Code for drawing new likelihood ratio slide rule

Steve Simon

2007-07-12

I have made some minor changes to my likelihood ratio slide. The original code was lost somewhere, so I wrote some new code and added documentation. I also changed the orientation of the slide rule so it can be held horizontally and shaded the regions that need to be cut out or away. This program runs in R. I've inserted images of the new slide rule on my tutorial page

The new version of the slide rule in PDF format has been placed on the web (SlideRule.pdf), and I am keepting the old version as well (SlideRuleOldVersion.pdf).

Here is the code.

#####################
# special functions #
#####################
hline <- function(x1,x2,y0) {segments(x1,y0,x2,y0)}
vline <- function(x0,y1,y2) {segments(x0,y1,x0,y2)}
rectangle <- function(x1,y1,x2,y2) {
  x0 <- c(x1,x1,x2,x2)
  y0 <- c(y1,y2,y2,y1)
  polygon(x=x0,y=y0,density=-1,border=NA,col="gray90")
}
triangle <- function(x1,y1,x2,y2,x3,y3) {
  x0 <- c(x1,x2,x3)
  y0 <- c(y1,y2,y3)
  polygon(x=x0,y=y0,density=-1,border=NA,col="gray90")
}

#####################################
# location of tick marks and labels #
#####################################

# where to draw probability tick marks

pr1 <- c(
  0.1,0.2,0.3,0.4,
  0.5,0.6,0.7,0.8,0.9,
  1,1.5,2,2.5,3,4,
  5,6,7,8,9,
  10,15,20,25,30,40,
  50,60,70,75,80,85,
  90,91,92,93,94,
  95,96,97,98,99)
  
# where to print probability labels

pr2 <- c(
  0.1,0.2,0.3,
  0.5,0.7,
  1,2,3,
  5,7,
  10,20,30,40,
  50,60,70,80,
  90,93,
  95,97,98,99)
  
# physical location of probability ticks and labels

pr3 <- 60+15*log(pr1/(100-pr1))/log(10)
pr4 <- 60+15*log(pr2/(100-pr2))/log(10)
n1 <- sort(c(1:9,1.5,2.5))
n2 <- c(1:3,5,7)

# where to draw likelihood ratio tick marks

pr5 <- c(n1/100,n1/10,n1,n1*10,100)

# where to print likelihood ratio labels

pr6 <- c(n2/100,n2/10,n2,n2*10,100)

# physical location of likelihood ratio ticks and labels

pr7 <- 50-15*log(pr5)/log(10)
pr8 <- 50-15*log(pr6)/log(10)

# odd and even probability labels

od2 <- paste(pr2[seq(1,length(pr2),by=2)],"%",sep="")
ev2 <- paste(pr2[seq(2,length(pr2),by=2)],"%",sep="")

# odd and even likelihood ratio labels

od4 <- pr4[seq(1,length(pr4),by=2)]
ev4 <- pr4[seq(2,length(pr2),by=2)]

# physical locations of odd/even labels

od6 <- pr6[seq(1,length(pr6),by=2)]
ev6 <- pr6[seq(2,length(pr6),by=2)]
od8 <- pr8[seq(1,length(pr8),by=2)]
ev8 <- pr8[seq(2,length(pr8),by=2)]

draw.frame <- function() {
  ################################
  # outline sleeve of slide rule #
  ################################
  
  hline( 5, 95, 0)
  
  # bottom edge
  
  hline( 0,100, 20)
  
  # fold line
  
  hline( 0,100, 50)
  
  # fold line
  
  hline( 5, 95, 70)
  
  # top edge
  
  vline( 0, 12, 28)
  
  # left edge
  
  vline( 0, 42, 58)
  
  # left edge
  
  vline(100, 12, 28)
  
  # right edge
  
  vline(100, 42, 58)
  
  # right edge
  
  ################
  # left notches #
  ################
  
  vline( 5, 0, 10)
  segments( 5, 10, 0, 12)
  segments( 0, 28, 5, 30)
  vline( 5, 30, 40)
  segments( 5, 40, 0, 42)
  vline( 5, 60, 70)
  segments( 0, 58, 5, 60)
  
  #################
  # right notches #
  #################
  
  vline( 95, 0, 10)
  segments( 95, 10,100, 12)
  segments(100, 28, 95, 30)
  vline( 95, 30, 40)
  segments( 95, 40,100, 42)
  vline( 95, 60, 70)
  segments(100, 58, 95, 60)
  
  ################################
  # outline insert of slide rule #
  ################################
  
  hline( 0,100, 71)
  
  # bottom edge
  
  hline( 0,100,100)
  
  # top edge
  
  vline( 0, 71,100)
  
  # left edge
  
  vline(100, 71,100) 
  # right edge
  
  ####################################
  # cut-out for pre-test probability #
  ####################################
  
  h <- 29
  hline( 17, 83,h+0)
  
  # bottom edge
  
  hline( 17, 83,h+7)
  
  # top edge
  
  vline( 17,h+0,h+7)
  
  # left edge
  
  vline( 83,h+0,h+7)
  
  # right edge
  
  #####################################
  # cut-out for post-test probability #
  #####################################
  
  h <- 46
  v <- 50
  hline(v-3,v+3,h+0)
  
  # top edge
  
  hline(v-3,v+3,h-6)
  
  # bottom edge
  
  vline(v-3,h+0,h-6)
  
  # left edge
  
  vline(v+3,h+0,h-6)
  
  # right edge
  
  vline(v+0,h+0,h+1)
  
  # top tick
  
  vline(v+0,h-6,h-7)
  
  # bottom tick
}

draw.ticks <- function() {
  ####################
  # Likelihood ratio #
  ####################
  
  h <- 29
  segments(pr7,h+0,pr7,h-1)
  
  # all ticks
  
  segments(od8,h-2,od8,h-1)
  
  # extend odd ticks
  
  segments(ev8,h-4,ev8,h-1)
  
  # extend even ticks
  
  text(od8,h-3,od6)
  
  # label odd ticks
  
  text(ev8,h-5,ev6) 
  
  # label even ticks
  
  ########################
  # Pre-test probability #
  ########################
  
  h <- 79
  
  segments(pr3,h-1,pr3,h+1)
  
  # all ticks
  
  segments(od4,h+2,od4,h+1)
  
  # extend odd ticks
  
  segments(ev4,h+4,ev4,h+1)
  
  # extend even ticks
  
  text(od4,h+3,od2)
  
  # label odd ticks
  
  text(ev4,h+5,ev2) 
  
  # label even ticks
  
  #########################
  # Post-test probability #
  #########################
  
  h <- 97
  
  segments(pr3,h+1,pr3,h-1) 
  
  # all ticks
  
  segments(od4,h-2,od4,h-1)
  
  # extend odd ticks
  
  segments(ev4,h-4,ev4,h-1)
  
  # extend even ticks
  
  text(od4,h-3,od2)
  
  # label odd ticks
  
  text(ev4,h-5,ev2)
  
  # label even ticks
}

draw.shade <- function() {
  xlo <- -999
  ylo <- -999
  xhi <-  999
  yhi <-  999
  
  #########################
  # shade extreme regions #
  #########################
  
  rectangle(xlo,ylo,xhi, 0)
  
  # bottom
  
  rectangle(xlo,100,xhi,yhi)
  
  # top
  
  rectangle(xlo,ylo, 0,yhi)
  
  # left
  
  rectangle(100,ylo,xhi,yhi)
  
  # right
  
  rectangle( 0, 70,100, 71)
  
  # between sleeve and insert
  
  ################
  # left notches #
  ################
  
  rectangle( 0, 0, 5, 10)
  triangle ( 0, 10, 5, 10, 0, 12)
  triangle ( 0, 30, 5, 30, 0, 28)
  rectangle( 0, 30, 5, 40)
  triangle ( 0, 40, 5, 40, 0, 42)
  triangle ( 0, 60, 5, 60, 0, 58)
  rectangle( 0, 60, 5, 70)
  
  #################
  # right notches #
  #################
  
  rectangle(100, 0, 95, 10)
  triangle (100, 10, 95, 10,100, 12)
  triangle (100, 40, 95, 40,100, 42)
  rectangle(100, 30, 95, 40)
  triangle (100, 30, 95, 30,100, 28)
  triangle (100, 60, 95, 60,100, 58)
  rectangle(100, 60, 95, 70)
  
  ########################
  # Pre-test probability #
  ########################
  
  h <- 29
  rectangle( 17,h+0, 83,h+7)
  
  #########################
  # Post-test probability #
  #########################
  
  h <- 46
  v <- 50
  rectangle(v-3,h-6,v+3,h+0)
}

draw.notes <- function() {
  m0 <- paste(
    "Line up the pre-test probability",
    "with the likelihood ratio, and read",
    "the post-test probability here.", sep="\n")
    
  m1 <- paste(
    "(C) The Children's Mercy Hospital.",
    "For more information, please go to",
    "www.childrensmercy.org/sliderule.asp", sep="\n")
    
  text(45,43,m0,adj=1)
  text(55,43,m1,adj=0)
  text(15,33,"Pre-test\nprobability",adj=1)
  text(15,25,"Likelihood\nratio",adj=1)
}

pdf(file="sliderule.pdf",width=8,height=10)
par(mar=rep(0.1,4),cex=0.75,adj=0.5)
plot(c(0,100),c(0,100),axes=F,type="n",xlab=" ",ylab=" ")
draw.notes()
draw.shade()
draw.frame()
draw.ticks()
dev.off()
## png 
##   2