# Prevalence Ratio, Odds Ratio and Relative Risk

I would like to know the differences among Prevalence Ratio, Odds Ratio and Relative Risk. Could any one please tell me?

Question

I would like to know the differences among Prevalence Ratio, Odds Ratio and Relative Risk. Could any one please tell me?

- Relative risk (RR) is the risk of an event (or of developing a disease) relative to exposure. Relative risk is a ratio of the probability of the event occurring in the exposed group versus a non-exposed group. In medical research, the odds ratio is commonly used for case-control studies, as odds, but not probabilities, are usually estimated. Relative risk is used in randomized controlled trials and cohort studies. http://www.childrensmercy.org/stats/journal/oddsratio.aspx
- Thank you very much for your information. Could you please also tell me the differences between Prevalence Ratio and them?
- For example, if 80 out of 100 exposed subjects have a particular disease and 50 out of 100 non-exposed subjects have the disease, then the odds ratio (OR) is (80/20)/(50/50) = 4. However, the prevalence ratio (PR) is (80/100)/(50/100) = 1.6. The latter indicates that the exposed subjects are only 1.6 times as likely to have the disease as the non-exposed subjects, and this is the number in which most people would be interested.
- Thank you so much. It does help me understand better.
- As Maria so nicely explained, when the outcome is common the OR tends to be inflated in comparison to the prevalence ratio. With common outcomes the confidence interval for the OR is also often quite wide. The prevalence ratio will give you a tighter CI given its smaller standard error.
- Thanks a lot, Alan, for great explanation!
- While all explanations are somewhat correct they freely make use concepts that are related but not the same. Prevalence and risk are being used interchangeably, but they are actually different epidemiologically and using them in the same way may cause confusion in some situations.

Risk is the probability of occurrence of a new event (say health outcome) over a period of time among those who are at risk for event occurrence (say developing/acquiring health outcome) at the beginning of the follow up period. Risk is usually expressed as a value between 0 and 1, as all probabilities. It is often estimated through follow-up or Cohort studies of two groups of subjects/individuals (with or without some characteristics/attribute – usually called exposed and unexposed groups). So, the Risk estimates the average probability of occurrence of an outcome over a specified period of time among individuals at risk for having the outcome at the beginning of the follow-up period.

Prevalence is the number or proportion of subjects/individuals with some attribute (can als be the level of attribute/characteristics) or outcome (event) in a point in time or period of time. Prevalence is usually expressed as a proportion (0 to 1 as probabilities; or as percentages). It is usually derived from cross-sectional studies or a random sample from a population of subjects/individuals in a point in time (or period of time) – no need to specify a follow up period.

Therefore, Prevalence Ratio (erroneously called Prevalence Rate Ratio- because prevalence is not a rate) indicates how large is the prevalence of an event/outcome in one group of subjects/individuals (with characteristics/attribute) relative to another group (without the characteristics/attributes).

While, the ratio of the risks (Risk Ratio or Cumulative Incidence Ratio) indicates how more or less likely one a group of individuals/subjects with attribute/characteristics (exposure) is to develop/acquire a health outcome or conditions over the follow up period relative to the other group of unexposed.

The mathematic of the Odds Ratio presented are also correct, but colleagues are freely throwing the concepts of Prevalence Odds Ratio and Risk Odds Ratio as interchangeable, while they are not for the reasons discussed above. The Exposure Odds Ratio of derived from Case-Control Studies or a Risk Odds Ratio derived from a Cohort study are only approximated estimates of RisK Ratio (or Relative Risk). The Prevalence Odds Ratio is not an approximate measure of the Risk Ratio - it is a paremter on its own that can be used in cross-sectional studies as a measure of the association between exposure/factors and the outcome of interest, without any need to mention Risk ratio.

In any circusntance in which an Odds Ratio is being estimated, it is important to know which fundamental measure is being estimated indirectly by the Odds Ratio: Risk ratio or Prevalence Ratio.

Finally, in exceptional circunstances the Prevalence may estimate another epidemiological measure the Incidence Rate (or incidence density), a true rate. In this situation the Prevalence Ratio is actually estimating the Incidence Rate Ratio.

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## Popular Answers

Eduardo J Simoes· University of MissouriRisk is the probability of occurrence of a new event (say health outcome) over a period of time among those who are at risk for event occurrence (say developing/acquiring health outcome) at the beginning of the follow up period. Risk is usually expressed as a value between 0 and 1, as all probabilities. It is often estimated through follow-up or Cohort studies of two groups of subjects/individuals (with or without some characteristics/attribute – usually called exposed and unexposed groups). So, the Risk estimates the average probability of occurrence of an outcome over a specified period of time among individuals at risk for having the outcome at the beginning of the follow-up period.

Prevalence is the number or proportion of subjects/individuals with some attribute (can als be the level of attribute/characteristics) or outcome (event) in a point in time or period of time. Prevalence is usually expressed as a proportion (0 to 1 as probabilities; or as percentages). It is usually derived from cross-sectional studies or a random sample from a population of subjects/individuals in a point in time (or period of time) – no need to specify a follow up period.

Therefore, Prevalence Ratio (erroneously called Prevalence Rate Ratio- because prevalence is not a rate) indicates how large is the prevalence of an event/outcome in one group of subjects/individuals (with characteristics/attribute) relative to another group (without the characteristics/attributes).

While, the ratio of the risks (Risk Ratio or Cumulative Incidence Ratio) indicates how more or less likely one a group of individuals/subjects with attribute/characteristics (exposure) is to develop/acquire a health outcome or conditions over the follow up period relative to the other group of unexposed.

The mathematic of the Odds Ratio presented are also correct, but colleagues are freely throwing the concepts of Prevalence Odds Ratio and Risk Odds Ratio as interchangeable, while they are not for the reasons discussed above. The Exposure Odds Ratio of derived from Case-Control Studies or a Risk Odds Ratio derived from a Cohort study are only approximated estimates of RisK Ratio (or Relative Risk). The Prevalence Odds Ratio is not an approximate measure of the Risk Ratio - it is a paremter on its own that can be used in cross-sectional studies as a measure of the association between exposure/factors and the outcome of interest, without any need to mention Risk ratio.

In any circusntance in which an Odds Ratio is being estimated, it is important to know which fundamental measure is being estimated indirectly by the Odds Ratio: Risk ratio or Prevalence Ratio.

Finally, in exceptional circunstances the Prevalence may estimate another epidemiological measure the Incidence Rate (or incidence density), a true rate. In this situation the Prevalence Ratio is actually estimating the Incidence Rate Ratio.