Determining sample size and length of follow-up for smartphone-based digital phenotyping studies

Abstract

Objective: Studies that use patient smartphones to collect ecological momentary assessment and sensor data, an approach frequently referred to as digital phenotyping, have increased in popularity in recent years. There is a lack of formal guidelines for the design of new digital phenotyping studies so that they are powered to detect both population-level longitudinal associations as well as individual-level change points in multivariate time series. In particular, determining the appropriate balance of sample size relative to the targeted duration of follow-up is a challenge.

Materials and methods: We used data from 2 prior smartphone-based digital phenotyping studies to provide reasonable ranges of effect size and parameters. We considered likelihood ratio tests for generalized linear mixed models as well as for change point detection of individual-level multivariate time series.

Results: We propose a joint procedure for sequentially calculating first an appropriate length of follow-up and then a necessary minimum sample size required to provide adequate power. In addition, we developed an accompanying accessible sample size and power calculator.

Discussion: The 2-parameter problem of identifying both an appropriate sample size and duration of follow-up for a longitudinal study requires the simultaneous consideration of 2 analysis methods during study design.

Conclusion: The temporally dense longitudinal data collected by digital phenotyping studies may warrant a variety of applicable analysis choices. Our use of generalized linear mixed models as well as change point detection to guide sample size and study duration calculations provide a tool to effectively power new digital phenotyping studies.

Keywords: digital phenotyping; longitudinal studies; mobile health; sample size; study design.

Figure 1.

Length of follow-up in relation to the power to detect change points in individual-level analysis. Power to detect a change point in the $p$ daily behavioral digital phenotyping features that occurs $m$ days in the past (ie, only $m$ days of data post-change point, are simulated using 10 000 iterations for each point on the $T$ axis). The dotted line represents large behavioral changes and the solid line represents smaller behavioral changes.

Figure 2.

Sample size and follow-up duration in relation to the power of association tests in population-level analysis. Simulations based on the number of days where both predictor and outcome are collected. For each power level and each fixed $T$, sample size was varied using a binary search with 500 iterations at each step in order to identify the sample size that led to the desired power.