Introduction
Data source
Statistical methods
Class | Measure | Note |
---|---|---|
1. Elementary measures of change | 1. Range | Basic descriptive statistics that ignore the temporal trend |
2. Mean-over-time | ||
3. Standard deviation (SD) | ||
4. Coefficient of variation | ||
5. Change | Last observation - First observation | |
6. Mean change per week | Weekly value of change | |
7. Change/first score | Rescale change based on the first observation | |
8. Change/mean-over-time | Rescale the change based on all of the observations | |
9. slop b | Achieve from a linear regression model of observations on times | |
10. R2 of the linear model | The proportion of variation of observation that could be explained by the linear trend of the time | |
2. Measures of nonlinearity and in-constituency of change | 11. Max Δ1 (Δ1, i = yi + 1 - yi) | indicates that there is at least one big increase between two consecutive scores |
12. SD Δ1 | A high value of measure indicates that the first differences are not constant and that the pattern is therefore not linear | |
13. SD Δ1 per week | Adjust for the time elapsed between two consecutive scores | |
14. Mean | Δ1| | A high value of measure indicates that there are many abrupt changes during the time | |
15. Max | Δ1| | A high value of measure indicates that there is at least one crucial abrupt change regardless of the sign | |
16. Ratio, max | Δ1|/mean-over-time | To measure the relative importance of the significant abrupt | |
17. ratio, max | Δ1|/b | b is the coefficient of linear regression | |
18. Ratio, SD Δ1/b | To assess the relative importance of the variability of the first differences | |
3. Measures sensitive to nonmonotonicity and abrupt short-term fluctuations | 19. Mean Δ2 (Δ2, i = Δ1, i + 1 - Δ1, i) | To detect rather regular but nonlinear patterns |
20. Mean |Δ2| | Useful for further classifying trajectories for that measure 19 is close to 0 | |
21. Max |Δ2| | Indicates whether there is an essential local peak or valley | |
22. Ratio, max |Δ2|/mean-over-time | To assess the relative importance of the local peak | |
23. Ratio, max |Δ2|/mean |Δ1| | To assess the relative importance of the local peak | |
24. Ratio, mean |Δ2|/mean |Δ1| | To assess the relative importance of the fluctuation around the general rate of change | |
4. Measures contrasting early vs. later change | 25. Ratio, early/later change | More remarkable than 1.0 if the magnitude of early change is more significant than the later change |
26. Ratio, early/total change | Share of early change from the total change | |
27. Ratio, late/total change | Share of late change from the total change |
Results
Clustering incidence
Clustering mortality
The geographical distribution of clusters
Mortality 1 (Moderate) - Incidence 1 (Mild) | |
Belgium, Isle of Man, Ireland, Mayotte, San Marino | |
Mortality 2 (Mild) - Incidence 1 (Mild) | |
Aruba, Andorra, Saint Lucia, Liechtenstein, Portugal, French Polynesia, Seychelles | |
Mortality 3 (Severe) - Incidence 1 (Mild) | |
Czechia | |
Mortality 1 (Moderate) - Incidence 2 (Severe) | |
Chile, Spain, Estonia, France, Italy, Jordan, Lebanon, Lithuania, Luxembourg, Monaco, North Macedonia, Malta, Poland, occupied Palestinian territory, including east Jerusalem, Serbia, Slovenia, Sweden, United States of America | |
Mortality 2 (Mild) - Incidence 2 (Severe) | |
Armenia, Austria, Azerbaijan, Bahrain, Belize, Bermuda, Barbados, Botswana, Switzerland, Cabo Verde, Cyprus, Denmark, Falkland Islands (Malvinas), Faroe Islands, Georgia, Guadeloupe, Equatorial Guinea, French Guiana, Guam, Croatia, Iceland, Israel, Lesotho, Maldives, Montserrat, Martinique, Netherlands, Panama, Puerto Rico, Qatar, Saint Pierre and Miquelon, Sao Tome and Principe, Turks and Caicos Islands, Turkey, Saint Vincent and the Grenadines, United States Virgin Islands | |
Mortality 3 (Severe) - Incidence 2 (Severe) | |
Bulgaria, Bosnia and Herzegovina, The United Kingdom, Hungary, Montenegro, Slovakia | |
Mortality 1 (Moderate) - Incidence 3 (Moderate) | |
Albania, Brazil, Canada, Germany, Greece, Latvia, Republic of Moldova, Mexico, Paraguay, Romania, Russian Federation, Ukraine, Uruguay | |
Mortality 2 (Mild) - Incidence 3 (Moderate) | |
Afghanistan, Angola, Anguilla, United Arab Emirates, Argentina, Antigua and Barbuda, Australia, Burundi, Benin, Burkina Faso, Bangladesh, Bahamas, Belarus, Bolivia (Plurinational State of), Brunei Darussalam, Bhutan, Central African Republic, China, Cameroon, Democratic Republic of the Congo, Congo, Colombia, Comoros, Costa Rica, Cuba, Cayman Islands, Djibouti, Dominica, Dominican Republic, Algeria, Ecuador, Egypt, Eritrea, Ethiopia, Finland, Fiji, Gabon, Ghana, Guinea, Gambia, Guinea-Bissau, Grenada, Greenland, Guatemala, Guyana, Honduras, Haiti, Indonesia, India, Iran (Islamic Republic of), Iraq, Jamaica, Japan, Kenya, Kyrgyzstan, Cambodia, Saint Kitts and Nevis, Republic of Korea, Kuwait, Lao People’s Democratic Republic, Liberia, Libya, Sri Lanka, Morocco, Madagascar, Mali, Myanmar, Mongolia, Northern Mariana Islands (Commonwealth of the), Mozambique, Mauritania, Mauritius, Malawi, Malaysia, Namibia, New Caledonia, Niger, Nigeria, Nicaragua, Norway, Nepal, New Zealand, Oman, Pakistan, Philippines, Papua New Guinea, Rwanda, Saudi Arabia, Sudan, Senegal, Singapore, Sierra Leone, El Salvador, Somalia, Suriname, Eswatini, Syrian Arab Republic, Chad, Togo, Thailand, Tajikistan, Timor-Leste, Trinidad and Tobago, Tunisia, United Republic of Tanzania, Uganda, Uzbekistan, Venezuela (Bolivarian Republic of), British Virgin Islands, Viet Nam, Yemen, South Africa, Zambia, Zimbabwe | |
Mortality 3 (Severe) - Incidence 3 (Moderate) | |
Kazakhstan, Peru | |
Mortality 1 (Moderate) - Incidence 1 | |
Belgium, Isle of Man, Ireland, Mayotte, San Marino | |
Mortality 2 (Mild) - Incidence 1 | |
Aruba, Andorra, Saint Lucia, Liechtenstein, Portugal, French Polynesia, Seychelles | |
Mortality 3 (Severe) - Incidence 1 | |
Czechia |