A Robust Functional EM Algorithm for Incomplete Panel Count Data
This work addresses missing data issues in panel count data for behavioral scientists, offering a robust method that is incremental as it builds upon existing EM theory and wraps popular inference methods.
The authors tackled the problem of missing data in panel count data, which hinders statistical learning in behavioral research, by proposing a functional EM algorithm that estimates the counting process mean function under MCAR assumptions, achieving robustness to misspecification and providing finite-sample guarantees.
Panel count data describes aggregated counts of recurrent events observed at discrete time points. To understand dynamics of health behaviors, the field of quantitative behavioral research has evolved to increasingly rely upon panel count data collected via multiple self reports, for example, about frequencies of smoking using in-the-moment surveys on mobile devices. However, missing reports are common and present a major barrier to downstream statistical learning. As a first step, under a missing completely at random assumption (MCAR), we propose a simple yet widely applicable functional EM algorithm to estimate the counting process mean function, which is of central interest to behavioral scientists. The proposed approach wraps several popular panel count inference methods, seamlessly deals with incomplete counts and is robust to misspecification of the Poisson process assumption. Theoretical analysis of the proposed algorithm provides finite-sample guarantees by expanding parametric EM theory to our general non-parametric setting. We illustrate the utility of the proposed algorithm through numerical experiments and an analysis of smoking cessation data. We also discuss useful extensions to address deviations from the MCAR assumption and covariate effects.