Assessing Seasonality Variation with Harmonic Regression: Accommodations for Sharp Peaks

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.

An analecta of visualizations for foodborne illness trends and seasonality

“…Measures of uncertainty enable formal testing and comparisons across diseases in the same location or locations for the same disease. In our previous works, we have demonstrated the broad utility of the δ-method and applications of peak timing and amplitude estimation in the context of epidemiological studies 6,29,[56][57][58][59][60][61][62] .…”

How Seasonality of Malnutrition Is Measured and Analyzed

“…Seasonality has been a critical component of research and programming around agriculture [ 18 ] and infectious diseases [ 26 , 29 , 30 , 31 , 32 , 33 ], but less so when it comes to nutrition. However, there is a growing body of evidence that aims to quantify the seasonality of acute malnutrition in drylands with a mix of different design and analytical approaches.…”

“…A handful of studies (4), on the other hand, utilized random-, fixed-, or mixed-effects modeling, treating time as a continuous variable and thus avoiding some of the built-in assumptions present with categorical data. Two of these studies applied harmonic regression analysis typical of epidemiology and used in the modeling of infectious diseases [ 26 , 31 , 38 ]. However, both studies limited the model to the inclusion of 2π sine and cosine terms that refer to a single seasonal peak and thus could not accommodate a more complex form in seasonal variations relevant to food security concepts.…”

“…Given that acute malnutrition is a symptom of disease [ 3 , 23 ], a cause of disease [ 24 , 25 ], and shows significant with-in year variability [ 11 ] similar to infectious diseases, we draw on analytical applications from the field of epidemiology that model and forecast oscillations in disease. Seasonality in the epidemiology literature is characterized by the magnitude, timing, and duration [ 26 ] of seasonal increases and thus requires sufficiently frequent observations, analyzed as a continuous variable, in order to capture those components and establish an understanding of seasonality. The use of a categorical time variable in both the design and analysis stage does not correspond to the reality of climatic variability, the relationship between that climatic variability and human activities, and instead might inadvertently support existing assumptions instead of contributing to a robust evidence base.…”

Effects of Data Aggregation on Time Series Analysis of Seasonal Infections

“…While it could be easier sometimes to illustrate a technique using simulated data with well-predefined properties [ 42 ], we intentionally selected a real-life data set that is rich in complexity. With these data, we show the challenges that are common but rarely addressed in epidemiological data analysis.…”