Risks and Odds Ratio

 DiseaseNo Disease
No Exposurecd

Absolute Risk Exposed Individuals

ARexposure = \frac{a}{a+b}<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />

Absolute Risk Non Exposed Individuals

ARnoexposure = \frac{c}{c+d}<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />

Relative Risk

Risk of exposed individuals getting the disease as compared to non exposed individuals:

RR=\frac{a \over (a+b)}{ c \over (c+d)}

Odds Ratio

The odds ratio is the ratio of the odds of a disease occurring among exposed individuals to that of it occurring in unexposed individuals:

OR=\frac{a \over (a+b) \over b \over (a+b)}{c \over (c+d) \over d \over (c+d)}=\frac{a \over b}{c \over d}=\frac{a \times d}{b \times c}<br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br /><br />

The absolute risk is always between zero and 1 and the relative risk is always larger than zero.

If the relative risk = 1, there is no increased risk for developing the disease. A relative risk less than 1 (but larger than zero) indicates that the exposure protects against disease. If the relative risk is larger than 1, there is an increased risk for developing the disease. The greater the value, the stronger the link is between exposure and disease.

In other words, if the relative risk = 1 the exposure is not a risk factor for disease. The larger the relative risk, the bigger the risk becomes. If the relative risk is very high, one could call it the cause of the disease. There is no cut-off point between risk factor and cause; but there is a spectrum.

Exactly the same is true for the odds ratio. If the value of the odds ratio is between zero and 1, the exposure protects against disease. An odds ratio greater than 1 indicates that the exposure is a risk factor. The larger the odds ratio becomes, the stronger the risk of developing disease. If the odds ratio =1, the exposure has no influence of the development of disease.

In JGR / R console 1:

mat<-matrix(c(a,c,b,d),ncol=2) {enter values!}
[,1] [,2]
[1,]   a  b
[2,]   c  d
Outcome +    Outcome –      Total        Inc risk *        Odds
Exposed +         
Exposed –          

Point estimates and 95 % CIs:
Inc risk ratio                              
Odds ratio                                
Attrib risk *                            
Attrib risk in population *          
Attrib fraction in exposed (%)              
Attrib fraction in population (%)        
* Cases per 100 population units

The package epiR 1 should be installed.

The odds ratio provided is the maximum likelihood estimate that is different from the cross product ratio. To obtain the cross product ratio :

                 est      lower      upper
diag.or  {This is the cross product (diagnostic) odds ratio}

Stevenson M, Nunes T, Heuer C, Marshall J, Sanchez J, Thornton R, et al. epiR: Tools for the Analysis of Epidemiological Data [Internet]. 2015. (R package). Available from: http://cran.r-project.org/package=epiR