Exposure No Effect on Incidence

For example, blue eyes have NO EFFECT on developing arthritis:

	Arthritis	No Arthritis
Blue Eyes	5	95
Brown Eyes	5	95

Absolute Risk Blue Eyes

$ARblueeyes = \frac{5}{5+95}=0.05$

Absolute Risk Brown Eyes

$ ARbrowneyes = \frac{5}{5+95}=0.05$

Relative Risk

$RR=\frac{5 \over (5+95)}{ 5 \over (5+95)}=1$

Odds Ratio

$OR=\frac{5 \times 95}{95 \times 5}=1$

Or in JGR / R console 1:

library(epiR)
mat<-matrix(c(5,5,95,95),ncol=2)
mat
 [,1] [,2]
[1,] 5 95
[2,] 5 95
epi.2by2(mat)
 Outcome + Outcome – Total Inc risk * Odds
Exposed + 5 95 100 5 0.0526
Exposed – 5 95 100 5 0.0526
Total 10 190 200 5 0.0526

Point estimates and 95 % CIs:
———————————————————
Inc risk ratio                               1.00 (0.30, 3.35)
Odds ratio                                   1.00 (0.22, 4.50)
Attrib risk *                                0.00 (-6.04, 6.04)
Attrib risk in population *                  0.00 (-5.23, 5.23)
Attrib fraction in exposed (%)               0.00 (-234.75, 70.13)
Attrib fraction in population (%)            0.00 (-82.96, 45.34)
———————————————————
* 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 (although the answer is the same in this case). To obtain the cross product ratio :

summary(epi.tests(mat))



http://pcool.dyndns.org:8080/statsbook/wp-content/plugins/zotpress/

336296



        
  
    1. 
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