The results presented below in Table 1, were obtained using the COVID-19 data recorded on 2020 July 27th [6]. No significant differences were observed in the results when using COVID-19 data recorded two weeks before or two weeks after that date because infection and mortality rates per one million population did not vary significantly.
Table 1 Mean level of 25(OH)D in increasing order, cases of COVID-19/1 M, deaths caused by COVID-19/1 M, lethality (27th July 2020)
Countries
|
25(OH)D means (nmol/L)
|
Cases/1 M
|
Deaths/1 M
|
Lethality
|
Portugal
|
39
|
4934
|
169
|
0.03
|
Spain
|
42.5
|
6969
|
608
|
0.09
|
Switzerland
|
46
|
3997
|
228
|
0.06
|
Denmark
|
47
|
2338
|
106
|
0.05
|
UK
|
47.4
|
4419
|
674
|
0.15
|
Belgium
|
49.3
|
5730
|
847
|
0.15
|
Italy
|
50
|
4074
|
581
|
0.14
|
Germany
|
50.1
|
2475
|
110
|
0.04
|
Estonia
|
51
|
1536
|
52
|
0.03
|
Turkey
|
51.8
|
2690
|
67
|
0.02
|
Ireland
|
56.4
|
5239
|
357
|
0.07
|
Island
|
57
|
5431
|
29
|
0.01
|
Netherlands
|
59.5
|
3101
|
358
|
0.12
|
France
|
60
|
2804
|
463
|
0.17
|
Hungary
|
60.6
|
461
|
62
|
0.13
|
Czechia
|
62.5
|
1449
|
35
|
0.02
|
Norway
|
63.5
|
1684
|
47
|
0.03
|
Finland
|
67.7
|
1336
|
59
|
0.04
|
Sweden
|
73.5
|
7858
|
564
|
0.07
|
Slovakia
|
81.5
|
404
|
5
|
0.01
|
The results for the number of cases, for mortality and for lethality were summarized in Table 2, Table 3 and Table 4, respectively.
K-means algorithm applied with k = 2 for example to Mortality variable, using the original Table 1 sample, yielded two clusters of countries, one cluster of 8 countries (Spain, United Kingdom, Belgium, Italy, Ireland, The Netherlands, France, Sweden) having an elevated mortality rate and a second cluster of 12 countries (Portugal, Switzerland, Denmark, Germany, Estonia, Turkey, Island, Hungary, Czechia, Norway, Finland, Slovakia) having a moderated or low mortality rate, see Table 3.
Table 2 Statistics for the Number of Cases/1 M
Methods
|
Cut points c (nmol/L)
|
Statistics for Cases/1 M
|
Sample size
Mean
Standard Deviation
Maximum
Minimum
|
|
n = 20
m = 3446 [2654 4403]
s = 2112 [1634 2699]
7,858 (Sweden)
404 (Slovakia)
|
Correlation to 25(OH)D
|
|
- 0.338 (p = 0.073)
|
K-means algorithm (K = 2)
Δ: cluster of countries having
a higher number of Cases/1 M
: cluster of countries having
a lower number of Cases/1 M
|
|
Δ = {Portugal, Spain, Switzerland, UK,
Belgium, Italy, Ireland Island, Sweden}.
Cases/1 M > 3200
= {Denmark, Germany, Estonia,
Turkey, Netherland, France, Hungary,
Czechia, Norway, Finland, Slovakia}.
Cases/1 M ≤ 3200
|
Maximal Between Class
Absolute Difference of means
|
49.3 [40 60]
|
m1 = 4731.17, m2 = 2895.86
m1 – m2 = 1835.61
m1 > m2(p = 0.026) at c = 49.3
|
Minimal t-test p-value
|
50 [43 67]
|
p = 0.019 at c = 50
|
Maximal Between Class
Variance
|
50 [42.5 59.5]
|
BCV = 765,000 at c = 50
|
Minimal Entropy
|
50 [42.5 57]
|
H = 0.7137at c = 50
|
Gaussian Kernel Regression
|
|
Rise starting at 61 ± 6 nmol/L
|
Class 1: Countries such that 25(OH)D ≤ c
Class 2: Countries such that 25(OH)D > c
Table 3 Statistics for Mortality/1 M
Methods
|
Cut points c (nmol/L)
|
Statistics for Mortality/1 M
|
Sample size
Mean
Standard Deviation
Maximum
Minimum
|
|
n = 20
m = 271 [171 396]
s = 263 [213 338]
847 (Belgium)
5 (Slovakia)
|
Correlation with 25(OH)D
|
|
- 0.276 (p = 0.119)
|
K-means algorithm (K = 2)
Δ: cluster of countries having a higher mortality/1 M
: cluster of countries having lower mortality/1 M
|
|
Δ = {Spain, UK, Belgium, Italy,
Ireland, Netherland, France,
Sweden}.
Deaths/1 M > 230
= {Portugal, Switzerland,
Denmark, Germany, Estonia,
Turkey, Island, Hungary,
Czechia, Norway, Finland,
Slovakia}.
Deaths/1 M ≤ 230
|
Maximal Between Class
Absolute Difference of means
|
50 [43 59]
|
m1 = 459.88, m2 = 169.85
m1 – m2 = 290.03
m1 > m2(p = 0.020) at c = 50
|
Minimal t-test p-value
|
50 [43 56]
|
p = 0.020 at c = 50
|
Maximal Between Class
Variance
|
50 [39 56]
|
BCV = 19,021 at c = 50
|
Minimal Entropy
|
60 [48 72]
|
H = 0.8950at c = 50
|
Gaussian Kernel Regression
|
|
Rise starting at 62s ± 6 nmol/L
|
Class 1: Countries such that 25(OH)D ≤ c
Class 2: Countries such that 25(OH)D > c
Table 4: Statistics for Lethality variable
Methods
|
Cut points c (nmol/L)
|
Statistics for Lethality
|
Sample size n = 20
Mean
Standard Deviation
Maximum
Minimum
|
|
n = 20
m = 0.072 [0.050 0.097]
s = 0.053 [0.042 0.063]
0.17 (France)
0.01 (Slovakia)
|
Correlation with 25(OH)D
|
|
- 0.195 (p = 0.205)
|
K-means algorithm (K = 2)
Δ: cluster of countries
having higher lethality
: cluster of countries
having lower lethality
|
|
Δ = {Spain, UK, Belgium, Italy,
Netherland, France, Hungary}.
Lethality > 0.08
= {Portugal, Switzerland,
Denmark, Germany, Estonia,
Turkey, Ireland, Island,
Czechia, Norway, Finland,
Sweden, Slovakia}.
Lethality < 0.08
|
Maximal Between Class
Absolute Difference of
means
|
60.6 [49 73]
|
m1 = 0.084, m2 = 0.034
m1 – m2 = 0.05
m1 > m2(p < 0.01)
at c = 60.6
|
Minimal t-test p-value
|
60.6 [49 73]
|
p = 0.0055 at c = 60.6
|
Maximal Between Class
Variance
|
60.6 [49 73]
|
BCV = 0.0005 at c = 60.6
|
Minimal Entropy
|
60.6 [48 67]
|
H = 0.7476at c = 60.6
|
Gaussian Kernel
Regression
|
|
Rise starting at 63 ± 6
nmol/L
|
Class 1: Countries such that 25(OH)D ≤ c
Class 2: Countries such that 25(OH)D > c
For the Cases variable, the cut point c was found around 50 nmol/L for any of the four criteria from Table 1 sample, see Fig. 1 and Fig. 2. The boot.ci function performed the procedure on each of the R = 1,000 bootstrapped samples to get a 95% CI displayed in Table 2.
Linear regressions applied to our data were not significant, confidence intervals were not acute enough and p-values derived from Dupont-Plummer formulas [7] were bad, even using bootstrap methods. The nonparametric Gaussian Kernel regression curve of the morbidity variable on 25(OH)D, showed a rising starting at 61 nmol/L when using Table 1 data, see Fig. 3. That of mortality variable showed a rising at 62 nmol/L when using Table 1 data, see Fig. 4.
In our Table 1 sample, we noticed that there was only one country, namely Sweden, over the 6 countries having 25(OH)D mean strictly greater than 60nmol/L, which had an elevated mortality rate, while 7 countries over the 14 having 25(OH)D less than 60 nmol/L, had an elevated mortality rate, see Fig. 4.
However, 25(OH)D is certainly not the only factor that could predict mortality clusters and : we observed that the AUC (Area Under Curve) of ROC curves were lower than 0.65 when performing the prediction function in the ROCR package of R software.