Inference for Longitudinal Data After Adaptive Sampling

Abstract: Adaptive sampling methods, such as reinforcement learning (RL) and bandit algorithms, are increasingly used for the real-time personalization of interventions in digital applications like mobile health and education. As a result, there is a need to be able to use the resulting adaptively collected user data to address a variety of inferential questions, including questions about time-varying causal effects. However, current methods for statistical inference on such data (a) make strong assumptions regarding the environment dynamics, e.g., assume the longitudinal data follows a Markovian process, or (b) require data to be collected with one adaptive sampling algorithm per user, which excludes algorithms that learn to select actions using data collected from multiple users. These are major obstacles preventing the use of adaptive sampling algorithms more widely in practice. In this work, we proved statistical inference for the common Z-estimator based on adaptively sampled data. The inference is valid even when observations are non-stationary and highly dependent over time, and (b) allow the online adaptive sampling algorithm to learn using the data of all users. Furthermore, our inference method is robust to miss-specification of the reward models used by the adaptive sampling algorithm. This work is motivated by our work in designing the Oralytics oral health clinical trial in which an RL algorithm will be used to select treatments, yet valid statistical inference is essential for conducting primary data analyses after the trial is over.

Bio:
Susan Murphy is the Mallinckrodt Professor of Statistics and of Computer Science, and the Radcliffe Alumnae Professor at the Radcliffe Institute at Harvard University. Her research focuses on improving sequential, individualized, decision making in digital health. She developed the micro-randomized trial for use in constructing digital health interventions; this trial design is in use across a broad range of health-related areas. Her lab works on online learning algorithms for developing personalized digital health interventions.  Dr. Murphy is a member of the National Academy of Sciences and of the National Academy of Medicine, both of the US National Academies.  In 2013 she was awarded a MacArthur Fellowship for her work on experimental designs to inform sequential decision making.  She is a Fellow of the College on Problems in Drug Dependence, Past-President of Institute of Mathematical Statistics, Past-President of the Bernoulli Society and a former editor of the Annals of Statistics.