Mortality rates and case-fatality

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Let’s say we want to figure out the risk of dying for people who live in a certain population, like the population of France in 2015, which was around 66.6 million people.
The first way we could do this is by calculating the all-cause mortality rate or death rate. That’s the total number of deaths from all causes in 1 year divided by the total number of people at risk in the population at mid-year, and typically that’s the number of people at risk of death in the entire population.
For example, in 2015, there were approximately 620,000 deaths. So, the all-cause mortality rate in France was 620,000 divided by 66.6 million, or 0.0093.
We can express the mortality rate in a few different ways. First, we could say that the absolute risk of dying from all causes in France in 2015 was 0.0093.
Alternatively, we might express it as a percentage, by multiplying it by 100 - so 0.0093 times 100 equals 0.93%. Most often though, we express mortality rate in terms of number of deaths per 100,000 people.
So, we multiply the mortality rate - 0.0093 - by 100,000, which is 930. This means that, in France, there were 930 deaths per 100,000 people in 2015.
Mortality rates can be calculated for any time period, like 1 month, 1 year, or 10 years, but it’s important to specify which time period is used in the calculation, since the rate might be different for different time periods.
For example, a natural disaster - like an earthquake or forest fire - might increase the number of deaths in a certain time period.
Sometimes we’re interested in the mortality rate in a certain subpopulation, like only women or only people who are older than 65 years.
In those situations, we use a specific rate - like an age-specific rate or a gender-specific rate - which is calculated by dividing the number of deaths from all causes in one year by the number of people at risk of death in the subpopulation at mid-year.
For example, there were around 33.9 million women in France in 2015, and 298,000 women who died in that year, so the female-specific mortality rate was 0.0088, or 880 deaths from all causes per 100,000 women in France in 2015.
We can also calculate a cause-specific or disease-specific mortality rate for people with a specific disease, like cancer.
For example, let’s say there were 148,000 deaths from cancer in France in 2015. The cancer-specific mortality rate would be 148,000 deaths divided by 66.6 million, which is the total population at risk, and that equals 0.0022, or 220 cancer-specific deaths per 100,000 people in France in 2015.
We can even calculate a specific mortality rate for multiple subpopulations at once. For example, let’s say we want to know the cancer-specific mortality rate for women in France, so we can calculate a disease- and gender-specific mortality rate.
So, let’s say that 91,000 women in France died from cancer during 2015. If there were 33.9 million women in France in mid-2015, the mortality rate would be 91,000 divided by 33.9 million, which is 0.00268, or 268 cancer deaths per 100,000 women in France in 2015.
Another way we can calculate the risk of dying in a certain population is by determining the case-fatality rate, which is the percent of people that die within a certain time after their disease was diagnosed, and it’s calculated by dividing the number of deaths after diagnosis by the total number of individuals who have been diagnosed.
Put differently, case-fatality is a measure of how severe a disease is, and diseases with high case-fatality - like Ebola - are more severe than diseases with low case-fatality - like chickenpox.
The major difference between case-fatality and mortality rate is their denominator. The denominator for case-fatality is the number of people who have the specified disease, and this is different than the denominator for a mortality rate, which is the number of people at risk of dying from the disease, including people who have the disease and people that don’t have the disease.
As a simple example, let’s say that in a population of 500,000 people, 100 people are sick with a certain disease called Disease X, and in one year, 90 of the 100 people die from Disease X.
So, the mortality rate from Disease X would be 90 deaths divided by 500,000 - the total population at risk - which is 0.00018, or 0.018%.
On the other hand, the case-fatality from Disease X would be 90 deaths divided by 100 - the number of people who have the disease - which is 90%.
In this example, Disease X is rare, so the mortality rate is very low; but once a person has Disease X, the chance of dying is pretty high.
Another measure of mortality is proportionate mortality, which is the number of people who die from a certain cause divided by the total number of deaths in a population.
In other words, the proportionate mortality is a fraction of the total number of deaths. For example, in 2015 there were 620,000 total deaths in France, and of these, 148,000 of them were from cancer.
So, 148,000 divided by 620,000 is 0.24, which means that 24% of the total number of deaths in France in 2015 were from cancer!
One thing to know about proportionate mortality is that it isn’t a measure of risk. For example, let’s say we have two communities - Community A and Community B - that each have a population of 1,000.
Now, the proportionate mortality from cancer is 10% in Community A and 20% in Community B. At this point, it might be tempting to say that the risk of dying from cancer is higher in Community A than it is in Community B, but really we need more information to figure out if that’s true.
So, say the all-cause mortality rate is 3,000 per 100,000 people in Community A and 1,500 per 100,000 people in Community B.
We can calculate the cancer-specific mortality rate by multiplying the proportionate mortality by the all-cause mortality rate.
So, in Community A, the cancer-specific mortality rate is 10% times 3,000 - which gives us 300 deaths from cancer per 100,000 people.
In Community B, the cancer-specific mortality rate is 20% times 1,500 - which also gives us 300 deaths from cancer per 100,000 people.
So, even though Community A had a higher proportionate mortality than Community B, their cancer-specific mortality rates were actually the same.
Alright, as a quick recap, you can calculate the risk of mortality in a population using the all-cause mortality rate, which is the total number of deaths from all causes in 1 year divided by the number of people at risk in the population at mid-year.
You can also calculate a specific mortality rate for subpopulations, like women, older people, or people with a certain disease, like cancer.
The risk of mortality can also be calculated by the case-fatality rate, which is the number of deaths after diagnosis divided by the total number of individuals who have been diagnosed.
Finally, you can calculate the proportionate mortality, which is not a measure of risk, but is the number of people who die from a specific cause divided by the total number of deaths in a population during a certain time period.