Statistical methods for detecting and comparing periodic data and their application to the nycthemeral rhythm of bodily harm: A population based study

A statistical method for detecting periodic patterns in time-related data via harmonic regression is described. The method is particularly capable of detecting nycthemeral rhythms in medical data. Additionally a method for simultaneously comparing two or more periodic patterns is described, which derives from the analysis of variance (ANOVA). This method statistically confirms or rejects equality of periodic patterns. Mathematical descriptions of the detecting method and the comparing method are displayed.Nycthemeral rhythms of incidents of bodily harm in Middle Franconia are analyzed in order to demonstrate both methods. Every day of the week showed a significant nycthemeral rhythm of bodily harm. These seven patterns of the week were compared to each other revealing only two different nycthemeral rhythms, one for Friday and Saturday and one for the other weekdays.Analysis of biological activities that fluctuate throughout the day is common in various fields of medicine. Blood pressure and heart rate as well as the occurrence of acute cardiovascular disease are subject to a twenty-four hour rhythm (also referred to as circadian or nycthemeral rhythm) [1,2]. This rhythm is also present in episodes of dyspnoea in nocturnal asthma [3], intraocular pressure [4,5], and hormonal pulses [6-8]. Nycthemeral fluctuations in neurotransmitters and hormones have been discussed as influencing human behavior [9-11]. Suicide as well as parasuicide and violence against the person show day-night variation [12-14]. Assaults presenting to trauma centers display a distinct nycthemeral pattern [8-12]. In this study the nycthemeral rhythm of violent crime rates is analyzed to demonstrate a detection method and a comparison method suitable for twenty-four hour time series, but not limited to this sampling period.Much mathematical effort was invested to detect and model the dependency on the time of day [15-19]. A classification of the data by identifying similarities and distinctions requ