Joint Modeling of Between- and Within-Individual Sources of Non-Random Missingness in mHealth: Empirical and Simulation Study (Preprint)
Authors: Cho Young Won , Chow Sy-Miin , Li Jixin , Wang Wei-Lin , Wang Shirlene , Ji Linying , Chinchilli Vernon M. , Intille Stephen S. , Dunton Genevieve Fridlund 
Published: October 2024

BACKGROUND

Missing data are inevitable in mHealth research and driven by both within- and between-person variations in compliance levels. Not distinguishing these different sources can lead to biases in health behavior inferences. However, current missing data handling techniques do not address disentangling these distinct missingness mechanisms. Compared to missingness at random (MAR), missingness not at random (MNAR) is particularly concerning—often termed non-ignorable missingness.

OBJECTIVE

We demonstrate the utility of a joint modeling approach that simultaneously accommodates dynamics of health behavior changes as well as within- and between-person missingness mechanisms. We also evaluate how conflating these distinct contributors of (possibly non-ignorable) missingness affects the validity of health behavior inferences. We provide practical recommendations for building such joint models with empirical data.

METHODS

We applied a joint model on empirical data comprising one year of daily observations of affect (i.e., feeling energetic) reported through smartphone- based ecological momentary assessment (EMA) and smartwatch-tracked physical activity (PA). We implemented a joint modeling approach combining (1) a multilevel vector autoregressive (VAR) model for examining the reciprocal influences between daily affect and PA, and (2) a multilevel probit model for missingness mechanisms. As a sensitivity analysis, we compared the results from the proposed approach against other methods that examined health behavior changes without simultaneously modeling missingness mechanisms. Additionally, we validated the joint modeling approach through simulated data mirroring missing data patterns observed in empirical data: temporally clustered (e.g., consecutive days of) missingness and across-individual heterogeneity in compliance rates.

RESULTS

Sensitivity analysis indicated relative robustness of the autoregressive (AR) effects across missing data handling approaches, whereas cross-regressive (CR) effects could only be detected under the joint modeling, but not with methods that did not simultaneously model the missingness mechanism. Specifically, under the joint modeling, participants had higher levels of PA on days following a previous day with higher energy levels (95% CI=[0.012, 0.049]), and a higher level of PA on one day was associated with higher energy levels the next day (95% CI=[0.006, 0.054]). Furthermore, the missing data model revealed both MAR and MNAR missing mechanisms. For example, lower PA was linked with higher missingness in PA at the within-person level (95% CI=[-1.528, -1.441]). Employment status was associated with compliance in wearables data (95% CI=[0.148, 0.574]). Finally, simulation studies demonstrated that joint modeling improves the accuracy of the substantive model’s estimate and identifies non-ignorable missing mechanisms effectively.

CONCLUSIONS

We recommend utilizing joint modeling, particularly with multilevel decomposition to address non-ignorable missingness in mHealth studies collecting intensive longitudinal data. Simulation study showed joint modeling yielded results as accurate as those from fully observed data and enhanced understanding of within- and between-individual sources of missingness.