Turbidimetric: Antibiotic turbidimetric assay
In pla: Parallel Line Assays
Description
Usage
Details
Source
References
Examples
Description
5.1.3. FOUR-DOSE RANDOMIZED BLOCK DESIGN
Usage
1
data("Turbidimetric")
Details
From Ph.Eur.:
This assay is designed to assign a potency in international
units per vial. The standard has an assigned potency of
670 IU/mg. The test preparation has an assumed potency of
20 000 IU/vial. On the basis of this information the stock
solutions are prepared as follows. 16.7 mg of the standard
is dissolved in 25 ml solvent and the contents of one vial
of the test preparation are dissolved in 40 ml solvent. The
final solutions are prepared by first diluting to 1/40 and
further using a dilution ratio of 1.5. The tubes are placed
in a water-bath in a randomized block arrangement (see
Section 8.5). The responses are listed in Table 5.1.3.-I.
Inspection of Figure 5.1.3.-I gives no rise to doubt the validity
of the assumptions of normality and homogeneity of variance
of the data. The standard deviation of S3 is somewhat high
but is no reason for concern.
Source
The example can also be found at CombiStats - EDQM,
Council of Europe (http://combistats.edqm.eu):
http://combistats.edqm.eu/content/view/188/199/
References
Chapter 5.3. Statistical analysis.
In EUROPEAN PHARMACOPOEIA version 8.0, 2014; 607-635.
Examples
1
2
3
4
5
6
7
8
9
data(Turbidimetric); Data <- Turbidimetric
Data <- readAssayTable(paste(system.file(package = "pla"),
"vignettes/PhEur/data/AntibioticTurbidimetric.txt",
sep = "/"))
plaModel <- plaRBD(Data,
assayTitle = "PhEur: Antibiotic turbidimetric assay")
plaModel
plots <- plot(plaModel)
Example output
Note: Two factors without labels: Sample, Dose .
================================================================================
Project: Europ. Pharm., 5th Ed. (2005), Ch. 5.3, 5.1.3
Assay: Antibiotic turbidimetric assay
================================================================================
================================================================================
Data values:
--------------------------------------------------------------------------------
S:1:1 S:2:2 S:3:3 S:4:4 T:1:1 T:2:2 T:3:3 T:4:4
1 252.0 207.0 168 113.0 242.0 206.0 146.0 115.0
2 249.0 201.0 187 107.0 236.0 197.0 153.0 102.0
3 247.0 193.0 162 111.0 246.0 197.0 148.0 104.0
4 250.0 207.0 155 108.0 231.0 191.0 159.0 106.0
5 235.0 207.0 140 98.0 232.0 186.0 146.0 95.0
Mean 246.6 203.0 162 107.4 237.4 195.4 150.4 104.4
SD 6.7 6.2 17 5.8 6.5 7.5 5.6 7.2
CV 2.7 3.0 11 5.4 2.7 3.8 3.7 6.9
================================================================================
================================================================================
Dilution ration: 1.5
Factor: 1 0.005 0.00558584323889534
Significance level alpha: 5 %
================================================================================
================================================================================
Regression, Restricted model (Common Slope), with adjusting for 'blocks'.:
--------------------------------------------------------------------------------
Call:
lm(formula = Response ~ -1 + factor(Sample) + factor(Replicate) +
Z, data = data)
Residuals:
Min 1Q Median 3Q Max
-9.530 -4.247 -0.695 3.009 26.580
Coefficients:
Estimate Std. Error t value Pr(>|t|)
factor(Sample)S 117.435 3.256 36.068 < 2e-16 ***
factor(Sample)T 109.485 3.256 33.627 < 2e-16 ***
factor(Replicate)2 -2.125 3.687 -0.576 0.568246
factor(Replicate)3 -5.125 3.687 -1.390 0.173781
factor(Replicate)4 -5.250 3.687 -1.424 0.163810
factor(Replicate)5 -13.750 3.687 -3.730 0.000719 ***
Z -111.255 2.572 -43.262 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 7.373 on 33 degrees of freedom
Multiple R-squared: 0.9987, Adjusted R-squared: 0.9984
F-statistic: 3523 on 7 and 33 DF, p-value: < 2.2e-16
--------------------------------------------------------------------------------
Slope:
Z
-111.2549
================================================================================
================================================================================
Regression, Unrestricted Model (Different slopes), with adjusting for 'blocks':
--------------------------------------------------------------------------------
Call:
lm(formula = Response ~ -1 + factor(Sample) + factor(Replicate) +
factor(Sample):Z, data = data)
Residuals:
Min 1Q Median 3Q Max
-9.885 -3.683 -1.565 3.141 26.935
Coefficients:
Estimate Std. Error t value Pr(>|t|)
factor(Sample)S 116.370 3.642 31.950 < 2e-16 ***
factor(Sample)T 110.550 3.642 30.352 < 2e-16 ***
factor(Replicate)2 -2.125 3.717 -0.572 0.571557
factor(Replicate)3 -5.125 3.717 -1.379 0.177558
factor(Replicate)4 -5.250 3.717 -1.412 0.167514
factor(Replicate)5 -13.750 3.717 -3.699 0.000809 ***
factor(Sample)S:Z -113.006 3.667 -30.815 < 2e-16 ***
factor(Sample)T:Z -109.504 3.667 -29.860 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 7.435 on 32 degrees of freedom
Multiple R-squared: 0.9987, Adjusted R-squared: 0.9984
F-statistic: 3032 on 8 and 32 DF, p-value: < 2.2e-16
--------------------------------------------------------------------------------
Slopes:
factor(Sample)S:Z factor(Sample)T:Z
-113.0060 -109.5039
================================================================================
--------------------------------------------------------------------------------
Randomized Block Design Analysis (RBD):
--------------------------------------------------------------------------------
Analysis of Variance Table
Response: Response
Df Sum Sq Mean Sq F value Pr(>F)
factor(Replicate) 4 877 219 4.0653 0.010099 *
factor(Sample) 1 632 632 11.7224 0.001921 **
Dilution 1 101746 101746 1887.1109 < 2.2e-16 ***
factor(Sample):Dilution 1 25 25 0.4675 0.499766
factor(Sample):factor(Dilution) 4 259 65 1.2016 0.332090
Residuals 28 1510 54
---
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: 1 632.025 632.025 11.72239 0.001920815 28
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F) F(critical)
Test of Blocks: 4 876.75 219.1875 4.065346 0.01009903 2.714076
This test passes if F(Blocks) < F(critical)
Test of Blocks: (Test failed)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F) F(critical)
Test of Regression: 1 101745.6 101745.6 1887.111 3.068778e-27 4.195972
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: 4 259.14 64.785 1.20159 0.3320901 2.714076
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 25.205 25.205 0.4674858 0.4997658 4.195972
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
1.0504837e+05 1.0174560e+05 1.5096500e+03 6.3202500e+02 9.8720618e-01
Radj
9.8650990e-01
DFres b s2 qt C
28.00000000 -111.25494919 53.91607143 2.04840714 1.00222844
V
0.41100488
WidthT - Log(Lower)T - Log(Potency)T - Log(Upper)T -
0.042932889 0.028683845 0.071457495 0.114549623
CMT -
0.071616734
exp(Width) Lower Potency Upper
1 1.0438678373 1.0290991887 1.0740724965 1.1213682855
0.005 0.0052193392 0.0051454959 0.0053703625 0.0056068414
0.00558584323889534 0.0058308821 0.0057483867 0.0059996006 0.0062637875
exp(CM)
1 1.0742435445
0.005 0.0053712177
0.00558584323889534 0.0060005560
--------------------------------------------------------------------------------
================================================================================
pla documentation built on May 2, 2019, 11:12 a.m.
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Description Usage Details Source References Examples
Description
5.1.3. FOUR-DOSE RANDOMIZED BLOCK DESIGN
Usage
1 | data("Turbidimetric")
|
Details
From Ph.Eur.:
This assay is designed to assign a potency in international units per vial. The standard has an assigned potency of 670 IU/mg. The test preparation has an assumed potency of 20 000 IU/vial. On the basis of this information the stock solutions are prepared as follows. 16.7 mg of the standard is dissolved in 25 ml solvent and the contents of one vial of the test preparation are dissolved in 40 ml solvent. The final solutions are prepared by first diluting to 1/40 and further using a dilution ratio of 1.5. The tubes are placed in a water-bath in a randomized block arrangement (see Section 8.5). The responses are listed in Table 5.1.3.-I. Inspection of Figure 5.1.3.-I gives no rise to doubt the validity of the assumptions of normality and homogeneity of variance of the data. The standard deviation of S3 is somewhat high but is no reason for concern.
Source
The example can also be found at CombiStats - EDQM, Council of Europe (http://combistats.edqm.eu): http://combistats.edqm.eu/content/view/188/199/
References
Chapter 5.3. Statistical analysis. In EUROPEAN PHARMACOPOEIA version 8.0, 2014; 607-635.
Examples
1 2 3 4 5 6 7 8 9 | data(Turbidimetric); Data <- Turbidimetric
Data <- readAssayTable(paste(system.file(package = "pla"),
"vignettes/PhEur/data/AntibioticTurbidimetric.txt",
sep = "/"))
plaModel <- plaRBD(Data,
assayTitle = "PhEur: Antibiotic turbidimetric assay")
plaModel
plots <- plot(plaModel)
|
Example output
Note: Two factors without labels: Sample, Dose .
================================================================================
Project: Europ. Pharm., 5th Ed. (2005), Ch. 5.3, 5.1.3
Assay: Antibiotic turbidimetric assay
================================================================================
================================================================================
Data values:
--------------------------------------------------------------------------------
S:1:1 S:2:2 S:3:3 S:4:4 T:1:1 T:2:2 T:3:3 T:4:4
1 252.0 207.0 168 113.0 242.0 206.0 146.0 115.0
2 249.0 201.0 187 107.0 236.0 197.0 153.0 102.0
3 247.0 193.0 162 111.0 246.0 197.0 148.0 104.0
4 250.0 207.0 155 108.0 231.0 191.0 159.0 106.0
5 235.0 207.0 140 98.0 232.0 186.0 146.0 95.0
Mean 246.6 203.0 162 107.4 237.4 195.4 150.4 104.4
SD 6.7 6.2 17 5.8 6.5 7.5 5.6 7.2
CV 2.7 3.0 11 5.4 2.7 3.8 3.7 6.9
================================================================================
================================================================================
Dilution ration: 1.5
Factor: 1 0.005 0.00558584323889534
Significance level alpha: 5 %
================================================================================
================================================================================
Regression, Restricted model (Common Slope), with adjusting for 'blocks'.:
--------------------------------------------------------------------------------
Call:
lm(formula = Response ~ -1 + factor(Sample) + factor(Replicate) +
Z, data = data)
Residuals:
Min 1Q Median 3Q Max
-9.530 -4.247 -0.695 3.009 26.580
Coefficients:
Estimate Std. Error t value Pr(>|t|)
factor(Sample)S 117.435 3.256 36.068 < 2e-16 ***
factor(Sample)T 109.485 3.256 33.627 < 2e-16 ***
factor(Replicate)2 -2.125 3.687 -0.576 0.568246
factor(Replicate)3 -5.125 3.687 -1.390 0.173781
factor(Replicate)4 -5.250 3.687 -1.424 0.163810
factor(Replicate)5 -13.750 3.687 -3.730 0.000719 ***
Z -111.255 2.572 -43.262 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 7.373 on 33 degrees of freedom
Multiple R-squared: 0.9987, Adjusted R-squared: 0.9984
F-statistic: 3523 on 7 and 33 DF, p-value: < 2.2e-16
--------------------------------------------------------------------------------
Slope:
Z
-111.2549
================================================================================
================================================================================
Regression, Unrestricted Model (Different slopes), with adjusting for 'blocks':
--------------------------------------------------------------------------------
Call:
lm(formula = Response ~ -1 + factor(Sample) + factor(Replicate) +
factor(Sample):Z, data = data)
Residuals:
Min 1Q Median 3Q Max
-9.885 -3.683 -1.565 3.141 26.935
Coefficients:
Estimate Std. Error t value Pr(>|t|)
factor(Sample)S 116.370 3.642 31.950 < 2e-16 ***
factor(Sample)T 110.550 3.642 30.352 < 2e-16 ***
factor(Replicate)2 -2.125 3.717 -0.572 0.571557
factor(Replicate)3 -5.125 3.717 -1.379 0.177558
factor(Replicate)4 -5.250 3.717 -1.412 0.167514
factor(Replicate)5 -13.750 3.717 -3.699 0.000809 ***
factor(Sample)S:Z -113.006 3.667 -30.815 < 2e-16 ***
factor(Sample)T:Z -109.504 3.667 -29.860 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 7.435 on 32 degrees of freedom
Multiple R-squared: 0.9987, Adjusted R-squared: 0.9984
F-statistic: 3032 on 8 and 32 DF, p-value: < 2.2e-16
--------------------------------------------------------------------------------
Slopes:
factor(Sample)S:Z factor(Sample)T:Z
-113.0060 -109.5039
================================================================================
--------------------------------------------------------------------------------
Randomized Block Design Analysis (RBD):
--------------------------------------------------------------------------------
Analysis of Variance Table
Response: Response
Df Sum Sq Mean Sq F value Pr(>F)
factor(Replicate) 4 877 219 4.0653 0.010099 *
factor(Sample) 1 632 632 11.7224 0.001921 **
Dilution 1 101746 101746 1887.1109 < 2.2e-16 ***
factor(Sample):Dilution 1 25 25 0.4675 0.499766
factor(Sample):factor(Dilution) 4 259 65 1.2016 0.332090
Residuals 28 1510 54
---
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: 1 632.025 632.025 11.72239 0.001920815 28
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F) F(critical)
Test of Blocks: 4 876.75 219.1875 4.065346 0.01009903 2.714076
This test passes if F(Blocks) < F(critical)
Test of Blocks: (Test failed)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Df Sum Sq Mean Sq F value Pr(>F) F(critical)
Test of Regression: 1 101745.6 101745.6 1887.111 3.068778e-27 4.195972
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: 4 259.14 64.785 1.20159 0.3320901 2.714076
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 25.205 25.205 0.4674858 0.4997658 4.195972
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
1.0504837e+05 1.0174560e+05 1.5096500e+03 6.3202500e+02 9.8720618e-01
Radj
9.8650990e-01
DFres b s2 qt C
28.00000000 -111.25494919 53.91607143 2.04840714 1.00222844
V
0.41100488
WidthT - Log(Lower)T - Log(Potency)T - Log(Upper)T -
0.042932889 0.028683845 0.071457495 0.114549623
CMT -
0.071616734
exp(Width) Lower Potency Upper
1 1.0438678373 1.0290991887 1.0740724965 1.1213682855
0.005 0.0052193392 0.0051454959 0.0053703625 0.0056068414
0.00558584323889534 0.0058308821 0.0057483867 0.0059996006 0.0062637875
exp(CM)
1 1.0742435445
0.005 0.0053712177
0.00558584323889534 0.0060005560
--------------------------------------------------------------------------------
================================================================================
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