Covid-19 mortality development in the Nordic countries

Will the Swedish Laissez-Faire Model for meeting the Covid-19 pandemic be successful or a failure? As a statistical epidemiologist I think, of course, of success and failure in terms of public health, not as measured by GNP or unemployment rates. Can the effects of governmental initiatives (or lack thereof) for implementing social distancing and self-isolation make a difference? Indications exist that social isolation reduces transmission and delays the spread of the virus, but that timing and duration is critical, see Mahtani et al. and Roosa et al.

To pass the time in my voluntary social isolation, I use statistical modeling to study the Covid-19 mortality development in Sweden, Denmark, Norway, and Finland. Italy is included as a reference. I collect data from the Wikipedia sections for the 2020 coronavirus events in Denmark, Finland, and Italy. For Norway, the data are collected from the Norwegian Institute of Public Health and for Sweden from the Public Health Agency of Sweden and the Swedish Association of Local Authorities and Regions.

In contrast to the Italian, Danish, Nowegian, and Finnish mortality data, the Swedish data do not appear to be entirely reliable. For example, the aggregated number of deaths do not always equal the sum of the daily deaths. However, I assume that this reflects poor statistical practices, that clerical errors exist, but that it does not have any implications for the modeling results other than somewhat lower goodness of fit (R²-value) and slightly wider confidence intervals for the parameters estimate.

For the statistical modeling, I use Stata release 16.1 and three-parameter Gompertz models, see Tjørve & Tjørve. The models can be described as:
deaths(day) = b1*exp(-exp(-b2*(day-b3)))
The parameters b1 and b2 can be described as shape parameters and b3 as a location parameter. The first shape parameter represents the upper asymptote, i.e. the expected overall number of deaths caused by the virus, and the second the rate with which deaths occur, a reflection of the effective reproduction number of infections. The location parameter is a time component that does not affect the shape of the curve. In the calculations I have set day=0 for the day of the first Covid-19 death, i.e. 11 March for Sweden, 12 March for Denmark and Norway, 21 March for Finland, and 21 February for Italy, Goodness of fit (R²) and parameter estimates (b1, b2, and b3) with confidence intervals are presented in the figures below. For more detailed information about the modeling or the results of the modeling, contact me at jonas.ranstam@mdas.se.


Results

The results are presented graphically and numerically in the figures below.


Literature

Mahtani KR, Heneghan C, Aronson JK. What is the evidence for social distancing during global pandemics? A rapid summary of current knowledge. On behalf of the Oxford COVID-19 Evidence Service Team Centre for Evidence-Based Medicine, Nuffield Department of Primary Care Health Sciences, University of Oxford. Downloaded from https://www.cebm.net/wp-content/uploads/2020/03/What-is-the-evidence-for-social-distancing-during-global-pandemics-final-1.pdf 24.03.2020.

Roosa K, Lee Y, Luo R, Kirpich A, Rothenberg R, Hyman JM, Yan P, Chowell G. Short-term Forecasts of the COVID-19 Epidemic in Guangdong and Zhejiang, China: February 13–23, 2020. J. Clin. Med. 2020, 9(2), 596; https://doi.org/10.3390/jcm9020596

Tjørve KMC, Tjørve E (2017) The use of Gompertz models in growth analyses, and new Gompertz-model approach: An addition to the Unified-Richards family. PLOS ONE 12(6): e0178691. https://doi.org/10.1371/journal.pone.0178691


Questions & Answers

Question: What is the purpose of this modeling? Do you try to predict the future number of Corona deaths?

Answer: The statistical challenge is to learn about the properties of an underlying mechanisms by analysing its observable characteristics. My goal is to find the statistical model that describes the Covid-19 pandemic consequences with as few parameters as possible yet retaining all important information. More specifically, I try to estimate the Gompertz model's 3 parameters that explain the mortality development in each country.


Question: How do you estimate the parameters in practice?

Answer: I run a Stata program that fits a statistical model to the observed data. The fitting is performed using non-linear least-squares estimation. The Stata compute command is pretty simple:
nl gom3: deaths day
There are, of course, as always, a number of complications. For example, the default number of iterations is not always sufficient, suitable intial values are often necessary but hard to find, and weighting observations by inverse variance weights is probably a good idea.


Question: What data is the latest analysis based on?

Answer: The dataset can be downloaded here.


[Home]

Figures

Figure 1



Figure 2




[Home]