Excess mortality methodology

This publication introduces a new research question and new method for estimating excess mortality in Australia and its states and territories. 

Earlier analysis on excess mortality (2020-2023) defined expected mortality as the level expected in the absence of a pandemic and this was appropriate for the time. As COVID-19 continues to be a substantial and ongoing cause of death and may contribute to other causes of death in the longer term, it is now important to include COVID-19 affected years when considering what level of mortality is expected going forward. Accordingly, the question for what expected mortality should be has shifted from ‘what would have occurred had pre-pandemic trends continued’ to ‘what would be expected in a context where COVID-19 is a persistent contributor to mortality’. This research question is applied to data from 2024. 

Results from this publication cannot be compared to the previous excess mortality publications produced by the ABS as they are answering two different research questions and different methodologies are applied to achieve this. This work does not replace any previous outputs published by the ABS. 

The production of excess mortality estimates for 2024 and 2025 mortality data uses a generalised additive model (GAM). This methodology provides an overview of how the GAM has been developed over time, key aspects of the model, and how the model has been adapted and applied by the ABS in this analysis

Since the COVID-19 pandemic, the ABS has produced a series of excess mortality reports. The most recent reports provided excess mortality estimates by state/territory, by remoteness areas, and by selected causes of death. The primary model used by the ABS in excess mortality estimation was originally developed by Serfling and later adapted by the US Centers for Disease Control and Prevention (CDC) and the Centre for Epidemiology and Evidence at New South Wales Ministry of Health (NSW Health). The key features of the Serfling model, alng with ABS’s adaptations, have been described previously. 

Six years after the onset of the COVID-19 pandemic, it is now essential for the ABS to update its method for estimating excess mortality. Reasons include: 

• COVID‑19 has transitioned from an emergency “pandemic shock” to an ongoing contributing cause of death, requiring an update to the measurement of expected mortality. In the early years of the pandemic, excess mortality was interpreted as mortality above what would have been expected had pre‑pandemic trends continued. This framing was appropriate when COVID‑19 represented an acute, external shock to usual mortality patterns. However, by 2024 and 2025, COVID‑19 mortality patterns have shifted, functioning more like other circulating respiratory pathogens such as influenza and respiratory syncytial virus (RSV). Given the likelihood that SARS‑CoV‑2 will remain a circulating pathogen and continue to contribute to seasonal mortality with variable magnitude and timing, excess mortality going forward can be understood as ‘mortality above what would be expected in a context where COVID‑19 is a persistent contributor to mortality’. 
• Under these conditions, excess mortality estimation models should incorporate the reality that COVID‑19 deaths — direct and indirect — are now part of the baseline mortality environment. A method that continues to assume a world without COVID‑19 is less appropriate for estimating excess mortality in 2024, 2025, and beyond. Updating the methodology allows expected‑death projections to reflect the evolving epidemiological landscape and to provide more realistic and policy‑relevant excess mortality estimates. This is consistent with ongoing practice in Australian mortality estimation, where seasonal influenza has been treated as a persistent contributor to baseline mortality rather than excluded through a disease‑free counterfactual.
• The existing baseline period (2013–2019) is now too distant from the period of interest.  The 2013–2019 baseline was appropriate for estimating excess mortality in the early pandemic years because it provided a stable pre‑COVID reference period and met the methodological requirements outlined in earlier ABS publications. However, as we analyse mortality outcomes up to 2025, the gap between the baseline and the period being assessed has become too large. Excess mortality estimation relies on the assumption that patterns observed in the baseline period, such as seasonality and long-term trends, remain broadly applicable to the years being predicted. The further the baseline is from the target period, the less plausible this assumption becomes. Continuing to use a baseline that ends in 2019 to estimate expected deaths in 2024 and 2025 risks embedding outdated mortality patterns and reduces the accuracy and relevance of expected‑death projections.
• Mortality trends since 2022 no longer follow the linear long-term trend assumed in the previous model. Between 2013 and 2019, mortality in Australia followed a relatively stable, linear trajectory, making a linear trend term a reasonable basis for estimating expected deaths in the absence of the pandemic. This assumption remained suitable for analyses of the early pandemic years. However, mortality patterns have shifted since then: mortality rose sharply to a peak in 2022 and declined in 2023 (see the figure below). This non‑linear trajectory indicates that the underlying long-term trend has changed. As a result, projections for 2024 and 2025 cannot rely on a simple linear extrapolation without introducing bias. A method that accommodates these essential non‑linear features of recent mortality will better reflect observed patterns and provide more robust estimates for future analyses.

Please refer to the methodology section of Provisional Mortality Statistics for a description of the scope of data used in the excess mortality estimation model. This publication presents excess mortality estimates for 2024 and 2025. 

The ABS conducted a systematic literature search in PubMed to identify articles on excess mortality published up to 30 September 2025. Articles were retrieved if they contained the phrase ‘excess mortality’ in the title or abstract, or if both terms ‘excess’ and ‘COVID-19’ appeared in the title or abstract. The ABS also reviewed methodological documentation for excess mortality methods from a number of national statistical offices as well as non-government agencies such as actuary institutes.  

The retrieved articles underwent title, abstract, and full-text screening, and the methodological documentation was assessed at the full-text level. Eligibility included articles and documentation which described a method that: 

1. included at least one year of the COVID-19 pandemic in the baseline period, rather than solely relying on pre-pandemic years. The World Health Organization (WHO) declared COVID-19 a global pandemic on 11 March 2020 
2. included at least one year after the emergency phase of the pandemic in the projection period, defined as the time following 5 May 2023, when WHO declared that COVID-19 was no longer a Public Health Emergency of International Concern 
3. accounted for non-linear long-term mortality trends within the baseline period 
4. used a baseline period spanning more than one year, as multi-year baselines generally provide more robust and reliable estimates of expected mortality. In contrast, a single‑year baseline may capture mortality patterns that are idiosyncratic to that specific year (e.g., unusual seasonal fluctuations or external events) and may not be representative of broader underlying trends or applicable to the target period.   

Across the screened literature, two models presented in a recent Eurosurveillance publication and the new model developed by the UK ONS were identified as meeting the eligibility criteria. The General Additive Model (GAM) and the General Linear Model (GLM) from the Eurosurveillance publication were both considered to be a better fit for the Australian setting. After extensive testing the GAM was chosen to be applied to the ABS data to estimate excess mortality from 2024 onwards. 

The ABS also undertook a peer review process with selected agencies to demonstrate the new research question and explain the selection of the GAM for estimating excess mortality. 

The model was evaluated using national (all‑Australia) weekly mortality data from 2013 to 2025 to assess suitability for estimating excess mortality in the Australian context. Weeks were defined as seven-day periods which start on a Monday as per the ISO (International Organization for Standardisation) week date system.

The ABS has used a seven‑year baseline period (2013–2019) when estimating expected deaths, and this has been retained for the new method as longer baselines are typically more robust than shorter alternatives. A seven-year moving baseline ensures continuity with existing practice, provides a stable yet up‑to‑date representation of mortality trends and seasonality, and supports timely public health surveillance.  The projection period has been restricted to the 12 months following the baseline period, because a one‑year horizon aligns with operational surveillance needs. It provides expected‑mortality estimates that are sufficiently stable for assessing excess mortality in the most recent period, avoids the uncertainty associated with longer‑term projections, and ensures that estimates remain relevant for identifying emerging public health events. The only exception to the 12-month projection period was for modelling expected mortality in 2023. Because 2022 recorded such high numbers of deaths with an atypical seasonal pattern (i.e. it is not representative of a “usual” year), including 2022 in the baseline period predicted an unrealistically elevated expected mortality level for 2023 and, consequently, for 2024 and 2025. Therefore, 2022 was excluded from all modelling inputs. Although lower mortality was observed in 2020, its inclusion in the baseline reflects the decision to retain pandemic-era years unless there is clear evidence of distortion; unlike 2022, its inclusion did not produce implausible expected mortality patterns.

For the long‑term trends, separate thin‑plate splines were fitted for each age group, with the number of basis functions set equal to the number of unique years in the baseline period (i.e., seven). Knots were placed automatically across the observed years, and smoothness was controlled through penalisation to capture gradual changes in mortality while limiting overfitting (when a model describes random error in the input data as opposed to the relationship between the variables of interest).  

Seasonality was modelled using a cyclic cubic spline for each age group, with 10 basis functions. The cyclic specification ensures continuity between the end and start of the year. Knots were distributed evenly across the weeks of the year, with penalisation controlling the smoothness of the seasonal pattern. The number of basis functions defines an upper bound on the flexibility of the smooth term, while the effective degrees of freedom are determined by the data through smoothing penalties and are typically lower than this bound.

The ABS incorporated an iterative age‑specific outlier suppression procedure, which progressively identified and removed atypical mortality weeks from the baseline period before estimating the expected mortality. Eight age groups were defined: 0-34, 35-54, 55-64, 65-74, 75-84, 85-89, 90-94, and 95+ years. While there were weeks of high and low mortality in 2019 and earlier years, outlier suppression was applied from 2020 onwards, as this was the first year in which COVID‑19‑related anomalies appeared in the mortality series. For each year from 2020 onwards, age‑specific outlier weeks were identified by comparing observed weekly deaths with the 95% credible interval of expected mortality, and weeks where observed deaths fell outside this interval were suppressed from the baseline used to estimate expected mortality for the following year. 

Before applying this procedure, we excluded the entire year of 2022 from all baseline periods used to estimate expected mortality for 2023, 2024 and 2025. Mortality in 2022 included a pronounced peak, and incorporating this year into the baseline would inflate expected‑mortality estimates and consequently would overestimate expected mortality and underestimate excess mortality in subsequent years. 

The iterative age‑specific outlier‑suppression process proceeded as follows:

• Step 1: Estimating expected mortality for 2020 and identifying outlier weeks for each age group. Using 2013–2019 as the baseline, we estimated age‑specific expected mortality for 2020 (with 95% credible intervals). For each age group, weeks where observed deaths fell below the lower bound or above the upper bound of the 95% credible interval were classified as outlier weeks.
• Step 2: Preparing data for estimating 2021 expected mortality. To estimate expected mortality for 2021, we used full mortality data from 2014–2019, and 2020 mortality with age‑specific outlier weeks suppressed. This prevents atypical mortality patterns in 2020 from influencing the baseline for 2021.
• Step 3: Identifying outlier weeks for 2021. We compared observed 2021 deaths with the 95% credible interval for each age group and flagged weeks outside the interval as 2021 age‑specific outlier weeks.
• Step 4: Preparing data for estimating 2022 expected mortality. To estimate expected mortality for 2022, we used full mortality data from 2015–2019, and 2020 and 2021 mortality with all previously identified age‑specific outlier weeks suppressed. This ensures that only representative mortality patterns contribute to the baseline.
• Step 5: Preparing data for estimating expected mortality for 2023, 2024 and 2025. For these years, the same iterative logic applies, with one modification: 2022 was excluded entirely. Accordingly, the baseline period was 2015-2021 for 2023, 2016-2023 for 2024, and 2017-2024 for 2025. 

This approach ensures that the baseline for recent years is informed by stable, representative mortality patterns.

The model generated 2,000 posterior samples of expected deaths for each age group. For each sample, age‑specific estimates were first aggregated to obtain the expected deaths for the total population.

Weekly estimates were derived by aggregating age‑specific weekly estimates at the posterior sample level, yielding 2,000 samples of total weekly expected deaths, from which medians and percentiles were calculated.

Annual estimates were obtained by aggregating weekly age‑specific estimates within each posterior sample to produce 2,000 samples of total yearly expected deaths for the population. Medians and percentiles were then calculated from these annual samples.

Predicted mortality in the evaluation years (i.e., 2020 to 2025) indicated that the GAM produced stable and coherent estimates of expected mortality over time (see the figure below). In particular, the GAM captured gradual changes in mortality patterns while maintaining continuity across years, resulting in estimates that aligned closely with observed long‑term trends.

The GAM uses a penalised spline framework to model long-term trends and seasonality as smooth functions, allowing it to accommodate gradual structural changes while down-weighting transient deviations. This results in more consistent estimates of expected mortality that better reflect the underlying trajectory in the absence of short-term disruptions.

The selected GAM was applied to state and territory data to estimate excess mortality across jurisdictions. Some states with fewer weekly deaths allowed fewer age groups to be modelled robustly, and the two territories were only modelled as a single age group. Age group classifications were specified as follows:

• NSW: 0-34, 35-54, 55-64, 65-74, 75-84, 85-89, 90-94, and 95+ years
• Vic: 0-34, 35-54, 55-64, 65-74, 75-84, 85-89, 90-94, and 95+ years
• Qld: 0-34, 35-54, 55-64, 65-74, 75-84, 85-89, 90-94, and 95+ years
• SA: 0-64, 65-74, 75-84, 85-89, 90+ years
• WA: 0-44, 45-64, 65-74, 75-84, 85-89, 90+ years
• TAS: 0-69, 70-79, 80-89, 90+ years
• NT: all ages
• ACT: all ages 

A sensitivity analysis was conducted by increasing the number of basis functions for the cyclic cubic spline from 10 to 15 and 20. The results remained stable across specifications, indicating that the chosen value (i.e., 10) was sufficiently large and did not constrain the flexibility of the GAM.

All data analyses were performed in R (version 4.4.1), using the packages “rstanarm”, “segmented”, “stats”, “forecast”, “data.table”, “dplyr”, and “tidyr”. R code accompanying the original Eurosurveillance publication describing the GAM was made publicly available by the authors who were consulted in the implementation of our data analysis.