# Estimation of Excess Mortality and Years of Life Lost to COVID-19 in Norway and Sweden between March and November 2020

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Sources

#### 2.2. Estimates of Years of Life Lost

#### 2.3. Estimate of Expected Mortality-Rate Signal

#### 2.4. Estimate of Excess Mortality Rate

#### 2.5. Estimate of Mortality Displacement

## 3. Results

#### 3.1. The Expected and Excess Mortality Rate

#### 3.2. Excess Mortality and Mortality Displacement

#### 3.3. The Tiny Effect of Mortality Displacement on Excess Deaths and YLL

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Expected and observed mortality. (

**A**) The weekly deaths in Norway and Sweden (red) together with the estimated baseline (black). (

**B**) Same as for Norway in (

**A**), but for the years 2016/17 to 2020/21. The gray region shows the interquartile range for the seasonal variation. (

**C**) As (

**B**), but for Sweden. (

**D**) The excess weekly mortality in Norway (red) and COVD-19-related deaths (black). The error bars is the 95% CI for the excess mortality based on the Monte–Carlo simulation for the estimate of the baseline. (

**E**) As (

**D**), but for Sweden.

**Figure 2.**Excess mortality. (

**A**) Weekly excess mortality for Norway from 2016/17 and through the first months of the epidemic year 2020/21. The blue lines are the average values for each of the five epidemic years. (

**B**) As (

**A**), but for Sweden. (

**C**) The annual excess mortality for Norway from 2000/01 to 2019/20. The error bars are the 95% confidence intervals. (

**D**) As (

**C**), but for Sweden.

**Figure 3.**Auto-correlation function of the excess mortality signal. (

**A**) The black curve shows the autocorrelation function estimated from the weekly excess mortality in Norway. The dashed lines indicate the 95% confidence interval under the assumption of uncorrelated data. The blue points show the autocorrelation function estimated from yearly excess mortality, and the blue error bars show the spread between the correlations estimated using different weeks of each year. (

**B**) As in (

**A**), but for Sweden.

**Figure 4.**Effect of mortality displacement. (

**A**) The yellow histogram shows the estimated probability density function for excess deaths obtained from the Monte–Carlo simulation of the baseline. The blue histogram is the excess mortality adjusted for displacement according to Equation (4). (

**B**) The blue curve is the estimated probability density function for years of life lost (YLL) obtained from Equation (1), and the blue curve is the probability density function for YLL after adjusting for mortality displacement.

**Table 1.**Proportion of deaths in 2020 in Sweden by age group and life expectancy by age group. Data source: Statistics Sweden (SCB).

Age Group (yrs) | Proportion of 2020 Deaths | Life Expectancy (yrs) Estimate (SD) |
---|---|---|

50–64 | $10\%$ | $27.5\phantom{\rule{0.166667em}{0ex}}\left(3.8\right)$ |

65–79 | $30\%$ | $15.6\phantom{\rule{0.166667em}{0ex}}\left(3.3\right)$ |

80–89 | $35\%$ | $7.0\phantom{\rule{0.166667em}{0ex}}\left(1.6\right)$ |

>90 | $25\%$ | $2.5\phantom{\rule{0.166667em}{0ex}}\left(0.9\right)$ |

**Table 2.**Excess mortality per (epidemic) year. The excess mortality is defined as the registered deaths per year minus the expected number of deaths. The expected number of deaths are obtained from a model with a linear trend superposed on a seasonal signal. The confidence intervals are obtained by repeated re-estimates of the linear trend and seasonal signal in a Monte–Carlo simulation. The asterisk in the last row indicates that epidemic year is not completed yet.

Year | Excess Mortality in Norway | Excess Mortality in Sweden | ||
---|---|---|---|---|

Estimate | (95% CI) | Estimate | (95% CI) | |

2000/01 | 334 | $(-180,838)$ | $-825$ | $(-1752,84)$ |

2001/02 | 866 | $(391,1331)$ | 587 | $(-261,1410)$ |

2002/03 | 621 | $(173,1050)$ | 1227 | $(466,1946)$ |

2003/04 | $-591$ | $(-1002,-192)$ | $-1609$ | $(-2281,-956)$ |

2004/05 | $-977$ | $(-1353,-606)$ | 331 | $(-261,903)$ |

2005/06 | $-1874$ | $(-2215,-1527)$ | $-2283$ | $(-2803,-1790)$ |

2006/07 | 59 | $(-254,373)$ | 758 | $(314,1188)$ |

2007/08 | $-371$ | $(-661,-95)$ | $-67$ | $(-449,305)$ |

2008/09 | 105 | $(-161,367)$ | 825 | $(497,1151)$ |

2009/10 | $-1043$ | $(-1298,-783)$ | $-2197$ | $(-2505,-1885)$ |

2010/11 | 163 | $(-98,435)$ | 87 | $(-241,422)$ |

2011/12 | 633 | $(362,933)$ | 1443 | $(1073,1825)$ |

2012/13 | 456 | $(160,777)$ | 1718 | $(1281,2156)$ |

2013/14 | $-732$ | $(-1048,-390)$ | $-1959$ | $(-2467,-1448)$ |

2014/15 | 608 | $(254,980)$ | 2131 | $(1547,2717)$ |

2015/16 | $-793$ | $(-1178,-390)$ | $-1046$ | $(-1707,-378)$ |

2016/17 | 682 | $(258,1111)$ | 1811 | $(1069,2564)$ |

2017/18 | 731 | $(281,1196)$ | 1450 | $(623,2283)$ |

2018/19 | $-15$ | $(-516,495)$ | $-1596$ | $(-2508,-680)$ |

2019/20 | 517 | $(-12,1074)$ | 4329 | $(3331,5325)$ |

2020/21${}^{*}$ | 646 | $(362,957)$ | $-1501$ | $(-1917,-1079)$ |

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**MDPI and ACS Style**

Rypdal, M.; Rypdal, K.; Løvsletten, O.; Sørbye, S.H.; Ytterstad, E.; Bianchi, F.M. Estimation of Excess Mortality and Years of Life Lost to COVID-19 in Norway and Sweden between March and November 2020. *Int. J. Environ. Res. Public Health* **2021**, *18*, 3913.
https://doi.org/10.3390/ijerph18083913

**AMA Style**

Rypdal M, Rypdal K, Løvsletten O, Sørbye SH, Ytterstad E, Bianchi FM. Estimation of Excess Mortality and Years of Life Lost to COVID-19 in Norway and Sweden between March and November 2020. *International Journal of Environmental Research and Public Health*. 2021; 18(8):3913.
https://doi.org/10.3390/ijerph18083913

**Chicago/Turabian Style**

Rypdal, Martin, Kristoffer Rypdal, Ola Løvsletten, Sigrunn Holbek Sørbye, Elinor Ytterstad, and Filippo Maria Bianchi. 2021. "Estimation of Excess Mortality and Years of Life Lost to COVID-19 in Norway and Sweden between March and November 2020" *International Journal of Environmental Research and Public Health* 18, no. 8: 3913.
https://doi.org/10.3390/ijerph18083913