Rényi and permutation entropy analysis for assessment of cardiac autonomic neuropathy

Cardiac autonomic neuropathy (CAN) is a complication of diabetes with a long asymptomatic phase that is associated with high morbidity and mortality. Early identification of CAN in Type 1 diabetes mellitus (T1DM) may be possible using heart rate variability (HRV). However, the power of HRV analysis to identify CAN depends on the selection of suitable features that provide reliable information regarding cardiac autonomic regulation. Our aim was to compare the performance of Rényi entropy (RE) and permutation entropy (PE) for identification of T1DM patients with CAN. RE and PE measures from 235 data points and 5 min of cardiac interbeat interval (RR) sequences were analysed in 18 T1DM patients without CAN, 14 T1DM patients with CAN, and healthy controls matched for age and sex. RE was calculated for different orders α (-5, 5), pattern lengths λ (2, 4, 8), and tolerance σ. For PE analysis λ was set to (3-4) and time delays τ to (1-10). A forward stepwise discriminant analysis was carried out for estimating the classification functions. Accuracy was estimated following a K-fold cross-validation (k = 14). RE calculated for RR sequences of λ = 2, α > 0 showed the best performance for differentiating T1DM patients with CAN (p < 0.0001). PE measures showed better performance with ordinal patterns and τ = 4, 5 and 7 for differentiating patients with CAN. RE and PE provide complementary information achieving 100% classification accuracy (p < 0.0001 and p < 0.001, respectively). This approach might be promising as a sensitive and specific tool for CAN diagnosis in T1DM.