Probabilidad y Teorema de Bayes

tabla=sample(0:1, 10, replace=TRUE)
print(tabla)

##  [1] 1 1 1 0 0 1 0 1 0 1

prop.table(table(tabla))

## tabla
##   0   1 
## 0.4 0.6

lanza_moneda=function(n){
tabla=sample(0:1, n, replace=TRUE)
p=prop.table(table(tabla))
return(p[1])
}

lanza_moneda(10)

##   0 
## 0.5

p=sapply(10:1000, lanza_moneda)
n=10:1000
plot(n,p,type="l")
abline(h=0.5,col="red")

a=85
b=65
c=45
d=55

hombres=a+b
mujeres=c+d
alcohol=a+c
Nalcohol=b+d
n=a+b+c+d

h=hombres/n
h

## [1] 0.6

al=alcohol/n
al

## [1] 0.52

m=1-(hombres/n)
m

## [1] 0.4

Nal=1-(alcohol/n)
Nal

## [1] 0.48

p1=h+al-(a/n)
p1

## [1] 0.78

p2=m+Nal-(d/n)
p2

## [1] 0.66

p3=(c/n)/m
p3

## [1] 0.45

Ejercicio No1

library(epiR)

## Loading required package: survival

## Package epiR 2.0.19 is loaded

## Type help(epi.about) for summary information

## Type browseVignettes(package = 'epiR') to learn how to use epiR for applied epidemiological analyses

## 

a=72
b=100
c=18
d=150

matrix(c(a,b,c,d), nrow=2, byrow=TRUE)

##      [,1] [,2]
## [1,]   72  100
## [2,]   18  150

tabla=as.table(matrix(c(a,b,c,d), nrow=2, byrow=TRUE))
colnames(tabla)=c("Enfermo", "Sano")
rownames(tabla)=c("Positivo", "Negativo")
tabla

##          Enfermo Sano
## Positivo      72  100
## Negativo      18  150

Probabilidades=epi.tests(tabla, conf.level=0.95)
Probabilidades

##           Outcome +    Outcome -      Total
## Test +           72          100        172
## Test -           18          150        168
## Total            90          250        340
## 
## Point estimates and 95 % CIs:
## ---------------------------------------------------------
## Apparent prevalence                    0.51 (0.45, 0.56)
## True prevalence                        0.26 (0.22, 0.31)
## Sensitivity                            0.80 (0.70, 0.88)
## Specificity                            0.60 (0.54, 0.66)
## Positive predictive value              0.42 (0.34, 0.50)
## Negative predictive value              0.89 (0.84, 0.94)
## Positive likelihood ratio              2.00 (1.66, 2.40)
## Negative likelihood ratio              0.33 (0.22, 0.51)
## ---------------------------------------------------------

a=120
b=140
c=480
d=260

matrix(c(a,b,c,d), nrow=2, byrow=TRUE)

##      [,1] [,2]
## [1,]  120  140
## [2,]  480  260

tabla1=as.table(matrix(c(a,b,c,d), nrow=2, byrow=TRUE))
colnames(tabla1)=c("niña", "niño")
rownames(tabla1)=c("menor24", "mayor24")
tabla1

##         niña niño
## menor24  120  140
## mayor24  480  260

Probabilidades1=epi.tests(tabla1, conf.level=0.95)
Probabilidades1

##           Outcome +    Outcome -      Total
## Test +          120          140        260
## Test -          480          260        740
## Total           600          400       1000
## 
## Point estimates and 95 % CIs:
## ---------------------------------------------------------
## Apparent prevalence                    0.26 (0.23, 0.29)
## True prevalence                        0.60 (0.57, 0.63)
## Sensitivity                            0.20 (0.17, 0.23)
## Specificity                            0.65 (0.60, 0.70)
## Positive predictive value              0.46 (0.40, 0.52)
## Negative predictive value              0.35 (0.32, 0.39)
## Positive likelihood ratio              0.57 (0.46, 0.70)
## Negative likelihood ratio              1.23 (1.13, 1.34)
## ---------------------------------------------------------