📊 epidemiology

Mortality Baselines and Excess Mortality Events in Belgian and Greek Cities Using Singular Spectrum Analysis

This study utilizes Singular Spectrum Analysis with automated component selection and outlier interpolation to establish reproducible mortality baselines for six Belgian and Greek cities, revealing that while pandemic periods accounted for the majority of excess deaths, a significant number of events remained unexplained by temperature extremes or known epidemics.

Original authors: Delforge, D., Charalampous, P., Bustos Sierra, N., De Clercq, E., Katragkou, E., Konstantinoudis, G., Kostoulas, P., Lambrou, A., Masquelier, B., Paraskevis, D., Thiery, W., Tonnelier, M., Speybroeck

Published 2026-10-07

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Delforge, D., Charalampous, P., Bustos Sierra, N., De Clercq, E., Katragkou, E., Konstantinoudis, G., Kostoulas, P., Lambrou, A., Masquelier, B., Paraskevis, D., Thiery, W., Tonnelier, M., Speybroeck, N.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

To understand how a society is faring, public health officials often look at the number of people dying each week. This is not just about counting the dead; it is about spotting the difference between what is normal and what is dangerous. Every year, death rates rise and fall with the seasons, peaking in winter when flu circulates and cold bites, and dipping in summer. This predictable rhythm is called a baseline. When the number of deaths suddenly climbs far above this expected line, it signals an excess mortality event. These spikes can be caused by a new virus, a severe heatwave, or a combination of both. The challenge for scientists is to draw that line of "normal" accurately. If the line is drawn too low, a routine winter might look like a crisis. If it is drawn too high, a real disaster might go unnoticed. Traditional methods often rely on rigid mathematical formulas that assume the past will repeat itself in a simple way, but they struggle when the data is messy or when a massive event, like a global pandemic, distorts the picture.

A team of researchers in Belgium and Greece set out to test a different way of drawing this line. They focused on six major cities: Brussels, Antwerp, and Liège in Belgium, and Athens, Thessaloniki, and Larisa in Greece. These locations were chosen because they offer a mix of climates and population sizes, allowing the team to see if their method could handle different real-world conditions. Instead of forcing the data into a pre-set formula, they used a technique called Singular Spectrum Analysis. Think of this method as a way to listen to a complex song and separate the steady beat from the melody and the background noise. By breaking down the weekly death records from 2015 to 2024 into their core patterns, the researchers could identify the true long-term rhythm of mortality without guessing what that rhythm should look like. To make sure they didn't accidentally include the chaos of the pandemic in their definition of "normal," they temporarily removed those extreme weeks from the data, rebuilt the pattern, and then checked if the result made sense statistically.

The results revealed that the rhythm of death is not the same everywhere. In the Belgian cities, the pattern was straightforward: a single, strong cycle where deaths rise in the winter and fall in the summer. However, in the Greek cities, the pattern was more complex. In addition to the winter peak, the data showed a second, significant rise in deaths during the summer months. This semi-annual cycle, which had been growing more pronounced in recent years, suggests that summer heat is a recurring driver of mortality in Greece that standard models might miss. By using this flexible, data-driven approach, the researchers were able to create a reliable baseline for each city that respected its unique local history.

With these baselines established, the team cataloged every week where deaths exceeded the expected number by a significant margin. Over the nine-year period, they identified 170 distinct excess mortality events, accounting for more than 14,000 extra deaths across the six cities. The vast majority of these deaths, about 77 percent, occurred during the years of the COVID-19 pandemic. The researchers also looked for connections between these spikes and extreme weather. They found that 96 of the excess weeks coincided with either severe heat or cold waves. For instance, a particularly deadly heatwave in August 2020, which struck Belgium between pandemic waves, was clearly captured as a major event. In Greece, a prolonged period of excess mortality in Thessaloniki during the autumn of 2020 overlapped with both a cold snap and the pandemic.

Interestingly, not every spike had a clear cause. The researchers found 56 events that did not line up with the pandemic, extreme temperatures, or known flu epidemics. These "unmatched" events made up a small fraction of the total excess deaths, but their existence highlights that mortality is often driven by a mix of factors that are hard to separate. The study does not claim to have solved the mystery of every death spike, nor does it prove that one specific factor caused a specific event. Instead, it offers a robust, reproducible tool for mapping the landscape of mortality. By showing that different countries have different seasonal rhythms and that flexible methods can reveal hidden patterns like the Greek summer peak, the work provides a clearer way to monitor public health. It suggests that to truly understand when a society is in crisis, we must first understand the unique, shifting beat of its own normal.

Technical Summary: Mortality Baselines and Excess Mortality Events in Belgian and Greek Cities Using Singular Spectrum Analysis

Problem Statement
Excess mortality estimation relies on defining an expected mortality baseline, an unobservable quantity typically derived from models with prescribed functional forms (e.g., log-linear Poisson models). These standard approaches often constrain seasonal patterns and rely on short reference periods that exclude exceptional events, such as the COVID-19 pandemic. While semi-parametric alternatives exist, they can struggle with extrapolation and overfitting. Nonlinear time-series decomposition methods, specifically Singular Spectrum Analysis (SSA), offer a non-parametric, data-driven alternative capable of identifying complex patterns over long periods. However, SSA faces two practical challenges in this context: the subjective selection of decomposed components and high sensitivity to extreme outliers (e.g., pandemic mortality spikes).

Methodology
The study analyzes weekly all-cause mortality data from 2015 to 2024 across six metropolitan areas: Brussels, Antwerp, and Liège (Belgium), and Athens, Thessaloniki, and Larisa (Greece). The authors employ a modified SSA framework to address the identified limitations:

Data Preprocessing: Mortality counts were converted to rates using interpolated population data. The time series were standardized and log-transformed.
SSA Implementation: The authors applied univariate SSA (following Broomhead & King, 1986) using a window length ( $L$ ) of 261 weeks (5 years) to maximize the separability of oscillatory components. The trajectory matrix was decomposed via Singular Value Decomposition (SVD).
Automated Component Selection: To remove subjectivity, components were selected using Monte Carlo SSA (MCSSA). This involved generating 5,000 surrogate time series based on an AR(1) process to establish a 95% confidence interval for singular values. Only components exceeding this interval were retained. A cutoff frequency of 4 cycles per year (3-month period) was applied to ensure smooth baselines.
Outlier Handling: To mitigate the influence of COVID-19 mortality spikes, an iterative interpolation approach was used. Observed values during defined pandemic periods were initially replaced with non-pandemic means. The SSA reconstruction was then applied iteratively, updating the pandemic values with the reconstructed baseline until convergence (RMSE < $10^{-3}$ ).
Excess Mortality Event (EME) Detection: The baseline was back-transformed to expected counts. EMEs were defined as weeks where observed deaths exceeded the baseline by two standard deviations, calculated using a quasi-Poisson variance model ( $V(Y) = \phi\mu$ ) with an overdispersion parameter estimated from non-pandemic weeks.
Coincidence Analysis: Identified EMEs were screened for overlap with extreme temperature events (ETEs). Heat and cold wave definitions were optimized using the $F_1$ -score against EMEs, resulting in adopted definitions of heat waves (≥2 days at or above the 99th percentile of daily maximum temperature) and cold waves (≥4 days at or below the 2.5th percentile of daily minimum temperature).

Key Results

Baseline Characteristics: The automated SSA extraction revealed consistent country-specific patterns. Belgian regions exhibited dominant annual cycles with winter peaks. Greek regions displayed both annual and significant semi-annual cycles, reflecting pronounced summer mortality peaks that have become more evident in recent years.
Excess Mortality Catalog: The study cataloged 170 EMEs spanning 456 weeks and 14,210 excess deaths.
- Pandemic Impact: 77% of total excess mortality occurred during pandemic weeks.
- Temperature Extremes: 96 weeks coincided with extreme temperature events.
- Unmatched Events: 56 EMEs (representing 3.7% of excess mortality) remained unmatched to temperature extremes, influenza, or the pandemic; 53 of these were single-week events.
Specific Events: The analysis identified major events, including the 2020 COVID-19 waves, the August 2020 heat wave in Belgium (during an inter-wave period), and the prolonged 2021–2022 period in Thessaloniki where a single EME (41 weeks) coincided with heat waves, cold waves, the pandemic, and influenza. Pre-pandemic clusters, such as the 2016–2017 cold waves and influenza epidemics, were also successfully detected across both countries.

Significance and Claims
The paper posits that SSA, when combined with MCSSA for automated component selection and iterative interpolation for outlier handling, yields reproducible, low-assumption baselines that effectively capture country-specific seasonality, including complex patterns like the semi-annual cycle in Greece.

The authors emphasize that while flexible baselines can absorb recurrent seasonal mortality, the choice of which components to include in the baseline is a substantive methodological decision. They argue that such choices, along with their sensitivity, must be explicitly reported to ensure transparency and interpretability. The study does not claim to provide cause-specific attribution but rather offers a systematic framework for cataloging mortality anomalies and contextualizing them against known drivers (temperature, influenza, pandemics). This approach serves as a screening tool to identify compound events and anomalies that may warrant further explicit epidemiological investigation, complementing traditional driver-based modeling.

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