Distributional Data Analysis via Quantile Functions and Its Application to Modeling Digital Biomarkers

• Activity Number: 45 - Recent Development in Mobile/Wearable Device Data Analysis
• Type: Invited
• Date/Time: Sunday, August 7, 2022 : 4:00 PM to 5:50 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Vadim Zipunnikov* and Rahul Ghosal
• Companies: Johns Hopkins University, Bloomberg School of Public Health and Johns Hopkins University, Bloomberg School of Public Health
• Keywords: distributional data; functional data; quantile functions

Abstract

With the advent of continuous health monitoring with wearable devices, users now generate their unique streams of continuous data such as minute-level step counts or heartbeats. Summarizing these streams via scalar summaries often ignores the distributional nature of wearable data and almost unavoidably leads to the loss of critical information. We propose to capture the distributional nature of wearable data via user-specific quantile functions (QF). We will talk about several recently developed models where QFs are used as predictors or outcomes. When QFs are predictors, we decompose them via L-moments and construct two alternative but mutually consistent regression models that provide interpretation either via moments and via quantile levels. When QFs are outcomes, we propose a constrained regression framework that accounts for non-decreasing nature of the QF outcome.