An Improved Method of Handling Missing Values in the Analysis of Sample Entropy for Continuous Monitoring of Physiological Signals

Abstract

Medical devices generate huge amounts of continuous time series data. However, missing values commonly found in these data can prevent us from directly using analytic methods such as sample entropy to reveal the information contained in these data. To minimize the influence of missing points on the calculation of sample entropy, we propose a new method to handle missing values in continuous time series data. We use both experimental and simulated datasets to compare the performance (in percentage error) of our proposed method with three currently used methods: skipping the missing values, linear interpolation, and bootstrapping. Unlike the methods that involve modifying the input data, our method modifies the calculation process. This keeps the data unchanged which is less intrusive to the structure of the data. The results demonstrate that our method has a consistent lower average percentage error than other three commonly used methods in multiple common physiological signals. For missing values in common physiological signal type, different data size and generating mechanism, our method can more accurately extract the information contained in continuously monitored data than traditional methods. So it may serve as an effective tool for handling missing values and may have broad utility in analyzing sample entropy for common physiological signals. This could help develop new tools for disease diagnosis and evaluation of treatment effects.

Keywords: complexity; medical information; missing values; physiological data; sample entropy.

Figure A1

Percentage errors for each method in three types of continuously monitoring physiological signals: blood glucose level (top panel), RR interval (middle panel), air flow (bottom panel). Each panel includes three conditions: r = 0.1 × σ (left), r = 0.15 × σ (middle) and r = 0.2 × σ (right). Values are given as means ± standard deviation. The results for BootSampEn are not shown in the Figure 2 when the percentage error is too large and out of range of the figure.

Figure 1

Two schemes for generating missing values.

Figure 2

Performance of methods for handling missing values in four types of continuously monitoring physiological signals: air flow (left), blood glucose level (middle left-skewed), EEG (middle right-skewed), RR interval (right). Values are given as means ± standard deviation. The results for BootSampEn are not shown in the Figure 2 when the percentage error is too large and out of range of the figure.

Figure 3

Average percentage errors for each method in four types of continuously monitoring physiological signals: air flow (left), blood glucose level (middle left-skewed), RR interval (right). The percentage errors by BootSampEn in the left and middle panels are higher than 120% and are not shown in the figure. Values are given as means ± standard error. NS means p > 0.05, * means p < 0.05, ** means p < 0.01, *** means p < 0.001.

Figure 4

Performance of methods for handling missing values in air flow time series of nine large data sizes. Values are given as mean ± standard deviation. The percentage error for BootSampEn is out of the range and not shown in the figure.

Figure 5

Performance of methods for handling missing values in a dataset with a small size (i.e., less than 2000 data points) for four types of physiological signals (i.e., air flow, blood glucose level, EEG and RR interval. Values are given as mean ± standard deviation. The percentage error for BootSampEn is out of the range and not shown in the figure.

Figure 6

Percentage errors for each method using random sample marking and group-based random marking schemes to generate missing values, respectively. Values are given as mean±standard deviation. The percentage error for BootSampEn is out of the range and not shown in the figure.

Figure 7

Evaluation of the running time of four methods for handling missing values. Each method is run on five values of percentage of missing values (i.e., 10%, 20%, 30%, 40% and 50%) on the air flow dataset. The running time for them are summed up to be the total running time. This process is repeated 10 times. The average total running time for the 10 repeats is shown in the y-axis. Values are given as mean ± standard deviation. Note, the standard deviation is tiny so that it can hardly been seen in the figure.