Supplementary appendix
This appendix formed part of the original submission and has been peer reviewed. We post it as supplied by the authors.
Supplement to: Faust JS, Renton B, Chen AJ, et al. Uncoupling of all-cause excess mortality from COVID-19 cases in a highly vaccinated state. Lancet Infect Dis 2022; published online Aug 22. https://doi.org/10.1016/S1473-3099(22)00547-3.

Table of Contents
Supplementary Appendix
Supplemental methods:…………………………………………………………………………………………… 1 Supplemental figure legends: …………………………………………………………………………………… 2
Supplemental Appendix Figure
Supplemental Appendix Figure
Supplemental Appendix Figure
Supplemental Appendix Figure
Supplemental Appendix Figure concentration/COVID-19 cases
Supplemental Appendix Figure Supplemental Appendix Figure
1: SARS-CoV-2 variant proportions for HHS Region 1 ………….. 3
2: All-cause excess mortality in Massachusetts………………….. 3
3A: Excess mortality and COVID-19 cases…………………………… 4
3B: COVID-19 hospitalizations and wastewater concentration 4
3C/3D: COVID-19 deaths and wastewater ………………………………………………………………………….. 4
4: COVID-19 tests…………………………………………………………. 5 5A: COVID-19 cases by age…………………………………………….. 6

Supplement to: Faust JS, Renton, B, Chen AJ et al. The uncoupling of all-cause excess mortality from Covid-19 cases and associated hospitalizations in late winter and spring of 2022 in a highly vaccinated state.
This appendix has been provided by the authors to give readers additional information about the work.
Supplemental methods:
All-cause excess mortality is defined as the number of observed deaths minus the number of expected deaths in any period. In order to project expected deaths, we used seasonal autoregressive integrated moving averages from January 2015 (week ending 1/11/15) up to early February 2020 (week ending 2/2/2020).
We assume there were 53 weeks within year 2020. For week 6 < 𝑖𝑖 ≤ 53, we defined the original projected population for three age groups (ages 18-49, 50-64, ≥65) and the total population (including the three adult age groups and ages 0-17) (denoted by 𝑘𝑘, where 1 ≤ 𝑘𝑘 ≤ 4) in week 𝑖𝑖 of 2020 to be 𝑛𝑛𝑖𝑖,𝑘𝑘; the original point estimate for all-cause deaths to be 𝑚𝑚�𝑖𝑖,𝑘𝑘; the sum of all previous weeks’ excess death to be 𝑃𝑃𝑖𝑖−1,𝑘𝑘 (starting𝑛𝑛from week 6). Therefore, the corrected expected deaths for week 𝑖𝑖 (since week 6, 2020. week ending 2/9/2020) after
correction(𝑚𝑚�𝑖𝑖,𝑘𝑘𝑎𝑎𝑎𝑎𝑎𝑎)satisfies: 𝑚𝑚�𝑖𝑖,𝑘𝑘𝑎𝑎𝑎𝑎𝑎𝑎=�𝑛𝑛𝑖𝑖,𝑘𝑘−𝑃𝑃𝑖𝑖−1,𝑘𝑘�×𝑚𝑚�𝑖𝑖,𝑘𝑘
The above equation also holds for the weeks in 2021 and 2022 (assuming both have 52 weeks), where 𝑃𝑃 denotes the sum of all previous weeks’ excess death and the sum of all previous
𝑖𝑖,𝑘𝑘
𝑖𝑖−1,𝑘𝑘
weeks’ decreases in inward immigration since week 6, 2020, respectively.
The sARIMA models in the study were based on weekly data and set the month indicators as well as the estimated weekly population as covariates. By adding the month indicators, we can not only capture the seasonal trends well in the models but also increase our model predictability by considering the month effects. Moreover, by adding the population, we can capture the death counts dynamically influenced by the number of people in each group.
The overall model in the study was comprised of component models for 4 age groups (ages 0- 17, 18-49, 50-64, ≥65) from week 1 2015, up to week 5, 2020, a total of 265 weeks previous to COVID-19, to ensure that our projections were based both on smooth data trends and sufficient data.
The weekly 95% CI boundaries directly from the sARIMA model in the auto.arima function in the R statistical software. The periodically CI boundaries were obtained through the 10,000 simulation samples from the estimated sARIMA model in each age group and the total MA group.
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Supplemental figure legends:
Supplemental Figure 1. SARS-CoV-2 variant proportions for HHS Region 1 (Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, Vermont), January 2021 through early June 2022.3
Supplemental Figure 2. All-cause excess mortality in Massachusetts: The weekly number of observed deaths from February 2015 through June 2022 (yellow line) and the weekly number of expected deaths from February 2020 through June 2022 (blue line). The area between the orange and blue lines starting February 2020 correspond to all-cause excess mortality during the Covid-19 pandemic period.
Supplemental Figure 3A shows the cumulative all-cause excess mortality (blue line) plotted against weekly wastewater SARS-CoV-2 RNA copies per mL mean values (yellow line) from counties for which there were available data in a given week (Barnstable, Berkshire, Bristol, Essex, Franklin, Hampshire, Middlesex, Nantucket, Plymouth, Suffolk, Worcester), Massachusetts, February 2020 through June 2022 in Massachusetts.8 Figure 1, Panel B is shown for comparison between documented cases and wastewater concentrations.
Supplemental Figure 3B shows the cumulative Covid-19-associated hospitalizations (blue line) plotted against weekly wastewater SARS-CoV-2 RNA copies per mL mean values (yellow line) from counties for which there were available data in a given week (Barnstable, Berkshire, Bristol, Essex, Franklin, Hampshire, Middlesex, Nantucket, Plymouth, Suffolk, Worcester), Massachusetts, February 2020 through June 2022 in Massachusetts.8 Figure 1, Panel C is shown for comparison between documented cases and wastewater concentrations.
Supplemental Figure 3C shows the cumulative Covid-19-associated deaths (blue line) plotted against weekly wastewater SARS-CoV-2 RNA copies per mL mean values (yellow line) from counties for which there were available data in a given week (Barnstable, Berkshire, Bristol, Essex, Franklin, Hampshire, Middlesex, Nantucket, Plymouth, Suffolk, Worcester), Massachusetts, February 2020 through June 2022 in Massachusetts.8
Supplemental Figure 3D shows the cumulative Covid-19-associated deaths (blue line) plotted against weekly confirmed new Covid-19 cases (yellow line), Massachusetts, February 2020 through June 2022 in Massachusetts.7
Supplemental Figure 4. Weekly number of reported molecular test results (blue line) and antigen test results (yellow line), Massachusetts, August 8, 2020 through June 25, 2022.7
Supplemental Figure 5A. Weekly mean age of newly infected Covid-19 persons (previous two weeks), Massachusetts, March 2020 through June 2022.7
Supplemental Figure 5B. Weekly rates (per 100,000 residents) of newly infected Covid-19 persons by age group, Massachusetts, August 8, 2020 through June 18, 2022.8
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Supplemental Appendix Figure 1
Supplemental Appendix Figure 2
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Supplemental Appendix Figure 3A
Duplicate of Figure 1, Panel A
Supplemental Appendix Figure 3B
Duplicate of Figure 1, Panel B
Supplemental Appendix Figure 3C
Supplemental Appendix Figure 3D
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Supplemental Appendix Figure 4
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Supplemental Appendix Figure 5A
Supplemental Appendix Figure 5B
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