support functions to perform experiments

intro-experimental-design/SImulateData.R

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+require(ggplot2)
+require(gridExtra)
+
+set.seed(1234)
+##do experiment
+PerformAssayGeneExpression <- function(NsamplesPerTime) {
+  N=NsamplesPerTime
+  Shape = 10
+  Rate = 0.5
+  delta = 0.2
+  Y1 <- rgamma(N, shape = Shape, rate = Rate)
+  Y2 <- rgamma(N, shape=(1+delta)*Shape, rate = Rate)
+  Y <- append(Y1, Y2)
+  Timepoint <- c(rep("E9_5", N), rep("E11_5", N))
+  PlotData <- data.frame(Y, Timepoint)
+  PlotData$Timepoint <- relevel(PlotData$Timepoint, ref="E9_5")
+  print(paste0("Mean expression of Gene at E9_5 = ", round(mean(Y1), digits = 1)))
+  print(paste0("Mean expression of Gene at E11_5 = ", round(mean(Y2), digits = 1)))
+  
+  print("=====")
+  print("=====")
+
+  if(NsamplesPerTime > 2) {
+      print(paste0("SD expression of Gene at E9_5 = ", round(sd(Y1), digits = 1)))
+      print(paste0("SD/sqrt(NsamplesPerTime) expression of Gene at E9_5 = ", round(sd(Y1)/sqrt(NsamplesPerTime), digits = 1)))
+   }
+  print(ggplot(PlotData, aes(x=Timepoint, y=Y)) + 
+          geom_boxplot() + 
+          geom_jitter(width=0.25) + 
+          xlab("embryonic time") + 
+          ylab("gene expression") +
+          ylim(10,35))
+}
+
+
+
+##Two models for expression of gene at E9_5: Gamma and Normal
+AssayExpression_E9_5_two_models <-  function(NsamplesPerTime = 100) {
+  N = NsamplesPerTime
+  Shape = 10
+  Rate = 0.5
+  ##Gamma distribution
+  Yg <- rgamma(N, shape = Shape, rate=Rate)
+  ##Normal distribution
+  Yn <- rnorm(N, mean=Shape/Rate, sd=sqrt(Shape)/Rate)
+  
+  ##Organize the data
+  Y <- append(Yg, Yn)
+  Distribution <- c(rep("Gamma", N), rep("Normal", N))
+  data <- data.frame(Y, Distribution, Condition=rep("E9_5", length(Y)))
+  
+  ##Visualize the data
+  p1 <- (ggplot(data, aes(x=Condition, y=Y, color=Distribution))  + geom_boxplot() + geom_jitter(width=0.25))
+  p2 <- (ggplot(data, aes(x=Condition, y=Y, color=Distribution))  + geom_violin() +  geom_jitter(width=0.25)) 
+  p3 <- (ggplot(data, aes(x=Y, color=Distribution))  + geom_histogram()) 
+  print(grid.arrange(p1,p2,p3,ncol=2))
+  # ggplot(data, aes(x=Y, color=Distribution))  + geom_freqpoly() 
+  
+  print(paste0("Mean of gene expression under Gamma model = ",round(mean(Y[Distribution=="Gamma"]), digits = 1)))
+  print(paste0("Mean of gene expression under Normal model = ", round(mean(Y[Distribution=="Normal"]), digits = 1)))
+
+  print("=====")
+  print("=====")
+  
+  print(paste0("SD of gene expression under Gamma model = ",round(sd(Y[Distribution=="Gamma"]), digits = 1)))
+  print(paste0("SD of gene expression under Normal model = ", round(sd(Y[Distribution=="Normal"]), digits = 1)))
+
+}
+
+
+##Repeat the experiment Nsim times to estimate mean gene expression at E9_5 under the two models of 
+##data generating distribution
+Repeat_AssayExpression_E9_5_two_models <- function(NsamplesPerTime=4, Nrepeat=1000) {
+  Shape = 10
+  Rate = 0.5
+  Nrepeat = Nrepeat
+  Ygmean <- vector(mode = "numeric")
+  Ygsd <- vector(mode = "numeric")
+  Zg <- vector(mode = "numeric")
+  
+  Ynmean <- vector(mode = "numeric")
+  Ynsd <- vector(mode = "numeric")
+  Zn <- vector(mode = "numeric")
+  
+  N = NsamplesPerTime
+  
+  for(i in 1:Nrepeat) {
+    Yg <- rgamma(N, shape = Shape, rate=Rate)
+    Ygmean[i] <- mean(Yg)
+    Ygsd[i] <- sd(Yg)
+    Zg[i] <- sqrt(N)*(Ygmean[i] - (Shape/Rate))/(sqrt(Shape)/Rate)
+    
+    Yn <- rnorm(N, mean=Shape/Rate, sd=sqrt(Shape)/Rate)
+    Ynmean[i] <- mean(Yn)
+    Ynsd[i] <- sd(Yn)
+    Zn[i] <- sqrt(N)*(Ynmean[i] - (Shape/Rate))/(sqrt(Shape)/Rate)
+  
+  }
+  
+  Ymean <- append(Ygmean, Ynmean)
+  Ysd <- append(Ygsd, Ynsd)
+  Z <- append(Zg, Zn)
+  Distribution <- c(rep("Gamma", Nrepeat), rep("Normal", Nrepeat))
+  Condition <- rep("E9_5", length(Ymean))
+  CLT_data <- data.frame(Ymean, Ysd, Z, Distribution, Condition)
+  
+  p1 <-  (ggplot(CLT_data, aes(x=Condition, y=Ymean, color=Distribution))  + geom_violin() )
+  p2 <- (ggplot(CLT_data, aes(x=Ymean, color=Distribution))  + geom_histogram() )
+  print(grid.arrange(p1, ncol=1))
+  
+  print(paste0("SD or Precision of mean gene expression under Gamma model = ",  round(sd(Ymean[Distribution=="Gamma"]), digits = 1)))
+  print(paste0("SD or Precision of gene expression under Normal model = ", round(sd(Ymean[Distribution=="Normal"]), digits = 1)))
+
+}
+