This is a strange case of difference in fatality rate between Chinese and Italian covid-19 outbreak.

In my knowdledge, fatality rate is a ratio between deaths from a certain disease compared to the total number of subjects diagnosed with the disease.

Starting from this assumption, I attempted to analyze difference in fatality rate between Chinese/Italian outbreak. Herein, I propose a reproducible R example for exploring this variable:

# Import dataset from authoritative source: 
# https://ourworldindata.org/coronavirus-source-data
covid <- read.csv("http://cowid.netlify.com/data/full_data.csv")

# Subsetting only data from China and Italy
dataset <- subset(covid, location == "China" | location == "Italy")

# Fatality ratio: is the proportion of deaths from a certain disease compared to the 
# total number of people diagnosed with the disease for a certain period of time.
dataset$fatality <- round(dataset$total_deaths/dataset$total_cases*100, 2)

# Generating plot
library(ggplot2)
ggplot(dataset, aes(as.numeric(date), fatality, color = location, group = location))+
  geom_smooth(size= .5, alpha=.25, color = "gray65")+
  geom_line()+
  geom_point()+
  labs(x="Outbreak duration (days)", y= "Fatality rate (%)", color = "Location")+
  theme_light(14)

EDT: Bar Plot

# Generating bar plot
library(ggplot2)
ggplot()+
  geom_bar(data=subset(dataset, location == "China"), 
           aes(as.numeric(date), fatality, fill = "China"), 
           stat = "identity", position = position_dodge(), alpha = .75)+
  
  geom_bar(data=subset(dataset, location == "Italy"), 
           aes(as.numeric(date), fatality, fill = "Italy"), 
           stat = "identity", position = position_dodge(), alpha = .75)+
  
  labs(x="Outbreak duration (days)", y= "Fatality rate (%)", fill = "Location")+
  scale_fill_brewer(palette = "Set1")+
  theme_light(14)

From this basis, I'm a little bit confused about such difference in terms of fatality rate between the two analyzed countries. In fact, China has the maximum fatality rate at 4%, while Italy at more than 6%. For this reason I've two questions:

1. Is my computation correct?

2. If yes, why such a huge difference in terms of fatality rate?

EDT II

I would like to enanche this question reporting a recent Science paper which can partially explain these differences. In fact, Li et al reported that for each COVID+ patient, other 5-10 are undocumented COVID+ leading to missleading fatality rate. Moreover, as reported in the comments, to date, there are no univocal diagnostic methods wordwide.