Sample size calculations for micro-randomized trials in mHealth

Abstract

The use and development of mobile interventions are experiencing rapid growth. In "just-in-time" mobile interventions, treatments are provided via a mobile device, and they are intended to help an individual make healthy decisions 'in the moment,' and thus have a proximal, near future impact. Currently, the development of mobile interventions is proceeding at a much faster pace than that of associated data science methods. A first step toward developing data-based methods is to provide an experimental design for testing the proximal effects of these just-in-time treatments. In this paper, we propose a 'micro-randomized' trial design for this purpose. In a micro-randomized trial, treatments are sequentially randomized throughout the conduct of the study, with the result that each participant may be randomized at the 100s or 1000s of occasions at which a treatment might be provided. Further, we develop a test statistic for assessing the proximal effect of a treatment as well as an associated sample size calculator. We conduct simulation evaluations of the sample size calculator in various settings. Rules of thumb that might be used in designing a micro-randomized trial are discussed. This work is motivated by our collaboration on the HeartSteps mobile application designed to increase physical activity. Copyright © 2015 John Wiley & Sons, Ltd.

Keywords: health; mirco-randomized trial; sample size calculation.

Copyright © 2015 John Wiley & Sons, Ltd.

Figures

Figure 4

Conditional expectation of proximal response, E[Yt+1|It = 1]. The horizontal axis is the decision time point. The vertical axis is E[Yt+1|It = 1].

Figure 5

Proximal Main Effects of Treatment, {d(t)}t=1T: representing maintained, slightly degraded and severely degraded time-varying treatment effects. The horizontal axis is the decision time point. The vertical axis is the standardized treatment effect. The “Max” in the title refers to the day of maximal effect. The average standardized proximal effect is 0.1 in all plots.

Figure 1

Availability Patterns. The x-axis is decision time point and y-axis is the expected availability. Pattern 2 represents availability varying by day of the week with higher availability on the weekends and lower mid-week. The average availability is 0.5 in all cases.

Figure 2

Standardized Proximal Main Effects of Treatment, {d(t)}t=1T: representing maintained and severely degraded time-varying proximal treatment effects. The horizontal axis is the decision time point. The vertical axis is the standardized treatment effect. The “Max” in the titles refer to the day of maximal proximal effect. The average standardized proximal effect is d̄= 0.1 in all plots.

Figure 3

Trend of σ̄t : For all trends, σ¯t2 is scaled so that (1/T)∑t=1Tσ¯t2=1. In Trend 3, the variance, σ¯t2=E[Var[Yt+1∣It=1,At]] peaks on weekends. In particular, σ̄7k+i = 0.8 for i = 1, …,5 and σ̄7k+i = 1.5 for i = 6,7.