Diphteria: Diphteria vaccine - Intradermal challenge
In pla: Parallel Line Assays
Description
Usage
Source
Examples
Description
Example 01 - Three-dose parallel line assay;
completely randomized; square transformation; explicit volume units,
from CombiStats - EDQM, Council of Europe (http://combistats.edqm.eu).
Usage
1
data("Diphteria")
Source
From CombiStats - EDQM, Council of Europe:
http://combistats.edqm.eu/images/stories/Examples/Diphtheria%20intradermal.pdf
Examples
1
2
3
4
5
6
7
8
9
Example <- "Example 1"
data(Diphteria); Data <- Diphteria
Data <- readAssayTable(paste(system.file(package = "pla"),
"vignettes/CombiStat/data/Diphteria.txt",
sep = "/"), fun = function(x) x^2,
rows = "Dilutions & Samples", columns = "Replicates")
plaModel <- plaCRD(Data); plaModel
plots <- plot(plaModel)
Example output
Some factors have problems with nesting in COLUMNS
Trying to fix 0.05/0.1/0.2/0.02/0.04/0.08 by S/T
================================================================================
Project: CombiStats - EDQM, Council of Europe
Assay: Example 1: Diphteria
================================================================================
================================================================================
Data values:
--------------------------------------------------------------------------------
S:1:0.05 S:2:0.1 S:3:0.2 T:1:0.02 T:2:0.04 T:3:0.08
1 0.00 4.0 16.0 1.00 4 4
2 0.00 9.0 16.0 1.00 4 16
3 1.00 4.0 9.0 0.00 4 16
4 0.00 4.0 16.0 1.00 4 16
Mean 0.25 5.2 14.2 0.75 4 13
SD 0.50 2.5 3.5 0.50 0 6
CV 200.00 47.6 24.6 66.67 0 46
================================================================================
================================================================================
Dilution ration: 2
Factor: 23.75 250 NA
Significance level alpha: 5 %
================================================================================
================================================================================
Regression, Restricted model (Common Slope), with adjusting for 'blocks'.:
--------------------------------------------------------------------------------
Call:
lm(formula = Response ~ -1 + factor(Sample) + Z, data = data)
Residuals:
Min 1Q Median 3Q Max
-8.4792 -1.9167 0.3125 2.5260 3.5208
Coefficients:
Estimate Std. Error t value Pr(>|t|)
factor(Sample)S 13.146 1.181 11.13 2.86e-10 ***
factor(Sample)T 12.479 1.181 10.57 7.29e-10 ***
Z 9.468 1.115 8.49 3.14e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.092 on 21 degrees of freedom
Multiple R-squared: 0.8903, Adjusted R-squared: 0.8746
F-statistic: 56.8 on 3 and 21 DF, p-value: 3.005e-10
--------------------------------------------------------------------------------
Slope:
Z
9.467686
================================================================================
================================================================================
Regression, Unrestricted Model (Different slopes), with adjusting for 'blocks':
--------------------------------------------------------------------------------
Call:
lm(formula = Response ~ -1 + factor(Sample) + factor(Sample):Z,
data = data)
Residuals:
Min 1Q Median 3Q Max
-8.0417 -1.9167 0.4167 2.4167 3.9583
Coefficients:
Estimate Std. Error t value Pr(>|t|)
factor(Sample)S 13.583 1.435 9.465 7.91e-09 ***
factor(Sample)T 12.042 1.435 8.391 5.53e-08 ***
factor(Sample)S:Z 10.099 1.604 6.297 3.79e-06 ***
factor(Sample)T:Z 8.837 1.604 5.510 2.15e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.144 on 20 degrees of freedom
Multiple R-squared: 0.892, Adjusted R-squared: 0.8704
F-statistic: 41.28 on 4 and 20 DF, p-value: 2.149e-09
--------------------------------------------------------------------------------
Slopes:
factor(Sample)S:Z factor(Sample)T:Z
10.098865 8.836507
================================================================================
--------------------------------------------------------------------------------
Completly Randomized Design Analysis (CRD):
--------------------------------------------------------------------------------
Analysis of Variance Table
Response: Response
Df Sum Sq Mean Sq F value Pr(>F)
factor(Sample) 1 2.67 2.67 0.2909 0.5962
Dilution 1 689.06 689.06 75.1705 7.652e-08 ***
factor(Sample):Dilution 1 3.06 3.06 0.3341 0.5704
factor(Sample):factor(Dilution) 2 32.71 16.35 1.7841 0.1964
Residuals 18 165.00 9.17
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
Df Sum Sq Mean Sq F value Pr(>F) DFresiduals
Test of Preparation: 1 2.666667 2.666667 0.2909091 0.5962479 18
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F) F(critical)
Test of Regression: 1 689.0625 689.0625 75.17045 7.651945e-08 4.413873
This test passes if F(regression) > F(critical)
Test of Regression: Test passed!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F) F(critical)
Test of Linearity: 2 32.70833 16.35417 1.784091 0.1963951 3.554557
This test passes if F(non-linearity) < F(critical)
Test of Linearity: Test passed!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F) F(critical)
Test of Parallelism: 1 3.0625 3.0625 0.3340909 0.5704212 4.413873
This test passes if F(non-parallelity) < F(critical)
Test of Parallelism: Test passed!
================================================================================
================================================================================
Sums of Squares, Slope, Variance, C, Potency and Confidence-intervals:
--------------------------------------------------------------------------------
SStot SSreg SSres SSsmp R Radj
892.50000000 689.06250000 165.00000000 2.66666667 0.88036736 0.86811437
DFres b s2 qt C V
18.00000000 9.46768621 9.16666667 2.10092204 1.06238110 0.64060402
WidthT - Log(Lower)T - Log(Potency)T - Log(Upper)T -
0.283323600 -0.358131114 -0.070414952 0.208516087
CMT -
-0.074807514
exp(Width) Lower Potency Upper exp(CM)
23.75 31.528949 16.600809 22.135166 29.256408 22.038149
250 331.883671 174.745356 233.001750 307.962187 231.980520
Rel. Est. 142.438274 74.997443 100.000000 132.171619 99.561707
--------------------------------------------------------------------------------
================================================================================
pla documentation built on May 2, 2019, 11:12 a.m.
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Description Usage Source Examples
Description
Example 01 - Three-dose parallel line assay; completely randomized; square transformation; explicit volume units, from CombiStats - EDQM, Council of Europe (http://combistats.edqm.eu).
Usage
1 | data("Diphteria")
|
Source
From CombiStats - EDQM, Council of Europe: http://combistats.edqm.eu/images/stories/Examples/Diphtheria%20intradermal.pdf
Examples
1 2 3 4 5 6 7 8 9 | Example <- "Example 1"
data(Diphteria); Data <- Diphteria
Data <- readAssayTable(paste(system.file(package = "pla"),
"vignettes/CombiStat/data/Diphteria.txt",
sep = "/"), fun = function(x) x^2,
rows = "Dilutions & Samples", columns = "Replicates")
plaModel <- plaCRD(Data); plaModel
plots <- plot(plaModel)
|
Example output
Some factors have problems with nesting in COLUMNS
Trying to fix 0.05/0.1/0.2/0.02/0.04/0.08 by S/T
================================================================================
Project: CombiStats - EDQM, Council of Europe
Assay: Example 1: Diphteria
================================================================================
================================================================================
Data values:
--------------------------------------------------------------------------------
S:1:0.05 S:2:0.1 S:3:0.2 T:1:0.02 T:2:0.04 T:3:0.08
1 0.00 4.0 16.0 1.00 4 4
2 0.00 9.0 16.0 1.00 4 16
3 1.00 4.0 9.0 0.00 4 16
4 0.00 4.0 16.0 1.00 4 16
Mean 0.25 5.2 14.2 0.75 4 13
SD 0.50 2.5 3.5 0.50 0 6
CV 200.00 47.6 24.6 66.67 0 46
================================================================================
================================================================================
Dilution ration: 2
Factor: 23.75 250 NA
Significance level alpha: 5 %
================================================================================
================================================================================
Regression, Restricted model (Common Slope), with adjusting for 'blocks'.:
--------------------------------------------------------------------------------
Call:
lm(formula = Response ~ -1 + factor(Sample) + Z, data = data)
Residuals:
Min 1Q Median 3Q Max
-8.4792 -1.9167 0.3125 2.5260 3.5208
Coefficients:
Estimate Std. Error t value Pr(>|t|)
factor(Sample)S 13.146 1.181 11.13 2.86e-10 ***
factor(Sample)T 12.479 1.181 10.57 7.29e-10 ***
Z 9.468 1.115 8.49 3.14e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.092 on 21 degrees of freedom
Multiple R-squared: 0.8903, Adjusted R-squared: 0.8746
F-statistic: 56.8 on 3 and 21 DF, p-value: 3.005e-10
--------------------------------------------------------------------------------
Slope:
Z
9.467686
================================================================================
================================================================================
Regression, Unrestricted Model (Different slopes), with adjusting for 'blocks':
--------------------------------------------------------------------------------
Call:
lm(formula = Response ~ -1 + factor(Sample) + factor(Sample):Z,
data = data)
Residuals:
Min 1Q Median 3Q Max
-8.0417 -1.9167 0.4167 2.4167 3.9583
Coefficients:
Estimate Std. Error t value Pr(>|t|)
factor(Sample)S 13.583 1.435 9.465 7.91e-09 ***
factor(Sample)T 12.042 1.435 8.391 5.53e-08 ***
factor(Sample)S:Z 10.099 1.604 6.297 3.79e-06 ***
factor(Sample)T:Z 8.837 1.604 5.510 2.15e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 3.144 on 20 degrees of freedom
Multiple R-squared: 0.892, Adjusted R-squared: 0.8704
F-statistic: 41.28 on 4 and 20 DF, p-value: 2.149e-09
--------------------------------------------------------------------------------
Slopes:
factor(Sample)S:Z factor(Sample)T:Z
10.098865 8.836507
================================================================================
--------------------------------------------------------------------------------
Completly Randomized Design Analysis (CRD):
--------------------------------------------------------------------------------
Analysis of Variance Table
Response: Response
Df Sum Sq Mean Sq F value Pr(>F)
factor(Sample) 1 2.67 2.67 0.2909 0.5962
Dilution 1 689.06 689.06 75.1705 7.652e-08 ***
factor(Sample):Dilution 1 3.06 3.06 0.3341 0.5704
factor(Sample):factor(Dilution) 2 32.71 16.35 1.7841 0.1964
Residuals 18 165.00 9.17
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
Df Sum Sq Mean Sq F value Pr(>F) DFresiduals
Test of Preparation: 1 2.666667 2.666667 0.2909091 0.5962479 18
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F) F(critical)
Test of Regression: 1 689.0625 689.0625 75.17045 7.651945e-08 4.413873
This test passes if F(regression) > F(critical)
Test of Regression: Test passed!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F) F(critical)
Test of Linearity: 2 32.70833 16.35417 1.784091 0.1963951 3.554557
This test passes if F(non-linearity) < F(critical)
Test of Linearity: Test passed!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F) F(critical)
Test of Parallelism: 1 3.0625 3.0625 0.3340909 0.5704212 4.413873
This test passes if F(non-parallelity) < F(critical)
Test of Parallelism: Test passed!
================================================================================
================================================================================
Sums of Squares, Slope, Variance, C, Potency and Confidence-intervals:
--------------------------------------------------------------------------------
SStot SSreg SSres SSsmp R Radj
892.50000000 689.06250000 165.00000000 2.66666667 0.88036736 0.86811437
DFres b s2 qt C V
18.00000000 9.46768621 9.16666667 2.10092204 1.06238110 0.64060402
WidthT - Log(Lower)T - Log(Potency)T - Log(Upper)T -
0.283323600 -0.358131114 -0.070414952 0.208516087
CMT -
-0.074807514
exp(Width) Lower Potency Upper exp(CM)
23.75 31.528949 16.600809 22.135166 29.256408 22.038149
250 331.883671 174.745356 233.001750 307.962187 231.980520
Rel. Est. 142.438274 74.997443 100.000000 132.171619 99.561707
--------------------------------------------------------------------------------
================================================================================
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