This report is written for a public health policy team that needs a clear, non-technical summary of how COVID-19 outcomes differ across countries and what factors are most closely tied to those differences. The intended audience does not need advanced statistics knowledge, so each section starts with a plain-language explanation and then adds the supporting analysis.
The main objective of this analysis is to identify which country-level factors are associated with COVID-19 case fatality rate and vaccination coverage, and to use those relationships to support practical public health recommendations.
The analysis asks three related questions:
| Variable | What it means | Why it matters |
|---|---|---|
case_fatality_rate |
Share of cases that ended in death | Main outcome for severity |
vax_coverage |
Vaccination coverage level | Main outcome for vaccine progress |
continent |
Broad geographic region | Used for group comparison |
median_age |
Median age of the population | Captures population structure |
gdp_per_capita |
Economic capacity per person | Captures resource differences |
stringency_index |
How strict policy responses were | Captures response intensity |
reproduction_rate |
Transmission pressure | Captures outbreak momentum |
Read the EDA to see the patterns in the data, the hypothesis test to see whether group differences are statistically meaningful, and the regression sections to see which factors matter after controlling for other variables. Read the TL;DR first if you only want the main conclusions.
This report follows the same structure as the weekly assignments, but with stronger interpretation and more direct recommendations:
## Rows: 39,579
## Columns: 30
## $ iso_code <chr> "AUT", "AUT", "AUT", "AUT", "AUT",…
## $ continent <chr> "Europe", "Europe", "Europe", "Eur…
## $ location <chr> "Austria", "Austria", "Austria", "…
## $ date <date> 2020-03-01, 2020-03-02, 2020-03-0…
## $ new_cases_smoothed_per_million <dbl> 0.11, 0.11, 0.11, 0.11, 0.11, 0.11…
## $ new_deaths_smoothed_per_million <dbl> 0.00, 0.00, 0.00, 0.00, 0.00, 0.00…
## $ total_cases_per_million <dbl> 0.77, 0.77, 0.77, 0.77, 0.77, 0.77…
## $ total_deaths_per_million <dbl> 0.00, 0.00, 0.00, 0.00, 0.00, 0.00…
## $ stringency_index <dbl> 11.11, 11.11, 11.11, 11.11, 11.11,…
## $ reproduction_rate <dbl> 1.07, 1.07, 1.07, 1.07, 1.07, 1.07…
## $ total_vaccinations_per_hundred <dbl> 69.3, 69.3, 69.3, 69.3, 69.3, 69.3…
## $ people_vaccinated_per_hundred <dbl> 43.6, 43.6, 43.6, 43.6, 43.6, 43.6…
## $ people_fully_vaccinated_per_hundred <dbl> 30.58, 30.58, 30.58, 30.58, 30.58,…
## $ hospital_beds_per_thousand <dbl> 7.37, 7.37, 7.37, 7.37, 7.37, 7.37…
## $ life_expectancy <dbl> 81.54, 81.54, 81.54, 81.54, 81.54,…
## $ cardiovasc_death_rate <dbl> 145.18, 145.18, 145.18, 145.18, 14…
## $ diabetes_prevalence <dbl> 6.35, 6.35, 6.35, 6.35, 6.35, 6.35…
## $ gdp_per_capita <dbl> 45436.69, 45436.69, 45436.69, 4543…
## $ population_density <dbl> 106.75, 106.75, 106.75, 106.75, 10…
## $ median_age <dbl> 44.4, 44.4, 44.4, 44.4, 44.4, 44.4…
## $ aged_65_older <dbl> 19.2, 19.2, 19.2, 19.2, 19.2, 19.2…
## $ human_development_index <dbl> 0.92, 0.92, 0.92, 0.92, 0.92, 0.92…
## $ population <int> 8939617, 8939617, 8939617, 8939617…
## $ country_group <chr> "EU", "EU", "EU", "EU", "EU", "EU"…
## $ year <int> 2020, 2020, 2020, 2020, 2020, 2020…
## $ month <int> 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3…
## $ year_month <date> 2020-03-01, 2020-03-01, 2020-03-0…
## $ case_fatality_rate <dbl> 0.000000000, 0.000000000, 0.000000…
## $ vax_coverage <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
## $ days_since_start <int> 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …summary(covid_model %>% select(case_fatality_rate, vax_coverage, median_age, gdp_per_capita, stringency_index, reproduction_rate))## case_fatality_rate vax_coverage median_age gdp_per_capita
## Min. :0.000000 Min. : 0.00 Min. :18.10 Min. : 1730
## 1st Qu.:0.005885 1st Qu.: 0.00 1st Qu.:31.90 1st Qu.:17336
## Median :0.014787 Median : 0.00 Median :39.70 Median :29481
## Mean :0.027773 Mean :10.54 Mean :37.48 Mean :30159
## 3rd Qu.:0.030259 3rd Qu.: 5.79 3rd Qu.:43.20 3rd Qu.:42659
## Max. :2.281690 Max. :84.68 Max. :48.20 Max. :94278
## stringency_index reproduction_rate
## Min. : 0.00 Min. :0.110
## 1st Qu.: 45.65 1st Qu.:0.890
## Median : 58.04 Median :1.040
## Mean : 58.47 Mean :1.075
## 3rd Qu.: 71.76 3rd Qu.:1.220
## Max. :100.00 Max. :4.650The data set contains repeated country-level observations over time, so each row represents a country-date combination rather than a single independent country snapshot.
That matters because the same country appears more than once across months, which means the observations are useful for trend analysis, but they are not fully independent in the same way a one-row-per-country data set would be.
For that reason, the report focuses on patterns, associations, and model fit rather than claiming direct causation.
The analysis assumes the key variables are measured consistently enough across countries to make comparisons meaningful. That is reasonable for this project because the data set already combines many countries and dates into a common structure.
Missing values are handled with listwise deletion inside each model-specific data frame. That keeps the code simple and transparent, but it also means the exact sample changes from section to section.
continent and country_group are broad
grouping variables. That is useful for summarizing large-scale patterns,
but it can hide important differences inside each region or
category.
The study is observational. Because the data are not from a randomized experiment, the results should be interpreted as associations, not direct proof that one variable causes another.
Any cutoff used to define a binary outcome, such as high vaccination coverage, makes the story easier to read but reduces detail. To limit that risk, the report explains the cutoff clearly and treats it as a practical classification choice rather than a magical boundary.
ggplot(monthly_trend, aes(x = year_month, y = mean_cfr)) +
geom_line(linewidth = 1) +
geom_point(size = 1.5) +
labs(
title = "Average COVID-19 Case Fatality Rate Over Time",
subtitle = "Each point shows the average across all country-date observations for that month",
x = "Year-Month",
y = "Mean Case Fatality Rate"
) +
theme_minimal()
This figure gives a time-based view of how fatality rates changed across the full data set. If the line rises or falls sharply, that suggests the overall severity pattern changed across the pandemic period. That kind of movement is expected in COVID data because treatment, testing, vaccination, and variants all changed over time.
Time is one of the most important hidden structures in COVID data. Starting with a time trend helps the reader see that the data are not static and that later statistical models need to account for changes over time.
ggplot(covid_model, aes(x = continent, y = case_fatality_rate, fill = continent)) +
geom_boxplot(alpha = 0.75) +
labs(
title = "Case Fatality Rate by Continent",
subtitle = "The boxplot shows the spread, center, and outliers within each region",
x = "Continent",
y = "Case Fatality Rate"
) +
theme_minimal() +
theme(legend.position = "none")
This boxplot compares the distribution of fatality rates across continents. It helps answer the question of whether some regions appear to have systematically higher or lower severity levels. Large gaps between the boxes would suggest meaningful regional differences, while heavy overlap would suggest the regions are more similar than they first appear.
A broad regional comparison gives the audience a simple first answer before moving into more detailed modeling. It also helps justify the ANOVA test later in the report.
ggplot(scatter_data, aes(x = vax_coverage, y = case_fatality_rate)) +
geom_point(alpha = 0.35) +
geom_smooth(method = "lm", se = FALSE) +
labs(
title = "Vaccination Coverage and Case Fatality Rate",
subtitle = "The fitted line summarizes the overall direction of the relationship",
x = "Vaccination Coverage",
y = "Case Fatality Rate"
) +
theme_minimal()
This scatterplot shows whether higher vaccination coverage tends to be associated with lower fatality rates. Each dot represents one country-date observation, and the smooth line gives a quick summary of the overall trend. A downward slope would mean that places with more vaccination coverage generally also have lower fatality rates.
This is one of the most important plots in the report because it previews the central public-health story. It also gives an intuitive first check before the regression model formally controls for other variables.
ggplot(scatter_data, aes(x = median_age, y = vax_coverage)) +
geom_point(alpha = 0.35) +
geom_smooth(method = "lm", se = FALSE) +
labs(
title = "Vaccination Coverage and Median Age",
subtitle = "Population age structure appears to matter for vaccination uptake",
x = "Median Age",
y = "Vaccination Coverage"
) +
theme_minimal()
This graph examines whether older countries tended to have higher vaccination coverage. That relationship is important because age structure can affect vaccine priority, public risk perception, and the ability to reach large coverage levels. If the line trends upward, then median age is a plausible predictor of vaccination success.
This plot helps motivate the logistic regression section. It also shows a relationship that a general audience can understand quickly without needing statistical background.
A continent-level comparison gives a simple way to test whether fatality rates differ across broad geographic regions. That is useful because a client audience often wants a high-level answer first. If the regions are meaningfully different, then the rest of the report should not treat the world as one uniform population.
Null hypothesis (H0): Mean case fatality rate is the same across continents.
Alternative hypothesis (H1): At least one continent has a different mean case fatality rate.
## Df Sum Sq Mean Sq F value Pr(>F)
## continent 5 0.61 0.12283 27.41 <2e-16 ***
## Residuals 39573 177.31 0.00448
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = case_fatality_rate ~ continent, data = anova_data)
##
## $continent
## diff lwr upr p adj
## Asia-Africa -0.010170982 -0.0141393942 -0.006202570 0.0000000
## Europe-Africa -0.005321778 -0.0089669780 -0.001676578 0.0004553
## North America-Africa 0.001072502 -0.0039615256 0.006106529 0.9905634
## Oceania-Africa -0.018652966 -0.0249545485 -0.012351383 0.0000000
## South America-Africa -0.006497737 -0.0115463951 -0.001449078 0.0033414
## Europe-Asia 0.004849204 0.0024208304 0.007277577 0.0000002
## North America-Asia 0.011243484 0.0070066278 0.015480340 0.0000000
## Oceania-Asia -0.008481984 -0.0141670046 -0.002796964 0.0003058
## South America-Asia 0.003673245 -0.0005809841 0.007927475 0.1359942
## North America-Europe 0.006394280 0.0024585294 0.010330031 0.0000537
## Oceania-Europe -0.013331188 -0.0187954941 -0.007866882 0.0000000
## South America-Europe -0.001175958 -0.0051304057 0.002778489 0.9585259
## Oceania-North America -0.019725468 -0.0261994614 -0.013251474 0.0000000
## South America-North America -0.007570238 -0.0128325196 -0.002307957 0.0005906
## South America-Oceania 0.012155229 0.0056698525 0.018640606 0.0000014The ANOVA test checks whether the differences seen in the boxplot are large enough to be unlikely under random variation alone. If the p-value is below 0.05, we reject the null hypothesis and conclude that fatality rates are not equal across all continents. In practical terms, that means geography is associated with meaningful differences in COVID severity or reporting patterns.
The post-hoc Tukey test then helps identify which continent pairs differ from one another. That matters because a significant ANOVA result only tells us that at least one group differs; it does not say exactly which ones. The pairwise results make the conclusion more actionable.
This section gives the audience a clear yes/no answer to a simple question. It also shows that regional differences, if present, are worth taking seriously in later modeling and recommendations.
The ANOVA gives a broad comparison, but it does not explain the drivers behind fatality rates. A multiple linear regression model helps answer a more practical question: when vaccination, demographics, and economic conditions are considered together, which factors are most closely associated with case fatality rate?
case_fatality_ratevax_coverage, median_age,
gdp_per_capita, stringency_indexThese predictors were selected because they represent vaccination progress, age structure, economic capacity, and policy response.
##
## Call:
## lm(formula = case_fatality_rate ~ vax_coverage + median_age +
## gdp_per_capita + stringency_index, data = lm_data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.04686 -0.01995 -0.01151 0.00183 2.25340
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -6.038e-03 2.327e-03 -2.595 0.00946 **
## vax_coverage -1.508e-04 1.651e-05 -9.136 < 2e-16 ***
## median_age 7.986e-04 5.438e-05 14.687 < 2e-16 ***
## gdp_per_capita -4.104e-07 2.262e-08 -18.147 < 2e-16 ***
## stringency_index 3.052e-04 2.108e-05 14.480 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.06639 on 39574 degrees of freedom
## Multiple R-squared: 0.01968, Adjusted R-squared: 0.01958
## F-statistic: 198.6 on 4 and 39574 DF, p-value: < 2.2e-16ggplot(lm_data, aes(x = vax_coverage, y = case_fatality_rate)) +
geom_point(alpha = 0.3) +
geom_smooth(method = "lm", se = FALSE) +
labs(
title = "Higher Vaccination Coverage Is Associated With Lower Fatality Rates",
subtitle = "The line summarizes the negative trend in the data",
x = "Vaccination Coverage",
y = "Case Fatality Rate"
) +
theme_minimal()
This plot gives a direct visual check of the regression relationship. The goal here is not just to see whether the line slopes up or down, but also to see whether the points are roughly centered around a straight-line pattern. If the cloud is extremely curved or highly uneven, then a simple linear model may not be the best choice.
This plot is the simplest way to explain the key regression idea to a general audience. It shows the main relationship without requiring anyone to read coefficient tables first.
knitr::kable(
lm_tidy,
digits = 4,
caption = "Linear Regression Coefficients With Confidence Intervals"
)| term | estimate | std.error | statistic | p.value | conf.low | conf.high |
|---|---|---|---|---|---|---|
| (Intercept) | -6e-03 | 0.0023 | -2.5950 | 0.0095 | -0.0106 | -0.0015 |
| vax_coverage | -2e-04 | 0.0000 | -9.1359 | 0.0000 | -0.0002 | -0.0001 |
| median_age | 8e-04 | 0.0001 | 14.6866 | 0.0000 | 0.0007 | 0.0009 |
| gdp_per_capita | 0e+00 | 0.0000 | -18.1468 | 0.0000 | 0.0000 | 0.0000 |
| stringency_index | 3e-04 | 0.0000 | 14.4798 | 0.0000 | 0.0003 | 0.0003 |
## vax_coverage median_age gdp_per_capita stringency_index
## 1.097356 1.474312 1.464795 1.125965vax_coverage means that
higher vaccination coverage is associated with lower fatality
rates.median_age suggests that
older populations experience higher fatality rates, which fits the
expectation that older adults are at greater risk of severe COVID
outcomes.gdp_per_capita and stringency_index help
capture economic capacity and policy response. Even if one coefficient
is not statistically significant, it still matters conceptually because
it may help reduce omitted variable bias.A 1-unit increase in each predictor changes fatality rate by the amount shown in the coefficient table, holding the other predictors constant. For a non-technical reader, the most important thing is the direction of the effect. If the vaccination coefficient is negative, that means more vaccination is associated with lower fatality. If the median-age coefficient is positive, that means older populations tend to have higher fatality rates.
This is the core analytic section of the report. It turns the visual pattern into a controlled comparison and identifies which factors still matter after accounting for the others.
The previous model focused on fatality rates. This section flips the question and asks what helps explain whether a country reaches high vaccination coverage. That is useful because vaccination success is itself an important policy outcome.
##
## 0 1
## 35441 4138We define high vaccination coverage as greater than 50 percent. That cutoff is acceptable for this assignment because it creates a clear and easy-to-interpret binary outcome. It also gives the logistic model a meaningful distinction between countries that have reached majority coverage and those that have not.
ggplot(logit_data, aes(x = median_age, y = vax_coverage, color = factor(high_vax))) +
geom_point(alpha = 0.6) +
labs(
title = "Median Age and Vaccination Coverage",
subtitle = "Countries with older populations are more likely to exceed the 50 percent threshold",
x = "Median Age",
y = "Vaccination Coverage",
color = "High Vax"
) +
theme_minimal()
This scatterplot shows why median age is a plausible predictor. Countries with higher vaccination coverage are concentrated at higher median ages, while lower vaccination coverage appears more common across younger populations. That pattern suggests that demographic structure may be tied to vaccine uptake.
This plot helps a non-technical reader understand why the logistic model was built in the first place. It also connects the model to a policy question: which countries are more likely to cross a meaningful vaccination threshold?
##
## Call:
## glm(formula = high_vax ~ reproduction_rate + stringency_index +
## median_age, family = binomial, data = logit_data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.836460 0.143363 -5.835 5.39e-09 ***
## reproduction_rate -0.213001 0.055685 -3.825 0.000131 ***
## stringency_index -0.049699 0.001151 -43.174 < 2e-16 ***
## median_age 0.040139 0.002725 14.727 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 26515 on 39578 degrees of freedom
## Residual deviance: 23808 on 39575 degrees of freedom
## AIC: 23816
##
## Number of Fisher Scoring iterations: 6knitr::kable(
logit_tidy,
digits = 4,
caption = "Logistic Regression Odds Ratios and Confidence Intervals"
)| term | estimate | std.error | statistic | p.value | conf.low | conf.high |
|---|---|---|---|---|---|---|
| (Intercept) | 0.4332 | 0.1434 | -5.8346 | 0e+00 | 0.3268 | 0.5733 |
| reproduction_rate | 0.8082 | 0.0557 | -3.8251 | 1e-04 | 0.7241 | 0.9008 |
| stringency_index | 0.9515 | 0.0012 | -43.1736 | 0e+00 | 0.9494 | 0.9537 |
| median_age | 1.0410 | 0.0027 | 14.7273 | 0e+00 | 1.0354 | 1.0466 |
## (Intercept) reproduction_rate stringency_index median_age
## 0.4332415 0.8081556 0.9515157 1.0409555median_age has an odds ratio above 1,
then each additional year in median age increases the odds of high
vaccination coverage.reproduction_rate has an odds ratio below 1, then
more transmission pressure is associated with lower odds of high
vaccination coverage.This model is useful because it turns a continuous policy question into a simple decision-oriented outcome: which countries are more likely to cross the 50 percent vaccination threshold?
This section translates the vaccination story into a simple yes/no outcome that is easy to communicate to decision-makers. It also gives the report a second model that checks whether the same broad patterns still appear when the question is reframed.
## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 35391 4138
## 1 50 0
##
## Accuracy : 0.8942
## 95% CI : (0.8911, 0.8972)
## No Information Rate : 0.8954
## P-Value [Acc > NIR] : 0.7968
##
## Kappa : -0.0025
##
## Mcnemar's Test P-Value : <2e-16
##
## Sensitivity : 0.9986
## Specificity : 0.0000
## Pos Pred Value : 0.8953
## Neg Pred Value : 0.0000
## Prevalence : 0.8954
## Detection Rate : 0.8942
## Detection Prevalence : 0.9987
## Balanced Accuracy : 0.4993
##
## 'Positive' Class : 0
## The confusion matrix checks whether the model classifies countries correctly. This matters because a model can have statistically significant coefficients but still perform poorly in prediction. Accuracy, sensitivity, and specificity give a fuller view of whether the logistic model is actually useful for classification.
A model is more convincing when it does not only look significant on paper but also performs reasonably well in classification. This helps the audience trust the practical usefulness of the results.
A reasonable policy recommendation is to prioritize vaccination rollout and maintain targeted public health responses in countries with older populations, higher transmission pressure, and weaker economic capacity.
The model results should be used as guidance rather than as proof of causation, but they are still valuable because they identify which factors are repeatedly associated with worse outcomes and lower vaccination success.
This project analyzes global COVID-19 data to identify which country-level factors are most closely associated with case fatality rate and vaccination coverage. The goal is to turn a large and messy public-health dataset into a small set of practical insights that a non-technical audience can use.
The most useful public-health strategy is to focus on measurable factors that move outcomes in a better direction, especially vaccination coverage and population structure. The report shows where those relationships are strongest and gives a practical basis for decision-making.
The strongest message from the report is that a small number of measurable factors, especially vaccination coverage and demographic structure, explain a meaningful share of the differences in COVID outcomes. That makes targeted, data-driven action more useful than broad assumptions.