  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.
