How to create a (total) Ghrelin calibration curve?

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1 == Computing Ghrelin calibration curve using R ==
2
3 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.
4 -
5 -
<math>n = 5</math>
6
7 We will assume a 4-parameter log-logistic model:
8
9 [[Image(LL4.png, 300px)]]
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11 The R code is attached below.
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13 The example assumes the data to be available in file "ghrelin_conc std_a std_b avg.csv"
14
15 The measured data:
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17 || '''Ghrelin (ng/ml)''' || '''Standard a''' || '''Standard b''' ||
18 || 1000000 ||-0.040596823||-0.052699697 ||
19 || 100000 ||0.136105144||0.119766263 ||
20 || 10000 ||0.61356354||0.606906959 ||
21 || 1000 ||0.846543873||0.839887292 ||
22 || 100 ||0.887693646||0.88345764 ||
23 ||0||0.896770802||0.896165658 ||
24
25 {{{
26
27 ##### Install libraries
28 install.packages("drc")
29 install.packages("sfsmisc")
30 require(drc)
31 library(sfsmisc)
32
33 ##### Read the data
34 hormone.data <- read.csv("ghrelin_conc std_a std_b avg.csv")
35 hormone.data <- hormone.data[,1:3]
36 colnames(hormone.data)[1:3] <- c("Concentration","Response_1", "Response_2")
37
38 ##### Reorganize the data
39 hormone.data <- reshape(hormone.data, varying=c("Response_1","Response_2"), direction="long", v.names=c("Response"))
40 hormone.data <- hormone.data[,c("Concentration", "Response")]
41
42 ##### Fitting the model (4-parameter log-logistic function)
43 hormone.data.model <- drm(Response ~ Concentration, data = hormone.data, fct = LL.4())
44 summary(hormone.data.model)
45
46 }}}
47
48 The resultant parameters of a log-logistic equation are:
49
50 {{{
51 Model fitted: Log-logistic (ED50 as parameter) (4 parms)
52 Parameter estimates:
53 Estimate Std. Error t-value p-value
54 b:(Intercept) 9.5057e-01 2.2294e-02 4.2638e+01 0
55 c:(Intercept) -7.6010e-02 6.9075e-03 -1.1004e+01 0
56 d:(Intercept) 8.9163e-01 3.3216e-03 2.6843e+02 0
57 e:(Intercept) 2.5221e+04 7.7727e+02 3.2448e+01 0
58 }}}
59
60 The calibration curve can be plotted using the commands below:
61
62 {{{
63 ##### Plotting a nice plot
64 par(pty="s", mar=c(5,5,1,1))
65 plot(hormone.data.model, type="confidence", cex.lab=2, axes=F, xlim=c(-10,10^6))
66 axis(side=1, at=hormone.data[1:6,1], labels=pretty10exp(hormone.data[1:6,1]), cex.axis=1.2)
67 axis(side=2, at=seq(0,1,0.2), labels=seq(0,1,0.2))
68 plot(hormone.data.model, type="all", add=T, pch=21, col="red", lwd=1, cex=2, bg="green")
69 }}}
70
71 [[Image(Ghrelin.png)]]
72
73 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.
74
75 [[Image(LL4-inv.png, 230px)]]
76
77 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.
78
79 {{{
80 ##### Computing the concentration from the response, for instance for a response=0.1, and alpha=1-0.95
81 ED(hormone.data.model, respLev=0.1, interval="delta", type="absolute", level=0.95)
82 }}}