  We address the personalized policy learning problem using longitudinal mobile
health application usage data. Personalized policy represents a paradigm shift
from developing a single policy that may prescribe personalized decisions by
tailoring. Specifically, we aim to develop the best policy, one per user, based
on estimating random effects under generalized linear mixed model. With many
random effects, we consider new estimation method and penalized objective to
circumvent high-dimension integrals for marginal likelihood approximation. We
establish consistency and optimality of our method with endogenous app usage.
We apply our method to develop personalized push ("prompt") schedules in 294
app users, with a goal to maximize the prompt response rate given past app
usage and other contextual factors. We found the best push schedule given the
same covariates varied among the users, thus calling for personalized policies.
Using the estimated personalized policies would have achieved a mean prompt
response rate of 23% in these users at 16 weeks or later: this is a remarkable
improvement on the observed rate (11%), while the literature suggests 3%-15%
user engagement at 3 months after download. The proposed method compares
favorably to existing estimation methods including using the R function "glmer"
in a simulation study.
