Individualized Inference

Borrowing Information from Other Smartphone Users

Individualized inference has become an area of great interest across many fields. Personalized medicine seeks to estimate individualized effects treatments, exposures, and policies and to tailor interventions to individuals. Because sensors continuously record multiple measurements on individuals, they introduce the potential for increased precision in individualized estimation. However, the burden of collecting sensor data means that often only 1-2 weeks of data can be collected on a particular individual, inadequate for very high-precision estimation. In studies with many participants, borrowing information from other individuals can potentially lead to substantial variance reduction. However, conventional statistical methods that assume fully exchangeable sampling models (estimating an individual effect using everyone's data) are inadequate for combining information across potentially different individuals. This is an example of the bias-variance tradeoff - using only the individual's data has low bias and high variance, while using everyone's data has low variance and high bias.

Ideally we would like to borrow intelligently from other "similar" individuals, decreasing variance while introducing minimal bias. Many methods for integrating supplementary information have been developed in the context of borrowing historical data in clinical trials - weighted likelihoods, power priors, and commensurate priors are common examples. Another recently developed method, the multi-source exchangeability model (MEM) utilizes a Bayesian model averaging approach to enable data-driven up-weighting of the contribution from similar sources and down-weighting of that from dissimilar sources.

MEMs were designed in the context of clinical trials for borrowing in the presence of fewer than 10 supplementary studies. In studies with smartphone sensor data, there are often 100 or more supplementary individuals from which to borrow, making MEMs computationally infeasible. I have developed the iterated MEM (iMEM), an adaptation of MEMs which allows them to be fit in the presence of many supplementary sources, allowing for substantial (up to 99%) decrease in posterior standard deviation with minimal increase in bias.

A manuscript describing iMEM is currently under review, code implementing iMEMs can be found on my Github page, and slides describing iMEM from my Distinguished Student Paper Award talk at the ENAR 2019 Spring Meeting can be found below.