Detrended Fluctuation Analysis in the prediction of type 2 diabetes mellitus in patients at risk: Model optimization and comparison with other metrics.

Complexity analysis of glucose time series with Detrended Fluctuation Analysis (DFA) has been proved to be useful for the prediction of type 2 diabetes mellitus (T2DM) development. We propose a modified DFA algorithm, review some of its characteristics and compare it with other metrics derived from continuous glucose monitorization in this setting. Several issues of the DFA algorithm were evaluated: (1) Time windowing: the best predictive value was obtained including all time-windows from 15 minutes to 24 hours. (2) Influence of circadian rhythms: for 48-hour glucometries, DFA alpha scaling exponent was calculated on 24-hour sliding segments (1-hour gap, 23-hour overlap), with a median coefficient of variation of 3.2%, which suggests that analysing time series of at least 24-hour length avoids the influence of circadian rhythms. (3) Influence of pretreatment of the time series through integration: DFA without integration was more sensitive to the introduction of white noise and it showed significant predictive power to forecast the development of T2DM, while the pretreated time series did not. (4) Robustness of an interpolation algorithm for missing values: The modified DFA algorithm evaluates the percentage of missing values in a time series. Establishing a 2% error threshold, we estimated the number and length of missing segments that could be admitted to consider a time series as suitable for DFA analysis. For comparison with other metrics, a Principal Component Analysis was performed and the results neatly tease out four different components. The first vector carries information concerned with variability, the second represents mainly DFA alpha exponent, while the third and fourth vectors carry essentially information related to the two "pre-diabetic behaviours" (impaired fasting glucose and impaired glucose tolerance). The scaling exponent obtained with the modified DFA algorithm proposed has significant predictive power for the development of T2DM in a high-risk population compared with other variability metrics or with the standard DFA algorithm.