There is a “standard” definition of the epidemiological measure of the case fatality rate (or case fatality ratio—preferred term) for a disease. This is the number of people diagnosed with a disease who died because of the disease in an interval of time after the diagnosis divided by the number of people who had been diagnosed with the disease in the same interval.
https://www.britannica.com/science/case-fatality-rate
There is also a standard definition for the mortality rate from a disease. This is the number of people who died from the disease in a specific period of time divided by the number of people who could have died from the disease in the same interval of time—the total population.
https://www.cdc.gov/csels/dsepd/ss1978/lesson3/section3.html
EXAMPLE FOR NON-INFECTIOUS DISEASE
For these two measures (the case fatality ratio and the mortality rate), an example for a non-infectious disease—pancreatic cancer in 2016--is useful.
The one-year case-fatality ratio for pancreatic cancer is the number of people diagnosed with pancreatic cancer in (for example) 2016 who died in the year after their diagnosis divided by the number of people diagnosed with pancreatic cancer in 2016.
In 2016, about 53,000 people were diagnosed with pancreatic cancer in the United States. In the year after diagnosis, about 38,000 of these people had died of pancreatic cancer. The one-year case fatality ratio for people with diagnosed with pancreatic cancer in 2016 was 0.72 or 72%.
The (crude) mortality rate from pancreatic cancer in 2016 in the United States is the number of people who died from pancreatic cancer in 2016 divided by the number of people in the United States in 2016.
In 2016, about 42,000 people died from pancreatic cancer. The population of the United States in 2016 was about 323,000,000. In 2016, the crude mortality rate for pancreatic cancer was 13 per 100,000 (it is common practice to state mortality rates for a large population per 100,000).
INFECTIOUS DISEASES
For many infectious diseases (e.g., polio, influenza, hepatitis C), there is a “pool” of people that have been infected and but who are not diagnosed as having the disease and do not know they have been infected. This is because they don’t have symptoms or because the symptoms are minimal and the infection is unrecognized.
For infectious diseases, a third measure of mortality is the “infection fatality ratio.” This is the number of people who died from the disease in a given time interval divided by the number of people who have been infected in the same time interval.
The number of people infected in a given time interval—the denominator--is usually difficult to measure directly. It requires information on point or period prevalence of infection.
The infection fatality ratio can be estimated if there is reliable information about the proportions of people infected who are asymptomatic, who are minimally symptomatic, who develop the potentially fatal disease/condition caused by the infection, and, the proportion of those with the potentially fatal disease/condition who actually die. The latter— the proportion of those with the potentially fatal disease/condition who actually die—is the case fatality ratio.
INFECTION FATALITY RATIO EXAMPLE FOR INFECTIOUS DISEASE
An example—poliomyelitis--helps.
Polio is a highly infectious disease caused by the polio virus. It mainly affects children under the age of 5. After decades of study, much is known about the course of polio infection in children. About 70% are asymptomatic, 25%of have people infected with the polio virus have minimal or non-specific symptoms. About 0.5-1% develop acute flaccid paralysis. Of children who develop acute flaccid paralysis, 2-10% die.
https://www.who.int/news-room/fact-sheets/detail/poliomyelitis
https://www.aappublications.org/news/2020/03/18/mmwr031720
With these known facts, the infection mortality ratio for polio in children less than age 5 years can be estimated.
In 100,000 children less age 5 years, infected with polio:
Estimated cases of acute flaccid paralysis (lower estimate) = 100,000 x 0.005 = 500
Estimated cases of acute flaccid paralysis (upper estimate) = 100,000 x 0.01 = 1,000
Deaths in children with acute flaccid paralysis (lower estimate) = 500 x 0.02 = 10
Deaths in children with acute flaccid paralysis (upper estimate) = 1,000 x 0.10 = 100
Infection fatality ratio (lower estimate) = 10 / 100,000 = 0.0001
Infection fatality ratio (upper estimate) = 100 / 100,000 = 0.001
Cause-specific mortality rate? Ref https://www.cdc.gov/csels/dsepd/ss1978/lesson3/section3.html – geotheory Mar 19 '20 at 23:34