Complications of applying approximate entropy to heart rate variability to locate optimal complexity in children with attention deficit hyperactivity disorder - Garner, David M.; de Carvalho, Tatiana Dias; Wajnsztejn, Rubens; Vanderlei, Luiz Carlos Marques [UNESP]; Valenti, Vitor Engracia [UNESP]; de Abreu, Luiz Carlos; Raimundo, Rodrigo Daminello (Springer Nature, 2025)
Introduction: The aim is to scrutinize approximate entropy (ApEn) to distinguish optimal complexity of heart rate variability (HRV) in children diagnosed with attention deficit hyperactivity disorder (ADHD). This was accomplished by varying their embedding dimension m and tolerance r. Determination of optimal m and r is heuristic. ApEn was enforced in ADHD to assess its effects on the HRV chaotic response. Methods: We studied 56 children divided equally into two groups: ADHD and control. Autonomic modulation of the heart rate was monitored for 20 min in the supine position without any physical, sensory or pharmacological stimuli. ApEn initially had r: 0.1 → 1.0 in 0.1 intervals and m: 1 → 10 in intervals of 1. The statistical significances were measured by three effect sizes: Cohen’s d, Hedges’ g and Glass’s Δ. Results: Those most statistically important were for r = 0.9334, and m = 1, 2 and 3. Cohen’s d (1.1277; m = 2) and Hedges’ g (1.1119; m = 2) are the most reliable effect sizes. Glass’s Δ (1.3724; m = 1) is unfortunately less reliable. ROC curve analysis shows AUC > 0.77 for r = 0.9334 and m = 1, 2, and 3. Conclusion: ApEn recognized the increased chaotic response in ADHD. This was confirmed by three effect sizes, AUC and p value during ROC analysis. Still, ApEn is an unreliable mathematical marker. ADHD discrimination was only achieved by extending the surveillance ranges for r; 0.8 → 1.0 and m; 1 → 3 at intervals of 0.0167. This necessitates an ‘a priori’ study making it inapt for online analysis. Even so, it could be useful in ‘post hoc’ analysis.
Keywords: Approximate entropy; Attention deficit hyperactivity disorder; Effect sizes; Embedding dimensions; Heart rate variability; Tolerances