Fever Time Series Analysis Using Slope Entropy. Application to Early Unobtrusive Differential Diagnosis

Figures

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  Figure 1. Block diagram of the study. Body temperature records from dengue and malaria patients were recorded over 24 h. The corresponding time series were processed using Slope Entropy, and then classified using a single threshold obtained from the Receiver Operating Characteristic (ROC) Curve. The performance was assessed using the Matthews Correlation Coefficient.

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  Figure 2. Example of body temperature records from the experimental dataset. Bottom record corresponds to a dengue patient. Top record corresponds to a malaria patient.

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  Figure 3. Heat map featuring the values of MCC achieved for different m and γ values of SlopEn. δ was kept constant at 1×10−6. The region of highest performance in terms of MCC lay in the region m = 6, 7, and γ=[0.25,0,35]. There was a reverse region in the vicinity of m=4 and similar γ values. Except for m=5 and high γ values, the performance seemed to be high and stable. Instead of using the peak parameter values (m=6,γ=0.27, MCC =0.9529, only two points with this performance), a more centred and stable region was selected (m=6,γ=0.25, MCC =0.9066, with 24 points with this performance in the vicinity of that specific parameter configuration) for the experiments.

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  Figure 4. Cloud plot of the two classes under analysis, dengue and malaria. Dengue records had a significant lower SlopEn values than malaria records. The separability of these two types of temperature records is visually very apparent, as confirmed by the numerical result of MCC (0.9066) for m=6 and γ=0.25.

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  Figure 5. Length (N) analysis results. Instead of using the entire records, shorter versions were used in this analysis. Starting at 60 samples long, length was progressively increased in 60 samples steps. With lengths slightly above 200 samples, the MCC obtained was very high already, that is, the records were clearly separable using only 3–4 h of temperature data.

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  Figure 6. Sliding window analysis results. Using a moving window of 240 samples, this analysis shows the MCC achieved depending on the location of such window at 60 samples steps. Two performance peaks become apparent at locations close to sample 200 and sample 800. It could be hypothesized that fever patterns are not equally different at any point in a 24 h cycle, and there are regions where differences become more apparent.

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  Figure 7. Comparison between pairs of diseases: dengue, malaria, malignancy, and leptospirosis. It has to be noted that the above results were achieved using different input parameter configurations. (a) Comparison of dengue and leptospirosis results. (b) Comparison of malaria and leptospirosis results. In this case, the performance is lower. In addition, the points are very close, which makes it difficult to see the possible separability, despite the numerical results in this regard. (c) Comparison of dengue and malignancy results. (d) Comparison of malaria and malignancy results. As in Figure 7b, the performance is lower and more than a single point falls almost in the same spot, giving the impression the classification error is higher, despite having only two incorrectly classified records for malaria, and 1 for malignancy.