Statsbook

Epidemiology

Screening is the application of a test to asymptomatic individuals to assess the likelihood that an individual has a particular disease.

Surveillance of disease is used to look for changes in trends or distribution of the disease.

\(Prevalence = \frac{Number Of Existing Cases Per Year}{PopulationAtRisk} \)
\(Incidence = \frac{NumberOfNewCasesPerYear}{PopulationAtRisk} \)

Prevalence ~ Incidence x Mean disease duration

(when population and disorder stable)

A risk factor is an exposure or attribute that increases the probability of a disease.

DiseaseNo Disease
Exposureab
No Exposurecd

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

Absolute Risk Exposed Individuals:

\(ARexposure = \frac{a}{a+b} \)

Absolute Risk Non Exposed Individuals:

\(ARnoexposure = \frac{c}{c+d} \)

Relative Risk:

The relative risk is the risk of developing the disease that is due to an exposure in the exposed group

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

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.

\(OR = \frac{a \cdot d}{b \cdot c} \)

An odds ratio or relative risk greater than 1 indicates the exposure is a risk factor for developing the disease. If the odds ratio or relative risk is 1, the exposure has no effect on the disease; if they are less than 1, the exposure protects against disease.

In the R console1:

library(epiR)
mat<-matrix(c(a,c,b,d),ncol=2)  {enter values!}
mat
[,1] [,2]
 [1,]   a  b
 [2,]   c  d
 epi.2by2(mat)
 Outcome +    Outcome -      Total        Inc risk *        Odds
 Exposed +          
 Exposed -           
 Total    
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 epiR2 should be installed.

Please note, the maximum likelihood odds ratio is a different estimate than the cross product ratio.

summary(epi.tests(mat))
                 est      lower      upper
aprev     
tprev     
se     
sp        
diag.acc  
diag.or  {This is the cross product (diagnostic) odds ratio}
nnd       
youden   
ppv       
npv      
plr      
nlr