Odds Ratios Comparison

library(stringr)

Summarise <- function(t,title) {
  n1 <- t[1] + t[2]
  n2 <- t[3] + t[4]
  m1 <- t[1] + t[3]
  m2 <- t[2] + t[4]
  padchar <- ' '
  
  print('',quote=FALSE)
  print(title,quote=FALSE)
  print      ('           D |  not D |  total',quote = FALSE)
  print(paste(
    'E    ',
    str_pad(t[1], 6, pad = padchar),'|',
    str_pad(t[2], 6, pad = padchar),'|',
    str_pad(n1, 6, pad = padchar)
    
  ),quote = FALSE)
  print(paste(
    'not E',
    str_pad(t[3], 6, pad = padchar),'|',
    str_pad(t[4], 6, pad = padchar),'|',
    str_pad(n2, 6, pad = padchar)
  ),quote = FALSE)
  print('----------------------------- ',quote = FALSE)
   print(paste(
    'total',
    str_pad(m1, 6, pad = padchar),'|',
    str_pad(m2, 6, pad = padchar),'|',
    str_pad(sum(t), 6, pad = padchar)
  ),quote = FALSE)
}

Analyse <- function(t,option=1) {
  
  a <- t[1]
  b <- t[2]
  c <- t[3]
  d <- t[4]
  
  if ( option == 1 ) {
    RelativeRisk <- (a/(a+b)) / (c/(c+d))
    OddsRatio <- (a*d) / (c*b)
  } else {
    RelativeRisk <- (a/(a+c)) / (b/(b+d))
    OddsRatio <- (a*d) / (c*b)
  }
  
  print('',quote=FALSE)
  if ( option == 1 ) {
    print('P( D | E )',quote=FALSE)
  } else {
    print('P( E | D )',quote=FALSE)
  }
  print('Relative Risk (RR) =',quote=FALSE)
  print(RelativeRisk,quote=FALSE)
  print('Odds Ratio (OR) =   ',quote=FALSE)
  print(OddsRatio,quote=FALSE)
  
}

Relative Risk and Odds Ratios

This shows examples of the effect of low disease rates and low exposure rates on RR and OR.

Note thet RR depends on whether we are calculating P ( D | E ) or P ( E | D ), and has the corresponding interpretation; OR does not and is the same in either case.

M249 Book 1 p 21

Table <- as.matrix(c(35,34,153,637),rows=2)
Summarise(Table,'M249 Book 1, example 2.3 Cannabis use and mental health')

## [1] 
## [1] M249 Book 1, example 2.3 Cannabis use and mental health
## [1]            D |  not D |  total
## [1] E         35 |     34 |     69
## [1] not E    153 |    637 |    790
## [1] ----------------------------- 
## [1] total    188 |    671 |    859

Analyse(Table,1)

## [1] 
## [1] P( D | E )
## [1] Relative Risk (RR) =
## [1] 2.619115
## [1] Odds Ratio (OR) =   
## [1] 4.285852

Analyse(Table,2)

## [1] 
## [1] P( E | D )
## [1] Relative Risk (RR) =
## [1] 3.674124
## [1] Odds Ratio (OR) =   
## [1] 4.285852

Low disease rates

Table.2 <- as.matrix(c(3,200,1,240),rows=2)
Summarise(Table.2,'Low disease rate example')

## [1] 
## [1] Low disease rate example
## [1]            D |  not D |  total
## [1] E          3 |    200 |    203
## [1] not E      1 |    240 |    241
## [1] ----------------------------- 
## [1] total      4 |    440 |    444

Analyse(Table.2,1)

## [1] 
## [1] P( D | E )
## [1] Relative Risk (RR) =
## [1] 3.561576
## [1] Odds Ratio (OR) =   
## [1] 3.6

Analyse(Table.2,2)

## [1] 
## [1] P( E | D )
## [1] Relative Risk (RR) =
## [1] 1.65
## [1] Odds Ratio (OR) =   
## [1] 3.6

Low exposure rates

Table.3 <- as.matrix(c(5,2,250,240),rows=2)
Summarise(Table.3,'Low exposure rate example')

## [1] 
## [1] Low exposure rate example
## [1]            D |  not D |  total
## [1] E          5 |      2 |      7
## [1] not E    250 |    240 |    490
## [1] ----------------------------- 
## [1] total    255 |    242 |    497

Analyse(Table.3,1)

## [1] 
## [1] P( D | E )
## [1] Relative Risk (RR) =
## [1] 1.4
## [1] Odds Ratio (OR) =   
## [1] 2.4

Analyse(Table.3,2)

## [1] 
## [1] P( E | D )
## [1] Relative Risk (RR) =
## [1] 2.372549
## [1] Odds Ratio (OR) =   
## [1] 2.4