### R code for Lazic SE (2008). Statistical evaluation of methods
### for quantifying gene expression by autoradiography in histological
### sections. BMC Neuroscience.


# load up required packages
library(lattice);  library(Hmisc); library(nlme)

# read in the data. "Int" are the integrated values.
MR.dat <- read.csv("MR-data.csv")


# convert rat ID into a factor
MR.dat$rat <- as.factor(MR.dat$rat)

#reorders rats based on mean GL value
MR.dat$rat <- reorder.factor(MR.dat$rat, MR.dat$line, max)


# Figure 2: Variability of grey level values at different levels of the sampling hierarchy
        trellis.device(x11, theme="col.whitebg", height=5, width=5)
        dotplot(factor(rat)~line, groups=section, data=MR.dat, auto.key=list(columns=3),
                xlab="Grey level", ylab="Rat", xlim=c(42,70))


## Variance Components Analysis

#fits a linear mixed model to the data for each method
mod.line <- lme(line~1, random=~1|rat/section, data=MR.dat)
mod.outline <- lme(outline~1, random=~1|rat/section, data=MR.dat)
mod.sd.thresh <- lme(sd.thresh~1, random=~1|rat/section, data=MR.dat)
mod.mix.mod <- lme(mix.mod~1, random=~1|rat/section, data=MR.dat)
mod.int.outline <- lme(int.outline~1, random=~1|rat/section, data=MR.dat)
mod.int.sd.thresh <- lme(int.sd.thresh~1, random=~1|rat/section, data=MR.dat)
mod.int.mix.mod <- lme(int.mix.mod~1, random=~1|rat/section, data=MR.dat)


var.calc <- function(mod){
  ## a function to extract the variance components and display as percentages
  
  vars <- VarCorr(mod)                                                  #calculates the variances
  ex.vars <- as.numeric(c(vars[,1][[2]],vars[,1][[4]],vars[,1][[5]]))   #extracts the variances
  values <- round(100*(ex.vars/sum(ex.vars)), 1)                        #calculates percentages
  cat("\n\n Percent variability at each level\n")
  cat("Rats\t", "Sections\t", "Side+error\n")
  cat(values[1], "\t", values[2], "\t\t", values[3], "\n\n")
}

var.calc(mod.line)
var.calc(mod.outline)
var.calc(mod.sd.thresh)
var.calc(mod.mix.mod)
var.calc(mod.int.outline)
var.calc(mod.int.sd.thresh)
var.calc(mod.int.mix.mod)



## Averaging values for each rat and looking for floor effects

avg.line <- summarize(MR.dat$line, MR.dat$rat, mean) #summarise line method for each rat
avg.sd.thresh <- summarize(MR.dat$sd.thresh, MR.dat$rat, mean) #summarise SD threshold method for each rat

all.equal(avg.line[,1], avg.sd.thresh[,1])              # a check to make sure order of rats is the same
                                                        # (should return "TRUE")

md <- function(x,y){
  ## a function to compare two methods and look for a floor-effect
  
  d <- y - x            # calculates difference
  m <- (x + y)/2        # calculates mean
  mod <- lm(d~m)        # fits a model to the mean and difference values

  x11(width=7,height=4)
  par(mfrow=c(1,2),
      las=1)
  lims <- range(x,y)    # calculates range of data for axes

  plot(x,y, xlim=lims, ylim=lims, pty="s"); abline(0,1)         # plots method1 vs. method2
  plot(d~m, type="n", pty="s")                                  # mean-difference plot
  abline(h=0, col="darkgrey", lty=2); abline(mod)
  points(d~m)

  summary(mod)         # output of regression to test for trend in mean-difference plot
}


md(avg.line[,2], avg.sd.thresh[,2]) # run the function to compare the SD threhold and line methods