Exposure Increases Incidence

For example, smoking INCREASES the risk of lung cancer:

	Lung Cancer	No Lung Cancer
Smoking	99	1
No Smoking	1	99

Absolute Risk Smoking

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

Absolute Risk Not Smoking

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

Relative Risk

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

Odds Ratio

$OR=\frac{99 \times 99}{1 \times 1}=9801$

Or in JGR / R console 1 :

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

Point estimates and 95 % CIs:
———————————————————
Inc risk ratio                               99.00 (14.08, 696.01)
Odds ratio                                   5977.53 (507.98, 4503599627370496.00)
Attrib risk *                                98.00 (95.24, 100.76)
Attrib risk in population *                  49.00 (41.80, 56.20)
Attrib fraction in exposed (%)               98.99 (92.90, 99.86)
Attrib fraction in population (%)            98.00 (86.14, 99.71)
———————————————————
* 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    5.000000e-01 4.286584e-01 5.713416e-01
tprev    5.000000e-01 4.286584e-01 5.713416e-01
se       9.900000e-01 9.455406e-01 9.997469e-01
sp       9.900000e-01 9.455406e-01 9.997469e-01
diag.acc 9.900000e-01 9.643453e-01 9.987867e-01
diag.or 9.801000e+03 6.045402e+02 1.588970e+05
nnd      1.020408e+00 1.000507e+00 1.122232e+00
youden   9.800000e-01 8.910812e-01 9.994937e-01
ppv      9.900000e-01 9.455406e-01 9.997469e-01
npv      9.900000e-01 9.455406e-01 9.997469e-01
plr      9.900000e+01 1.408177e+01 6.960064e+02
nlr      1.010101e-02 1.436768e-03 7.101382e-02



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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