Handling of outcome missing data dependent on measured or unmeasured background factors in micro-randomized trial: Simulation and application study

Abstract

Background: Micro-randomized trials (MRTs) enhance the effects of mHealth by determining the optimal components, timings, and frequency of interventions. Appropriate handling of missing values is crucial in clinical research; however, it remains insufficiently explored in the context of MRTs. Our study aimed to investigate appropriate methods for missing data in simple MRTs with uniform intervention randomization and no time-dependent covariates. We focused on outcome missing data depending on the participants' background factors.

Methods: We evaluated the performance of the available data analysis (AD) and the multiple imputation in generalized estimating equations (GEE) and random effects model (RE) through simulations. The scenarios were examined based on the presence of unmeasured background factors and the presence of interaction effects. We conducted the regression and propensity score methods as multiple imputation. These missing data handling methods were also applied to actual MRT data.

Results: Without the interaction effect, AD was biased for GEE, but there was almost no bias for RE. With the interaction effect, estimates were biased for both. For multiple imputation, regression methods estimated without bias when the imputation models were correct, but bias occurred when the models were incorrect. However, this bias was reduced by including the random effects in the imputation model. In the propensity score method, bias occurred even when the missing probability model was correct.

Conclusions: Without the interaction effect, AD of RE was preferable. When employing GEE or anticipating interactions, we recommend the multiple imputation, especially with regression methods, including individual-level random effects.

Keywords: Micro-randomized trial; missing data; mobile app; mobile health; multiple imputation.

Figure 1.

Directed acyclic graph illustrating non-negligible bias generation mechanisms due to unmeasured background factors.

Figure 2.

Simulation results of mean point estimates ± average standard errors when all covariates were accounted for, there was no interaction, and the effects of covariates on missingness were (a) large and (b) small.

Figure 3.

Simulation results of mean point estimates ± average standard errors when only one covariate was accounted for, there was no interaction, and the effects of covariates on missingness were (a) large and (b) small. Values in parentheses are average standard errors.

Figure 4.

Simulation results of mean point estimates ± average standard errors when all covariates were accounted for, there was the interaction, and the effects of covariates on missingness were (a) large and (b) small.

Figure 5.

Simulation results of mean point estimates ± average standard errors when only one covariate was accounted for, there was the interaction, and the effects of covariates on missingness were (a) large and (b) small.