Measuring excess mortality in Victoria during the COVID-19 pandemic

Provisional deaths data for measuring changes in patterns of mortality during the COVID-19 pandemic and recovery period.

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Released
10/03/2021
Source
Provisional Mortality Statistics, Jan-Nov 2020

Introduction

Since the emergence of COVID-19, the number of deaths has been monitored closely in Australia and around the world in order to provide estimates of excess mortality that may potentially be related to the pandemic. Excess mortality is typically defined as the difference between the observed number of deaths in a specified time period and the expected numbers of deaths in that same time period. Measures of excess mortality can account for deaths due to COVID-19, any potentially misclassified or undiagnosed COVID-19 deaths and other mortality that may be indirectly related to the pandemic (e.g. relating to social isolation or changed access to health care). 

Over the period from January to November 2020, Australia recorded lower than expected mortality (see graph below) with decreases in the winter months being statistically significant. Lower than expected numbers of deaths were particularly notable for respiratory diseases including pneumonia. This is in contrast to many other countries where excess deaths have been recorded during the pandemic. 

Australia had two waves of COVID-19 infections during 2020. The first wave was recorded from mid-March to mid-April, with most states in Australia recording active infections and associated mortality. The second wave started in June, with the largest number of active infections and deaths occurring in Victoria. This report will focus specifically on Victorian deaths to examine the impact of COVID-19 and especially the second wave of infections, on all-cause and cause-specific patterns of mortality. 

  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.

Measuring excess mortality

Across the world, health and statistical authorities have sought to measure excess mortality during the COVID-19 pandemic. There are many different methodologies that are designed for this purpose, with the suitability of particular methods often dependent on factors such as data quality and collection methods, or outcomes sought from analysis. 

The ABS has adopted aspects of a methodology used by New South Wales (NSW) Health, applying a cyclical linear regression with a robust estimation procedure to produce an expected number of deaths for 2020 for all cause and cause-specific mortality to identify significant changes in patterns of mortality over time. See the methodology section at the end of this article for detailed information about the model applied.

Interpreting results

Each section below presents two graphs – The first graph is a time series of doctor certified deaths from January 2015 to November 2020 that has the number of actual observations plotted against the expected number of deaths estimated from the regression. The upper and lower thresholds (1.96 standard errors) of the regression are also plotted. The second graph focusses only on 2020, allowing closer inspection of patterns of death during the COVID-19 pandemic. 

At any point in time, if no temporary health hazards influence the number of deaths (i.e. community transmission of influenza or COVID-19) then there is a 95% chance that the expected number of deaths would lie between the upper and lower bounds of the confidence intervals. When actual observations (counts of death) exceed the upper threshold or drop below the lower threshold this indicates a statistically significant change in the pattern of mortality. 

Different approaches can be used to calculate the number of excess deaths. Counts of excess can be taken as the difference between the average expected number of deaths and the actual observed number. This approach risks over-estimating the number of excess deaths as the expected count lies between the upper and lower bound. Counts of excess can also be taken as the difference between the upper threshold of the expected number of death and the actual observed number. This approach results in a lower number of excess deaths, but focusses more clearly on statistically significant changes in mortality. 

Identifying significant changes in the pattern of mortality during the COVID-19 pandemic compared to previous years is the aim of this report. Counts of deaths that are above the upper bound of the confidence interval (threshold) are considered to be “excess” and will be referred to as such in this report. Counts of excess deaths described in this report refer only to the number above the upper threshold.

A single week above threshold does not necessarily suggest excess mortality. Prolonged periods (2 or more weeks) where counts exceed thresholds suggest more strongly that the numbers of deaths are above or below normal. This should be considered when analysing the data in this report. 

All-cause mortality in Victoria (doctor certified deaths)

  • Excess mortality for all doctor certified deaths in Victoria was observed during the first wave of COVID-19 in the weeks starting 23 and 30 March 2020. Observed numbers of deaths exceeded the upper threshold of expected numbers by 28 during that period. 
  • Those weeks in March coincided with high rates of COVID-19 infections and the implementation of stricter lock-down measures across Australia.
  • Excess mortality for all doctor certified deaths was observed during the second wave of COVID-19 in the four weeks between 27 July and 17 August 2020. Observed numbers of deaths exceeded the upper threshold of expected numbers by 125 during that period. 
  • The graph tracking mortality through 2020 shows counts both with COVID-19 deaths included and without. This provides insight into both direct COVID-19 mortality as well as patterns of mortality from causes other than COVID-19. 
  • During wave 2, excess mortality recorded in Victoria was largely due to deaths from COVID-19. Observed numbers of deaths from causes other than COVID-19 track more closely to expected numbers for the 4 weeks beginning 27 July. 
  • Between 6 April and 3 May the observed number of deaths was largely above expected numbers. However, numbers of deaths did not exceed upper thresholds during that period so no excess mortality was recorded. 
  • Numbers of death in Victoria were below lower thresholds for the weeks beginning 6 July and 13 July, with 25 deaths less than lower threshold counts recorded in those two weeks. Analysis of deaths for all of Australia highlighted significantly lower than expected counts from 1 June to mid-July. 
  • There were 21 COVID-19 deaths in Victoria that were certified by a doctor during the first wave of the pandemic and 730 during the second wave. Coroner referred deaths are excluded from this analysis. 
  • The last time excess mortality was observed in Victoria was in 2017 when a severe influenza season led to 103 excess deaths between July and September of that year.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.

All-cause mortality by region (Greater Melbourne vs Rest of Victoria)

  • There were 165 excess deaths in the Greater Melbourne region during the second wave of the pandemic. Deaths that exceeded the upper threshold of expectation occurred between the weeks beginning 27 July and 17 August. 
  • Excess deaths during the second wave in Greater Melbourne were largely due to COVID-19. 
  • During the first wave there were two weeks (23 and 30 March) in Greater Melbourne where deaths exceeded the upper threshold, accounting for 6 excess deaths. 
  • From September, numbers of deaths have remained in the expected range for Greater Melbourne. 
  • In the week beginning 18 May the rest of Victoria recorded 22 deaths above the upper threshold of expectation. While this is a single time point it follows a number of weeks where deaths are above expected projections, though not reaching statistical significance. 
  • During the second wave of the pandemic, the rest of Victoria experienced no excess mortality. Numbers of deaths were generally within the expected range except for the week beginning August 31 where deaths fell below lower the threshold. 
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  5. There are 1898 deaths excluded from the all counts for greater Melbourne and rest of Victoria due to being an interstate or not stated death. 
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  5. There are 225 deaths excluded from the all counts for greater Melbourne and rest of Victoria due to being an interstate or not stated death. 
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  5. There are 1898 deaths excluded from the all counts for greater Melbourne and rest of Victoria due to being an interstate or not stated death.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  5. There are 225 deaths excluded from the all counts for greater Melbourne and rest of Victoria due to being an interstate or not stated death.

Cause-specific mortality

While all cause mortality provides a more accurate picture of patterns of mortality during the pandemic it is important to look at cause-specific mortality to provide insights into how individual causes have changed. Specific causes may experience significant changes which can be masked at the all-cause level. The following section focusses on excess mortality analysis for selected causes of death certified by a doctor in Victoria in 2020. Deaths are analysed by underlying cause of death only. 

Ischaemic heart disease (I20-I25)

  • Numbers of deaths in Victoria from ischaemic heart disease were generally within the expected range throughout 2020. 
  • Numbers of deaths exceeded upper thresholds by small amounts in the weeks beginning 6 April, 28 September and 9 November (4, 2 and 1 death respectively). These were only single observations and are therefore not considered to be statistically significant. 
  • Ischaemic heart disease is the leading cause of death in Australia. Deaths due to ischaemic heart disease have been declining over time. This has resulted in the regression producing a reduced number of expected deaths each year.
  • Excess mortality was recorded for ischaemic heart disease in July and September of 2017. This aligns with a severe influenza season and excess mortality recorded among other causes at that time. 
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.

Cerebrovascular diseases (I60-I69)

  • Deaths due to cerebrovascular diseases (CVD) exceeded the upper threshold in the weeks beginning 3 and 10 August, accounting for a total of 15 excess deaths. 
  • In the weeks beginning 18 May and 9 November 2020 the number of deaths due to CVD exceeded the upper threshold by 9 and 4 deaths respectively. Both of these weeks are both single points in time and as such caution is advised when interpreting these results. 
  • Deaths have remained in expected ranges for CVD in all other weeks for 2020. 
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.

Respiratory diseases (J00-J99)

  • Deaths due to Respiratory diseases (including diseases such as influenza, pneumonia and chronic lower respiratory diseases) exceeded the upper threshold in weeks beginning 23 and 30 March accounting for 10 excess deaths.
  • From the week beginning 8 June until the week beginning 9 November there were significantly lower than expected numbers of deaths due to respiratory diseases in Victoria (excluding the week beginning 2 November). A total of 199 deaths less than lower thresholds were recorded during that period. 
  • In 2017 there were 128 excess deaths due to respiratory diseases. The majority of those excess deaths were due to the severe influenza season.
  • Deaths due to COVID-19 are not included in the analysis for respiratory diseases. For a weekly count of deaths due to COVID-19 that were certified by a doctor see Table 1.1 in the weekly dashboard in data downloads. 
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.

Chronic lower respiratory conditions (J40-J47)

  • Deaths due to Chronic lower respiratory diseases (e.g. emphysema and asthma) exceeded the upper threshold in weeks beginning 23 and 30 March accounting for 5 excess deaths. 
  • Numbers of deaths from Chronic lower respiratory conditions have been below expected counts since 25 May, with counts below lower thresholds observed for several weeks through July, August and September.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.

Influenza and pneumonia (J09-J18)

  • Numbers of deaths due to influenza and pneumonia were above expected counts from the week beginning 16 March 2020 to the week beginning 13 April. 
  • The week beginning 13 April was the only week where the number of deaths exceeded the upper threshold. This is a single point in time and should be interpreted with caution. 
  • In Victoria in 2020 there were 7 deaths due to influenza. 
  • Public health measures put in place to prevent the spread of COVID-19 infections can also be effective in limiting the spread of other infectious agents including influenza. 
  • The influenza season resulted in excess mortality in 2015, 2016, 2017 and 2019. 
  • In 2017 there were 124 excess deaths due to influenza and pneumonia with excess deaths recorded between July and October.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.

Pneumonia (J12-J18)

  • Pneumonia is commonly caused by seasonal viruses including influenza. Pneumonia is the most commonly certified consequence of COVID-19 leading to death. 
  • To remove the confounding effect of influenza on projected number of expected deaths pneumonia has been analysed separately with results detailed in the two graphs below. 
  • There were 14 excess deaths due to pneumonia during wave 1 of the COVID-19 pandemic in Victoria. 
  • From 1 June the number of deaths due to pneumonia has been lower than expected numbers, with numbers falling below lower thresholds for several weeks between August and November.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.

Cancer (C00-C97, D45, D46, D47.1, D47.3-D47.5)

  • In the weeks beginning 4 May and 9 November 2020 the number of deaths due to cancer exceeded the upper threshold by 13 and 9 deaths respectively. Both of these weeks are single points in time and as such caution is advised when interpreting these results. 
  • For the two week period from 13 July 2020 numbers of cancer deaths dropped below the lower threshold. 
  • Between 2015-2019 cancer mortality has generally fallen between expected ranges. Intermittent points where the number of deaths have exceeded the upper threshold or dropped below the lower threshold of expectation have not been prolonged. This same pattern of death is seen for cancer mortality in 2020. 
  • This analysis has covered all cancers grouped together. Results may differ for specific cancer types. 
     
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.

Diabetes (E10-E14)

  • During the first wave of the COVID-19 pandemic, deaths due to diabetes were above expected projections from the week beginning 23 March to 4 May. For two of these weeks (30 March and 13 April) diabetes mortality exceeded upper thresholds. 
  • In the week beginning 10 August 2020 the number of diabetes deaths slightly exceeded the upper threshold (2 excess deaths). This is a single point in time and should be interpreted with caution. 
  • People with diabetes can be susceptible to infections due to a compromised immune system. Mortality can be influenced by infectious disease activity in the community. 
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.

Dementia (F01, F03, G30)

  • Victoria recorded no excess mortality from dementia during either the first or second wave of the COVID-19 pandemic. 
  • At the national level, there were 10 excess deaths due to dementia recorded in the week beginning 23 March. This week coincided with stricter lockdown measures being implemented in Australia. 
  • During the winter months dementia mortality was below expected projections for all weeks except the week beginning July 20.  
  • People who have dementia can be at higher risk of dying from acute respiratory infections including influenza and pneumonia. The level of activity of acute respiratory disease can affect the death rate of dementia.
     
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.
  1. This graph is compiled by the date the death occurred.
  2. This data is considered to be provisional and subject to change as additional data is received.
  3. Weeks in this graph always start on a Monday, with each year following on from the previous one (eg week 52 has 28 December 2015 to 3 January 2016). In the main publication, week 1 is always 1-7 January. 
  4. Refer to explanatory notes in the Methodology section for this article for more information regarding the data in this graph.

Methodology

The analysis of 2020 mortality data undertaken by the ABS is based on a model developed by Serfling (10) and later adapted by the US Center for Disease Control (CDC) and New South Wales Health (NSW Health). This section provides an overview of the how the model 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.

Historical development of model

Historically this model has been used to estimate excess mortality caused by influenza.

  • As early as 1932, Collins determined that excess mortality during winter months in the United States of America (USA) was a consequence of epidemic influenza and therefore could be used as an indicator for the recognition of influenza outbreaks.²
  • In 1963, Serfling described a regression model, based on the seasonal pattern of pneumonia and influenza (P&I) deaths, to infer excess deaths due to influenza.
  • Since then, models based on Serfling's has been applied in a number of temperate countries (USA,³,⁴ France,⁴ Australia,⁴ and Italy⁵) to demonstrate that excess mortality occurring during winter months is associated with pandemic and seasonal epidemics of influenza.
  • The CDC took the approach further and established the 122 Cities Surveillance System to provide timely, prospective information on excess mortality due to influenza. ⁶,⁷
  • The New South Wales Influenza Surveillance Program runs from May to September each year, and uses an adaptation of the Serfling model to monitor for influenza epidemics. This system primarily monitors the proportion of influenza positive specimens among all respiratory specimens from the major public health laboratories, the proportion of emergency department visits diagnosed with influenza, and outbreaks of influenza reported to Public Health Units by residential care facilities.⁹ 

Aspects of the Serfling model and its implementations

The Serfling model uses historical data to predict current patterns of mortality. This then enables the identification of any deviation from that prediction that may signal an influenza epidemic. In developing this model, Serfling recognised that past influenza epidemics could overly influence the regression, limiting the ability of the model to identify any new epidemic. For this reason, Serfling manually excluded past epidemics when fitting the model. 

An important feature of this methodology is the identification of a threshold that can be used as the upper and/or lower limit for the data. Observations that lie between these upper and lower limits are considered to be normal. The chosen threshold will vary depending on the desired specificity of the analysis and the methods used for calculation. In statistics there are default or familiar thresholds used in measuring these boundaries such as 1.96 standard errors either side of the mid-point.

An upper threshold was chosen to define the upper limit of the expected number of deaths in the absence of an influenza epidemic. This upper threshold was calculated as the predicted number of deaths in a given week plus a constant multiple of the standard error of the time series (the differences between each value predicted by the model and the actual observed values, or the 'model residuals'). Serfling chose the constant multiple to be 1.64 standard errors, and considered 2 consecutive weeks above the threshold to indicate epidemic behaviour.¹⁰

The NSW Health model used for the Influenza Surveillance Program is based on the Serfling model. This variant of the model fits a cyclic linear regression to data for the previous 5 calendar years and then forecasts the current year's time series from data up to the end of the previous year. Receiver operating characteristic curves are used to identify the most useful balance between sensitivity (the true positive rate) and specificity (=1-false positive rate) when determining the threshold that helps identify the start of an Influenza epidemic.¹⁰

Data source

Refer to the methodology section of Provisional Mortality Statistics for a description of the scope of data used in this model.

ABS adaptation of Model

The ABS have applied key characteristics of the model used in the New South Wales Influenza Surveillance Program. The ABS model is also based on the application of a cyclical linear regression model to the time series of weekly numbers of deaths. The model has been applied to doctor certified deaths from all causes and to deaths from specific causes. Most diseases covered in both the Provisional Mortality Statistics reports and in this analysis show some cyclical pattern in numbers of deaths, indicating that the model should prove suitable for this broader application. 

The approach used by the ABS involves use of a 'robust' estimation procedure for fitting the model. Epidemics can cause increased mortality which leads to outliers in time series data. By down-weighting outliers it aims to fit the model to patterns of mortality that would have been expected to have occurred in the absence of an epidemic. This robust regression down-weights the influence of extreme observations (outliers) and is applied to a 5-year baseline time series. This baseline time series runs from 5 January 2015 to 5 January 2020 (weeks commencing on a Monday). The regression is then used to forecast expected numbers of deaths for the current year.

The cyclical regression model includes: a linear time term, t, with values 1, 2, 3, ... for each week of the time series, and the square of the time term, t2, to accommodate long-term linear and curvilinear changes in the background proportion of the cause of death arising from factors such as population growth or improved disease prevention or treatment.

Also included are annual seasonal harmonic variables to describe the cyclical seasonal background pattern. The harmonic variables are functions of the week number, t, and the periodicity in the same units – in this case, yearly (52.18 weeks). The 2 harmonic variables in this case are: sine(2π t/52.18) and cosine(2π t/52.18).

The final model was:

Expected(proportion) = A + Bt + Ct2 +D sine(2πt/52.18) + E cosine(2πt/52.18)

where A, B, C, D, and E are the coefficients calculated from the regression.

To evaluate the approach, the model was fitted using PROC ROBUSTREG in SAS Software with the simplest, default 'M estimation' method.¹² The PROC SCORE procedure was then used to forecast values for 2020.¹³ The standard error and threshold is derived from the stdi option in PROC ROBUSTREG which is run a second time with the 2020 results attached.

Threshold identification

Identifying the threshold at which to signal excess mortality will vary depending on the goals of the research, application of the method, seasonality of diseases of interest. Several national statistical organisations are using different models including Farrington surveillance algorithms, z -scores and prediction intervals to inform such thresholds.

While the ABS closely followed the NSW Health methodology for calculating the regression, a different method was chosen for calculating thresholds. This was because the ABS analysis covers deaths from several causes, rather than focusing specifically on influenza and pneumonia. While many of those diseases follow some cyclical pattern of mortality, they may not have a specific season in the same way as influenza and pneumonia. Supported systems developed by NSW Health to clarify the accuracy of results of the surveillance for influenza and pneumonia are also not available for analysis of deaths from other causes.

As a result, a method for calculating the threshold for this analysis was selected which had a broader application and was more easily interpreted across a range of conditions, namely 1.96 standard errors or a 95% confidence interval. Use of the 95% confidence interval does introduce the expectation that random weekly variation could lead to counts that exceed thresholds 5% of the time. As such, individual weeks that exceed thresholds should be interpreted with caution. However, any prolonged period of weeks, 2 or more, exceeding the expected range can suggest excess mortality has been signalled.

The SAS function PROC ROBUSTREG offers the STDI parameter to calculate the 'standard error of prediction' of the model.¹² Which is used to define 1 standard error. The standard error of prediction is a more logical choice for assigning the threshold of excess mortality than the root mean square error (standard error of the model residuals) because it incorporates not only the variance of the residuals but also the variance of the model parameter estimates. This provides an estimate of the expected variability of the observed values in the absence of an epidemic.

References

1. CDC. Excess Deaths Associated with COVID-19 https://www.cdc.gov/nchs/nvss/vsrr/covid19/excess_deaths.htm#techNotes

2. Collins SD. Excess mortality from causes other than influenza and pneumonia during influenza epidemics. Public Health Rep 1932;47:2159–2180.

3. Reichert T, Simonsen L, Sharma A, Pardo S, Fedson D, Miller M. Influenza and the winter increase in mortality in the United States, 1959–1999. Am J Epidemiol 2004;160:492–502.

4. Viboud C, Boelle P, Pakdaman K, Carrat F, Valleron A, Flahault A. Influenza epidemics in the United States, France, and Australia, 1972–1997. Emerg Infect Dis 2004;10:32–39.

5. Rizzo C, Bella A, Viboud C, Simonsen L, Miller M, Rota M, et al. Trends for influenza-related deaths during pandemic and epidemic seasons, Italy, 1969–2001. Emerg Infect Dis 2007;5:694–699.

6. Centers for Disease Control and Prevention. 122 Cities Mortality Reporting System, Manual of Procedures. Atlanta (Georgia, United States): US Department of Health and Human Services; 2004.

7. Simonsen L, Clarke MJ, Stroup DF, Williamson GD, Arden NH, Cox NJ. A method for timely assessment of influenza-associated mortality in the United States. Epidemiology 1997;8:90–395.

8. O'Brien K, Barr IG. Annual Report of the National Influenza Surveillance Scheme, 2006. Commun Dis Intell 2007;31:167–179.

9. NSW Health, Communicable Diseases Branch. New South Wales Influenza Surveillance Report. NSW Health.

10. Serfling RE. Methods for current statistical analysis of excess pneumonia-influenza deaths. Public Health Rep 1963;78:494–506.

11. The ROBUSTREG procedure. SAS/STAT(R) 12.3 User's Guide. Cary (USA): SAS Institute, 2013. Available from: https://support.sas.com/documentation/onlinedoc/stat/123/rreg.pdf

12. Model Fit and Diagnostic Statistics. SAS/STAT(R) 9.2 User's Guide. Cary (USA): SAS Institute, 2008.