Attack rates and case fatality rates are an example of how the epidemiological jargon may be confusing.
An attack rate is not an incidence rate. It is actually a risk (also called incidence proportions), and the time contribution of each individual is not included in the denominator.
The denominator consists of the number of people present at the beginning of the outbreak, disregarding those who will leave, develop illness, or die. This means that the cases (numerator) are also included in the denominator: it is therefor a true proportion.
In outbreaks of short duration, attack rate is a term frequently used instead of risk or incidence proportion. In a foodborne outbreak, we will often refer to "food specific attack rates". In this circumstance, the denominator will consist of the number of people who ate a specific food, while the numerator will consists of the number of people who ate that food and became ill.
No! These are distinct different concepts, though in many epidemiological manuscripts (and even text books) you will find that case fatality, case fatality rate and case fatality ratio are used as synonyms. However, they are not.
Case fatality is the concept used to express the proportion of cases of a certain disease that actually dies due to the consequences of that disease. Since it is a proportion, it is usually expressed as %, or per 1000. The case fatality can be seen as a cumulative incidence. It is relevant to keep in mind that the death has to be due to the consequences of the disease, since otherwise each disease would have a case fatality of 100% (since all people die eventually). It is a true proportion, since the denominator includes all cases, even those who died (the numerator).
Example of case fatality: around 1850, the case fatality of cholera (for which then there was no effective treatment) was up to 40%. This means that out of each 100 cases of cholera, 40 would eventually die due to the disease, usually within 2 weeks after onset. In comparison, the case fatality of tuberculosis in those times was almost 100% within the first 2 years after diagnosis, since there was no cure for tuberculosis either.
The CFR is a case fatality expressed over time. It is therefore a true rate, since time is included in the denominator. It can be expressed as number of deaths among cases per 100 or 1000 person-years. Depending on the disease, it may also be expressed per person-weeks or person months.
As a rate, it reflects the dynamic of the fatality over time, among cases.
To stay with the same example as above, around 1850, most cases of cholera had either recovered after 2 weeks, or had died. Once recovered from the disease, a person is no longer a case. That means that the person time of that person may no longer contribute to the denominator. If we assume that of the 100 cases of cholera, 40 die due to the disease after 2 weeks and the rest (60) recover from the disease after the same amount of time, then the CFR for cholera is in that situation 40 per 200 person-weeks (=1 per 5 person-weeks = 4 per 5 person-months = 10 per 1 person-year).
Likewise, of the 100 newly diagnosed tuberculosis patients, 50 would die in the first year and 50 would die in the second year. That comes down to a case fatality of 1 per 2 person years for the first year after diagnosis.
Here we can clearly see the major difference between case fatality and CFR: tuberculosis is clearly the 'greater killer' compared to cholera (because the case fatality is 100%, and of cholera 'only' 40%), however M.tuberculosis kills its victims much slower than Vibrio cholerae does.
This is simply the comparison of two case fatalities, expressed as a ratio. So the cholera:tuberculosis case fatality ratio is 40:100 (or 4:10). Usually we put the greater killer first, so the TB:cholera case fatality ratio is 2.5:1. In this sense, it is a comparison between 2 populations, similar as we do with odd ratio, risk ratio, sex ratio etc.
The Case Fatality Ratio could also be used to assess the impact of an intervention. For examples, if untreated cholera has a case fatality of 40% and when treatment is given in time, the fatality could be below 1%. This leads to a Case Fatality Ratio of 40 or more when comparing untreated and treated groups of cholera patients.