# Within- and Between-Individual Compliance in Mobile Health: Joint Modeling Approach to Nonrandom Missingness in an Intensive Longitudinal Observational Study

## TL;DR

This paper introduces a joint modeling approach to handle missing data in mobile health studies by considering both within- and between-person factors, improving the accuracy of health behavior inferences.

## Contribution

The paper presents a novel joint modeling framework that simultaneously models health behavior and missingness mechanisms in intensive longitudinal mHealth data.

## Key findings

- Joint modeling revealed that higher self-reported energy levels predicted increased physical activity the following day.
- Lower physical activity levels were associated with higher missingness in physical activity data at the within-person level.
- Employment status was linked to higher missingness in device-tracked physical activity at the between-person level.

## Abstract

Missing data are inevitable in mobile health (mHealth) and ubiquitous health (uHealth) research and are often driven by distinct within- and between-person factors that influence compliance. Understanding these distinct mechanisms underlying nonresponse can inform strategies to improve compliance and strengthen the validity of inferences about health behaviors. However, current missing data handling techniques rarely disentangle these different sources of nonresponse, especially when data are missing not at random.

We demonstrate the usability of joint modeling in the mHealth context, showing how simultaneously accounting for the dynamics of health behavior and both within- and between-person missingness mechanisms can affect the validity of health behavior inferences. We also illustrate how joint modeling can inform distinct sources of (possibly nonignorable) missingness in studies using ecological momentary assessment and wearable devices. We provide a practical workflow for applying joint models to empirical data.

We applied joint modeling on empirical data comprising 1 year of daily smartphone-based ecological momentary assessment data (affect and energetic feeling) and smartwatch-tracked physical activity (PA). The approach combined (1) a multilevel vector autoregressive model for examining the reciprocal influences between daily affect and PA, and (2) a multilevel probit model for missingness. Unlike conventional 2-stage imputation methods—which first impute missing data before fitting the main model—joint modeling handles missingness during model fitting without explicit imputation. Sensitivity analyses compared results from the proposed method to other missing data approaches that do not explicitly model missingness. A simulation study designed to mirror the temporally clustered (eg, consecutive days of missing data) and person-specific missingness patterns of the empirical data validated the feasibility of the proposed approach.

Sensitivity analysis indicated relative robustness of the autoregressive effects across missing data handling approaches, whereas cross-regressive effects could be detected only under the joint modeling but not with methods that did not simultaneously model missingness mechanisms. Specifically, under joint modeling approaches, participants had higher levels of PA on days following a previous day with higher self-report energy levels (95% credible interval [CrI] 0.012-0.049). Furthermore, the missing data model revealed both missing not at random and missing at random mechanisms. For example, lower PA predicted higher missingness in PA at the within-person level (95% CrI –1.528 to –1.441). Being employed was associated with higher missingness in device-tracked PA at the between-person level (95% CrI 0.148-0.574). Finally, simulation showed that joint modeling could improve the accuracy of estimates and identify nonignorable missingness.

We recommend joint modeling with multilevel decomposition for addressing nonignorable missingness in mHealth/uHealth studies collecting intensive longitudinal data. We also suggest using a missing data model to explore the missingness mechanism and inform data collection strategies.