# Absolute risk and prevalence?

From Wikipedia

If the absolute risk in the control group is available, conversion between the two is calculated by: $$RR \approx \frac{OR}{1 - R_C + (R_C \times OR)}$$ where:

RR = relative risk

OR = odds ratio

RC = absolute risk in the unexposed group, given as a fraction (for example: fill in 10% risk as 0.1)

What is the difference between absolute risk and (point) prevalence (used in rare disease assumption)?

Thanks!

The critical point, alluded to by Azula R in the comments, is that the risk reflects incident cases, while prevalence reflects both new and existing cases. Thus prevalance is a function of incidence and duration of disease. This distinction is important when trying to identify potentially modifiable causes of disease. If we identify a variable that is strongly associated with increased prevalance, intervening on that variable might do nothing to prevent future cases, because it might only be related to disease duration.

From epidemiological perspective, the absolute risk is the same as incidence rate, i.e, the rate at which new cases arise in a population during a certain time period. Absolute risk is not expressed in relation to an exposure, something that distinguishes it from relative risk that is expressed as a rate of a new cases given a certain exposure. In other words, relative risk is the ratio of two incidence rates.

Prevalence is the proportion of the population that has a certain condition. Point prevalence adds the time frame to this definition, and it is the proportion of the population having the condition at a certain point of time.

Incidence can't be directly estimated from a case-control study, but if you select the controls carefully, case-control study will allow you to estimate the risk ratio, that is the relative risk.

For more information, see the following two Chapters from a book published by IARC: http://www.iarc.fr/en/publications/pdfs-online/epi/cancerepi/CancerEpi-4.pdf http://www.iarc.fr/en/publications/pdfs-online/epi/cancerepi/CancerEpi-9.pdf

• Thanks! So the relation between RR and OR presented under given absolute risk is different from the one under small prevalence in rare disease assumption? – Tim Aug 9 '13 at 13:49
• Yes. However, I like to think about the issue a bit differently. How you can interpret the OR depends largely on how you select the controls. You do not necessarily need to make the rare disease assumption, if some other assumptions are met. In addition to the IARC publication linked above, see also journals.lww.com/smajournalonline/fulltext/2008/07000/…, and especially aje.oxfordjournals.org/content/168/9/1073.long. – JTT Aug 9 '13 at 15:25
• Absolute risk is not the same as incidence rate. Risk is calculated as (# new cases)/(total population), and is thus unit-less but often presented as percent or per 1000 population. Incidence rate is calculated as (# new cases)/(total person-time) where person-time is the total amount of time spent under observation across all people, and has units of cases per person-time. Prevalence is calculated as (# cases)/(total population), where cases includes both existing and new cases. Point prevalence is calculated at a given point in time. Period prevalence is calculated over a given time period. – Ellie Aug 9 '13 at 21:04