Classifying attention deficit hyperactivity disorder in children with non-linearities in actigraphy

Objective This study provides an objective measure based on actigraphy for Attention Deficit Hyperactivity Disorder (ADHD) diagnosis in children. We search for motor activity features that could allow further investigation into their association with other neurophysiological disordered traits. Method The study involved $n=29$ (48 eligible) male participants aged $9.89\pm0.92$ years (8 controls, and 7 in each group: ADHD combined subtype, ADHD hyperactive-impulsive subtype, and autism spectrum disorder, ASD) wearing a wristwatch actigraph continuously for a week ($9\%$ losses in daily records) in two acquisition modes. We analyzed 47 quantities: from sleep duration or movement intensity to theory-driven scaling exponents or non-linear prediction errors of both diurnal and nocturnal activity. We used them in supervised classification to obtain cross-validated diagnostic performance. Results We report the best performing measures, including a nearest neighbors 4-feature classifier providing $69.4\pm1.6\%$ accuracy, $78.0\pm2.2\%$ sensitivity and $60.8\pm2.6\%$ specificity in a binary ADHD vs control classification and $46.5\pm1.1\%$ accuracy (against $25\%$ baseline), $61.8\pm1.4\%$ sensitivity and $79.30 \pm0.43\%$ specificity in 4-class task (two ADHD subtypes, ASD, and control). The most informative feature is skewness of the shape of Zero Crossing Mode (ZCM) activity. Mean and standard deviation of nocturnal activity are among the least informative. Conclusion Actigraphy causes only minor discomfort to the subjects and is inexpensive. The range of existing mathematical and machine learning tools also allow it to be a useful add-on test for ADHD or differential diagnosis between ADHD subtypes. The study was limited to a small, male sample without the inattentive ADHD subtype.