HeparinSodium: Heparin Sodium - European Pharmacopoeia (1997), 2.7.5
In pla: Parallel Line Assays
Description
Usage
Source
Examples
Description
Example 05 - Three-dose parallel line assay; completely randomized;
custom transformation; explicit content notation,
from CombiStats - EDQM, Council of Europe (http://combistats.edqm.eu).
Usage
1
data("HeparinSodium")
Source
From CombiStats - EDQM, Council of Europe:
http://combistats.edqm.eu/images/stories/Examples/Heparin%20sodium.pdf
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Example <- "Example 5"
data(HeparinSodium); Data <- HeparinSodium
Data <- readAssayTable(paste(system.file(package = "pla"),
"vignettes/CombiStat/data/HeparinSodium.txt",
sep = "/"),
fun = function(x)
apply(array(x, dim = c(6, 2, 2)), c(1, 3), mean),
log = 10,
rows = "Dilutions & Samples",
columns = "Inner & Replicates")
plaModel <- plaCRD(Data); plaModel
plots <- plot(plaModel)
Example output
Some factors have problems with nesting in COLUMNS
Trying to fix 1.044/1.321/1.670/1.000/1.265/1.600 by S/T
================================================================================
Project: CombiStats - EDQM, Council of Europe
Assay: Example 5: Heparin Sodium
================================================================================
================================================================================
Data values:
--------------------------------------------------------------------------------
S:1:1.044 S:2:1.321 S:3:1.670 T:1:1.000 T:2:1.265 T:3:1.600
1 1.8995 2.044 2.252 1.8927 2.029 2.2299
2 1.8979 2.082 2.235 1.8965 2.070 2.2330
Mean 1.8987 2.063 2.243 1.8946 2.049 2.2315
SD 0.0012 0.027 0.012 0.0027 0.029 0.0022
CV 0.0613 1.306 0.532 0.1446 1.424 0.0969
================================================================================
================================================================================
Dilution ration: 1.26483533222663
Factor: 1044 104.4 101.364395168284
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
-0.029713 -0.001024 0.002872 0.009172 0.013754
Coefficients:
Estimate Std. Error t value Pr(>|t|)
factor(Sample)S 2.238652 0.008238 271.74 < 2e-16 ***
factor(Sample)T 2.228827 0.008238 270.55 < 2e-16 ***
Z 0.725028 0.022955 31.58 1.57e-10 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.01525 on 9 degrees of freedom
Multiple R-squared: 1, Adjusted R-squared: 0.9999
F-statistic: 7.352e+04 on 3 and 9 DF, p-value: < 2.2e-16
--------------------------------------------------------------------------------
Slope:
Z
0.7250282
================================================================================
================================================================================
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
-0.0297127 -0.0000737 0.0032428 0.0076300 0.0137543
Coefficients:
Estimate Std. Error t value Pr(>|t|)
factor(Sample)S 2.24055 0.01037 216.03 2.36e-16 ***
factor(Sample)T 2.22693 0.01037 214.72 2.48e-16 ***
factor(Sample)S:Z 0.73312 0.03419 21.44 2.36e-08 ***
factor(Sample)T:Z 0.71694 0.03419 20.97 2.81e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.01607 on 8 degrees of freedom
Multiple R-squared: 1, Adjusted R-squared: 0.9999
F-statistic: 4.97e+04 on 4 and 8 DF, p-value: < 2.2e-16
--------------------------------------------------------------------------------
Slopes:
factor(Sample)S:Z factor(Sample)T:Z
0.7331170 0.7169394
================================================================================
--------------------------------------------------------------------------------
Completly Randomized Design Analysis (CRD):
--------------------------------------------------------------------------------
Analysis of Variance Table
Response: Response
Df Sum Sq Mean Sq F value Pr(>F)
factor(Sample) 1 0.000290 0.000290 1.0024 0.3554
Dilution 1 0.232124 0.232124 803.4166 1.276e-07 ***
factor(Sample):Dilution 1 0.000029 0.000029 0.1000 0.7625
factor(Sample):factor(Dilution) 2 0.000332 0.000166 0.5742 0.5913
Residuals 6 0.001734 0.000289
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
Df Sum Sq Mean Sq F value Pr(>F)
Test of Preparation: 1 0.0002896138 0.0002896138 1.002396 0.3553838
DFresiduals
Test of Preparation: 6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F) F(critical)
Test of Regression: 1 0.2321244 0.2321244 803.4166 1.276434e-07 5.987378
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 0.0003317754 0.0001658877 0.5741614 0.5913455 5.143253
This test passes if F(non-linearity) < F(critical)
Test of Linearity: Test passed!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F)
Test of Parallelism: 1 2.889203e-05 2.889203e-05 0.09999953 0.7625422
F(critical)
Test of Parallelism: 5.987378
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
0.23450826018 0.23212444902 0.00173352996 0.00028961381 0.99552490449
Radj
0.99452770422
DFres b s2 qt C
6.00000000000 0.72502819536 0.00028892166 2.44691185114 1.00750835017
V
0.07359695453
WidthT - Log(Lower)T - Log(Potency)T - Log(Upper)T -
0.033265344 -0.046918805 -0.013551710 0.019611882
CMT -
-0.013653461
exp(Width) Lower Potency Upper exp(CM)
1044 1079.31311 996.148122 1029.94745 1064.67690 1029.842655
104.4 107.93131 99.614812 102.99474 106.46769 102.984265
101.364395168284 104.79303 96.718345 100.00000 103.37196 99.989825
--------------------------------------------------------------------------------
================================================================================
pla documentation built on May 2, 2019, 11:12 a.m.
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Description Usage Source Examples
Description
Example 05 - Three-dose parallel line assay; completely randomized; custom transformation; explicit content notation, from CombiStats - EDQM, Council of Europe (http://combistats.edqm.eu).
Usage
1 | data("HeparinSodium")
|
Source
From CombiStats - EDQM, Council of Europe: http://combistats.edqm.eu/images/stories/Examples/Heparin%20sodium.pdf
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | Example <- "Example 5"
data(HeparinSodium); Data <- HeparinSodium
Data <- readAssayTable(paste(system.file(package = "pla"),
"vignettes/CombiStat/data/HeparinSodium.txt",
sep = "/"),
fun = function(x)
apply(array(x, dim = c(6, 2, 2)), c(1, 3), mean),
log = 10,
rows = "Dilutions & Samples",
columns = "Inner & Replicates")
plaModel <- plaCRD(Data); plaModel
plots <- plot(plaModel)
|
Example output
Some factors have problems with nesting in COLUMNS
Trying to fix 1.044/1.321/1.670/1.000/1.265/1.600 by S/T
================================================================================
Project: CombiStats - EDQM, Council of Europe
Assay: Example 5: Heparin Sodium
================================================================================
================================================================================
Data values:
--------------------------------------------------------------------------------
S:1:1.044 S:2:1.321 S:3:1.670 T:1:1.000 T:2:1.265 T:3:1.600
1 1.8995 2.044 2.252 1.8927 2.029 2.2299
2 1.8979 2.082 2.235 1.8965 2.070 2.2330
Mean 1.8987 2.063 2.243 1.8946 2.049 2.2315
SD 0.0012 0.027 0.012 0.0027 0.029 0.0022
CV 0.0613 1.306 0.532 0.1446 1.424 0.0969
================================================================================
================================================================================
Dilution ration: 1.26483533222663
Factor: 1044 104.4 101.364395168284
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
-0.029713 -0.001024 0.002872 0.009172 0.013754
Coefficients:
Estimate Std. Error t value Pr(>|t|)
factor(Sample)S 2.238652 0.008238 271.74 < 2e-16 ***
factor(Sample)T 2.228827 0.008238 270.55 < 2e-16 ***
Z 0.725028 0.022955 31.58 1.57e-10 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.01525 on 9 degrees of freedom
Multiple R-squared: 1, Adjusted R-squared: 0.9999
F-statistic: 7.352e+04 on 3 and 9 DF, p-value: < 2.2e-16
--------------------------------------------------------------------------------
Slope:
Z
0.7250282
================================================================================
================================================================================
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
-0.0297127 -0.0000737 0.0032428 0.0076300 0.0137543
Coefficients:
Estimate Std. Error t value Pr(>|t|)
factor(Sample)S 2.24055 0.01037 216.03 2.36e-16 ***
factor(Sample)T 2.22693 0.01037 214.72 2.48e-16 ***
factor(Sample)S:Z 0.73312 0.03419 21.44 2.36e-08 ***
factor(Sample)T:Z 0.71694 0.03419 20.97 2.81e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.01607 on 8 degrees of freedom
Multiple R-squared: 1, Adjusted R-squared: 0.9999
F-statistic: 4.97e+04 on 4 and 8 DF, p-value: < 2.2e-16
--------------------------------------------------------------------------------
Slopes:
factor(Sample)S:Z factor(Sample)T:Z
0.7331170 0.7169394
================================================================================
--------------------------------------------------------------------------------
Completly Randomized Design Analysis (CRD):
--------------------------------------------------------------------------------
Analysis of Variance Table
Response: Response
Df Sum Sq Mean Sq F value Pr(>F)
factor(Sample) 1 0.000290 0.000290 1.0024 0.3554
Dilution 1 0.232124 0.232124 803.4166 1.276e-07 ***
factor(Sample):Dilution 1 0.000029 0.000029 0.1000 0.7625
factor(Sample):factor(Dilution) 2 0.000332 0.000166 0.5742 0.5913
Residuals 6 0.001734 0.000289
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
Df Sum Sq Mean Sq F value Pr(>F)
Test of Preparation: 1 0.0002896138 0.0002896138 1.002396 0.3553838
DFresiduals
Test of Preparation: 6
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F) F(critical)
Test of Regression: 1 0.2321244 0.2321244 803.4166 1.276434e-07 5.987378
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 0.0003317754 0.0001658877 0.5741614 0.5913455 5.143253
This test passes if F(non-linearity) < F(critical)
Test of Linearity: Test passed!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F)
Test of Parallelism: 1 2.889203e-05 2.889203e-05 0.09999953 0.7625422
F(critical)
Test of Parallelism: 5.987378
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
0.23450826018 0.23212444902 0.00173352996 0.00028961381 0.99552490449
Radj
0.99452770422
DFres b s2 qt C
6.00000000000 0.72502819536 0.00028892166 2.44691185114 1.00750835017
V
0.07359695453
WidthT - Log(Lower)T - Log(Potency)T - Log(Upper)T -
0.033265344 -0.046918805 -0.013551710 0.019611882
CMT -
-0.013653461
exp(Width) Lower Potency Upper exp(CM)
1044 1079.31311 996.148122 1029.94745 1064.67690 1029.842655
104.4 107.93131 99.614812 102.99474 106.46769 102.984265
101.364395168284 104.79303 96.718345 100.00000 103.37196 99.989825
--------------------------------------------------------------------------------
================================================================================
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