How to create a (total) Ghrelin calibration curve?

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1 2 3 4 - $x=2$ + == Computing Ghrelin calibration curve using R == + ===This article describes creating calibration curve, and measuring the total-ghrelin concentration === + 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. - + We will assume a 4-parameter log-logistic model: - x = {\left( {\frac{{{e^b}\left( {y - d} \right)}}{{c - y}}} \right)^{\frac{1}{b}}} + - [/itex] + [[Image(LL4.png, 300px)]] + + 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 equation 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") + }}} + + [[Image(Ghrelin.png)]] + + The parameters of the eqution can be plugged into the formula below (an inverse of the model), and used in Excel, or other spreadsheet program. + + [[Image(LL4-inv.png, 230px)]] + + 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) + }}}