hypothesis of no causal effect of treatment on response, and evaluate its performance in a large scale simulation study encompassing data generated from linear and non-linear time series models under several simulation conditions. In particular, we evaluate the empirical power of the proposed test under varying degrees of compliance between the suggested and actual treatment adopted by the participant. Our investigations provide encouraging results in terms of power and control of type I error rates. Finally, we compare the proposed instrumental variable approach to a simple intent-to-treat strategy, and develop randomization confidence intervals for the causal effects.