Assessing Seasonality Variation with Harmonic Regression: Accommodations for Sharp Peaks.

Elena N. Naumova,Shalini Anandan,Kavitha Ramanathan,Balaji Veeraraghavan,Lakshmanan Jeyaseelan,Mani Thenmozhi,Sebastian George

doi:10.3390/ijerph17041318

Abstract

The use of the harmonic regression model is well accepted in the epidemiological and biostatistical communities as a standard procedure to examine seasonal patterns in disease occurrence. While these models may provide good fit to periodic patterns with relatively symmetric rises and falls, for some diseases the incidence fluctuates in a more complex manner. We propose a two-step harmonic regression approach to improve the model fit for data exhibiting sharp seasonal peaks. To capture such specific behavior, we first build a basic model and estimate the seasonal peak. At the second step, we apply an extended model using sine and cosine transform functions. These newly proposed functions mimic a quadratic term in the harmonic regression models and thus allow us to better fit the seasonal spikes. We illustrate the proposed method using actual and simulated data and recommend the new approach to assess seasonality in a broad spectrum of diseases manifesting sharp seasonal peaks.

Highlights

Understanding temporal changes in disease occurrence in human populations is one of priorities in epidemiology, public health, and life science related disciplines
The conceptual framework to describe periodic oscillations is expressed as Zt = μ + γ cos(2πωt + φ) + εt where, Zt is a time series of an outcome of interests measured at time t, t = 1, 2,...., N with N—An effective length of a time series; μ is the constant reflecting the general baseline of Zt ; the periodic component has a frequency of ω, an amplitude of γ, and a phase angle of φ; and εt, are independently and identically distributed normal random variables with E[εt ] = 0 and Var[εt ] = σ2
With the simulation we have introduced seasonality, trend using auto regression (AR) and moving average (MA) parameter values and the performance of the new model was compared with commonly used model

Summary

Introduction

Understanding temporal changes in disease occurrence in human populations is one of priorities in epidemiology, public health, and life science related disciplines. This lofty goal implies ability to describe, quantify, and examine temporal patterns, which include increasing or declining trends, seasonal patterns, unusual spikes associated with outbreaks or disappearance of periodic episodes that mark disease eradication. It is well known that majority of infections exhibit strong seasonal patterns in disease incidence or prevalence [3,4,5,6,7,8,9,10,11]. Our own work illustrate that infections caused by bacteria, like Vibrio cholerae [4]

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