Exposure Decreases Incidence

For example, vaccination PROTECTS against polio:

	Polio	No Polio
Vaccinated	1	99
Not Vaccinated	99	1

Absolute Risk Vaccination

$ARvaccination = \frac{1}{1+99}=0.01$

Absolute Risk No Vaccination

$ARnovaccination = \frac{99}{99+1}=0.99$

Relative Risk

$RR=\frac{1 \over (1+99)}{ 99 \over (99+1)}\approx 0.01$

Odds Ratio

$OR=\frac{1 \times 1}{99 \times 99}\approx 0.0001$

Or in the JGR / R console 1 :

library(epiR)
mat<-matrix(c(1,99,99,1),ncol=2)
mat
     [,1] [,2]
[1,]    1   99
[2,]   99    1
epi.2by2(mat)
             Outcome +    Outcome –      Total        Inc risk *        Odds
Exposed +            1           99        100                 1      0.0101
Exposed –           99            1        100                99     99.0000
Total              100          100        200                50      1.0000

Point estimates and 95 % CIs:
———————————————————
Inc risk ratio                               0.01 (0.00, 0.07)
Odds ratio                                   0.00 (0.00, 0.00)
Attrib risk *                                -98.00 (-100.76, -95.24)
Attrib risk in population *                  -49.00 (-56.20, -41.80)
Attrib fraction in exposed (%)               -9800.00 (-69500.64, -1308.18)
Attrib fraction in population (%)            -98.00 (-127.12, -72.61)
———————————————————
* 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 :

summary(epi.tests(mat))
                   est         lower        upper
aprev     0.5000000000 4.286584e-01   0.57134157
tprev     0.5000000000 4.286584e-01   0.57134157
se        0.0100000000 2.531460e-04   0.05445939
sp        0.0100000000 2.531460e-04   0.05445939
diag.acc 0.0100000000 1.213349e-03   0.03565467
diag.or   0.0001020304 6.293387e-06   0.00165415
nnd      -1.0204081633 -1.122232e+00 -1.00050655
youden   -0.9800000000 -9.994937e-01 -0.89108123
ppv       0.0100000000 2.531460e-04   0.05445939
npv       0.0100000000 2.531460e-04   0.05445939
plr       0.0101010101 1.436768e-03   0.07101382
nlr      99.0000000000 1.408177e+01 696.00641424



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    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