Computing Ghrelin calibration curve using R
The calibration curve can be created using R, and libracy “drc”. Optionally, one can use library “sfmisc” for formatting of the labels on plot axis. The R code is attached below.
The example assumes the data to be available in file “ghrelin_conc std_a std_b avg.csv”
The measured data:
| Ghrelin (ng/ml) | Standard a | Standard b |
| 1000000 | -0.040596823 | -0.052699697 |
| 100000 | 0.136105144 | 0.119766263 |
| 10000 | 0.61356354 | 0.606906959 |
| 1000 | 0.846543873 | 0.839887292 |
| 100 | 0.887693646 | 0.88345764 |
| 0 | 0.896770802 | 0.896165658 |
##### Install libraries
install.packages("drc")
install.packages("sfsmisc")
require(drc)
library(sfsmisc)
##### Read the data
hormone.data <- read.csv("ghrelin_conc std_a std_b avg.csv")
hormone.data <- hormone.data[,1:3]
colnames(hormone.data)[1:3] <- c("Concentration","Response_1", "Response_2")
##### Reorganize the data
hormone.data <- reshape(hormone.data, varying=c("Response_1","Response_2"), direction="long", v.names=c("Response"))
hormone.data <- hormone.data[,c("Concentration", "Response")]
##### Fitting the model (4-parameter log-logistic function)
hormone.data.model <- drm(Response ~ Concentration, data = hormone.data, fct = LL.4())
summary(hormone.data.model)
The resultant parameters of a log-logistic equations are:
Model fitted: Log-logistic (ED50 as parameter) (4 parms)
Parameter estimates:
Estimate Std. Error t-value p-value
b:(Intercept) 9.5057e-01 2.2294e-02 4.2638e+01 0
c:(Intercept) -7.6010e-02 6.9075e-03 -1.1004e+01 0
d:(Intercept) 8.9163e-01 3.3216e-03 2.6843e+02 0
e:(Intercept) 2.5221e+04 7.7727e+02 3.2448e+01 0
The calibration curve can be plotted using the commands below:
##### Plotting a nice plot par(pty="s", mar=c(5,5,1,1)) plot(hormone.data.model, type="confidence", cex.lab=2, axes=F, xlim=c(-10,10^6)) axis(side=1, at=hormone.data[1:6,1], labels=pretty10exp(hormone.data[1:6,1]), cex.axis=1.2) axis(side=2, at=seq(0,1,0.2), labels=seq(0,1,0.2)) plot(hormone.data.model, type="all", add=T, pch=21, col="red", lwd=1, cex=2, bg="green")
The parameters of the eqution can be plugged into the formula below, and used in Excel, or other spreadsheet program.
However, the concentration can be also easily estimated in R using “ED” function of the “drc” library. The code below demonstrates the concentration estimated from the response of 0.1, assuming alpha=0.05. The code returns the estimation, the error, and the condfidence interval.
##### Computing the concentration from the response, for instance for a response=0.1, and alpha=1-0.95 ED(hormone.data.model, respLev=0.1, interval="delta", type="absolute", level=0.95)