Missing Data Statistics Provide Causal Insights into Data Loss in Diabetes Health Monitoring by Wearable Sensors

Abstract

Background: Data loss in wearable sensors is an inevitable problem that leads to misrepresentation during diabetes health monitoring. We systematically investigated missing wearable sensors data to get causal insight into the mechanisms leading to missing data.

Methods: Two-week-long data from a continuous glucose monitor and a Fitbit activity tracker recording heart rate (HR) and step count in free-living patients with type 2 diabetes mellitus were used. The gap size distribution was fitted with a Planck distribution to test for missing not at random (MNAR) and a difference between distributions was tested with a Chi-squared test. Significant missing data dispersion over time was tested with the Kruskal-Wallis test and Dunn post hoc analysis.

Results: Data from 77 subjects resulted in 73 cleaned glucose, 70 HR and 68 step count recordings. The glucose gap sizes followed a Planck distribution. HR and step count gap frequency differed significantly (p < 0.001), and the missing data were therefore MNAR. In glucose, more missing data were found in the night (23:00-01:00), and in step count, more at measurement days 6 and 7 (p < 0.001). In both cases, missing data were caused by insufficient frequency of data synchronization.

Conclusions: Our novel approach of investigating missing data statistics revealed the mechanisms for missing data in Fitbit and CGM data.

Keywords: activity trackers; biomedical sensors; continuous glucose monitoring; health monitoring; heart rate; missing data; signal processing; vital signs; wearable sensors.

Figure 1

Overview of the data processing steps.

Figure 2

Overview of the tests to determine the missing data mechanism in continuous data using missing data statistics. MAR = missing at random, MCAR = missing completely at random, MNAR = missing not at random.

Figure 3

Gap size probability distribution (light grey) with the fitted Planck probability mass function (pmf) in dark grey for the three types of data. (a) Glucose gap frequency of glucose data with Planck pmf. (b) Heart rate gap frequency with fitted Planck and Zipf pmf in orange. (c) Step count gap frequency with Planck pmf, which starts at 16 samples due to the step count pre-processing.

Figure 4

Three missing data dispersions over time in the left panels with (in red) the ratio of missing data. In the right panels, the subsequent Dunn post hoc analysis. (a) Missing data dispersion in glucose data in hours of the day and (b) post hoc analysis to test for differences in glucose data between hours of the day. (c) Missing data dispersion in heart rate data over measurement days and (d) post hoc analysis for test differences between heart rate measurement days. (e) Missing data dispersion in step count data over measurement day and (f) post hoc analysis for test differences between step count measurement days.

Figure 5

The missing data dispersion (left panels) and corresponding post hoc analysis (right panels) of missing data for every hour of the day in missing data subgroups. In (a,c,e), the red bars indicate the median ratio of missing data, and the error bars indicate the IQR. (a) Missing dispersion for hour of the day in group <10% missing data in glucose data. (b) Post hoc analysis for hour of the day in group <10% missing data in glucose data. (c) Missing dispersion for hour of the day in group 10–20% missing data in glucose data. (d) Post hoc analysis for hour of the day in group 10–20% missing data in glucose data. (e) Missing dispersion for hour of the day in group >20% missing data in glucose data. (f) Post hoc analysis for hour of the day in group >20% missing data in glucose data.

Figure 6

Missing data distribution (left panels) in glucose data in the subgroups based on years of type 2 diabetes diagnosis for every hour of the day and corresponding post hoc analysis (right panels). In (a,c,e), the red bars indicate the median ratio of missing data, and the error bars are the IQR. (a) Glucose missing data dispersion for every hour of the day in subgroup <10 years since diagnosis of type 2 diabetes (n = 33). (b) Post hoc analysis for hour of the day dispersion in <10 years since diagnosis of type 2 diabetes. (c) Glucose missing dispersion for every hour of the day in subgroup 10–20 years since diagnosis of type 2 diabetes (n = 25). (d) Post hoc analysis for hour of the day dispersion in 10–20 years since diagnosis of type 2 diabetes. (e) Glucose missing dispersion for every hour of the day in subgroup >20 years since diagnosis of type 2 diabetes (n = 16). (f) Post hoc analysis for hour of the day dispersion in >20 years since diagnosis of type 2 diabetes.