10.6.1. CylinderPlate 5+1 Assay
This is an implementation of the cylinderplate assay defined in United States Pharmacopoeia (2010) Chapter <81> AntibioticsMicrobial Assays, which is widely known as the 5+1 assay.
Assay design consists of five concentrations of the standard preparation and one concentration each for one or more unknown preparations. The first four plates contain different concentrations of the standard preparation. One or more plates can be added for unknown (or test) preparations. Each plate contains six wells and only two treatments. Odd numbered wells on all plates contain the median standard concentration S3. Even numbered wells on the first four plates contain the remaining standard concentrations of S1, S2, S4 and S5. Even numbered wells on the fifth, sixth, etc. plates contain the unknown preparations U1, U2, etc.
This table shows the dose configuration of a 5+1 design with two test preparations, which constitutes one replicate.
Plates \ Wells 
1 
2 
3 
4 
5 
6 
1 
S3 
S1 
S3 
S1 
S3 
S1 
2 
S3 
S2 
S3 
S2 
S3 
S2 
3 
S3 
S4 
S3 
S4 
S3 
S3 
4 
S3 
S5 
S3 
S5 
S3 
S4 
5 
S3 
U1 
S3 
U1 
S3 
U1 
6 
S3 
U2 
S3 
U2 
S3 
U2 
… 
… 
… 
… 
… 
… 
… 
In each replicate with one unknown (i.e. a set of five plates) there are 15 median standard concentrations S3, three of each one of other four standard concentrations S1, S2, S4, S5 and three of the unknown U1. There are usually three replicates, totalling 15 plates and 90 wells.
This data is entered into a spreadsheet for analysis with UNISTAT as in the following table, where Rows and Columns variables refer to the rows (Plates) and columns (Wells) of the above table. The Response and Dose variables are numeric and Rows and Columns are alphanumeric. Ordering of the plates and replicates is not significant, as long as the rows of the table are kept intact. The odd column numbers should always correspond to the median standard concentration of S3. The Replicates column here is for reference only and is not required as a variable in the analysis.
Response 
Dose 
Rows 
Columns 
Replicates 
D1 
S3 
1 
1 
1 
D2 
S1 
1 
2 
1 
D3 
S3 
1 
3 
1 
D4 
S1 
1 
4 
1 
D5 
S3 
1 
5 
1 
D6 
S1 
1 
6 
1 
D7 
S3 
2 
1 
1 
D8 
S2 
2 
2 
1 
D9 
S3 
2 
3 
1 
D10 
S2 
2 
4 
1 
D11 
S3 
2 
5 
1 
D12 
S2 
2 
6 
1 
D13 
S3 
3 
1 
1 
D14 
S4 
3 
2 
1 
D15 
S3 
3 
3 
1 
D16 
S4 
3 
4 
1 
D17 
S3 
3 
5 
1 
D18 
S4 
3 
6 
1 
D19 
S3 
4 
1 
1 
D20 
S5 
4 
2 
1 
D21 
S3 
4 
3 
1 
D22 
S5 
4 
4 
1 
D23 
S3 
4 
5 
1 
D24 
S5 
4 
6 
1 
D25 
S3 
5 
1 
1 
D26 
U1 
5 
2 
1 
D27 
S3 
5 
3 
1 
D28 
U1 
5 
4 
1 
D29 
S3 
5 
5 
1 
D30 
U1 
5 
6 
1 
D31 
S3 
1 
1 
2 
D32 
S1 
1 
2 
2 
D33 
S3 
1 
3 
2 
D34 
S1 
1 
4 
2 
D35 
S3 
1 
5 
2 
D36 
S1 
1 
6 
2 
D37 
S3 
2 
1 
2 
… 
… 
… 
… 
… 
UNISTAT first calculates the corrected means and related statistics as described in Table 13 of US Pharmacopoeia (2010) Chapter <81> and displays this information in the output. The corrected means are then analysed using the Parallel Line Method. Because 5+1 assays will always have a zero residual degree of freedom, fiducial confidence intervals of the estimated potency is based on the linearity sum of squares and degrees of freedom. Note that USP does not report confidence limits of the estimated potency.
It is also possible to run multiple 5+1 assays and to combine their results in a single run. See section 10.0.4. Multiple Assays with Combination.
Example
Data is given in Table 13 of US Pharmacopoeia (2010) Chapter <81>.
Open SPECIFICASSAYS and select Bioassay → Specific Assays → CylinderPlate 5+1 Assay. From the Variable Selection Dialogue select C1 Response, C2 Dose, C3 Rows, C4 Columns, as [Response], [Dose], [Row Factor] and [Col Factor] respectively. From the Output Options Dialogue check the Data, Validity of Assay, Potency and Plot of Treatments options and click [Finish] to obtain the following output.
Parallel Line Method
Completely Randomised Design
5+1 Assay
Preparations 
Dose 
Mean (Odd well nos) 
Standard Deviation 
%RSD 
Standard 
3.2 
15.8667 
0.2000 
1.3 
Standard 
4 
15.5667 
0.1581 
1.0 
Standard 
5 
15.7222 


Standard 
6.25 
15.7889 
0.1691 
1.1 
Standard 
7.8125 
15.6667 
0.1414 
0.9 
Sample 1 
5 
15.6778 
0.1787 
1.1 
Preparations 
Mean (Even well nos) 
Standard Deviation 
%RSD 
Corrected Means 
Standard 
14.1667 
0.3240 
2.3 
14.0222 
Standard 
14.8333 
0.2646 
1.8 
14.9889 
Standard 



15.7222 
Standard 
16.5778 
0.2333 
1.4 
16.5111 
Standard 
17.1667 
0.2236 
1.3 
17.2222 
Sample 1 
15.4778 
0.3073 
2.0 
15.5222 
Data

Response 
Dose 
Preparations 
1 
14.02222222222 
3.2 
Standard 
2 
14.98888888889 
4 
Standard 
3 
15.72222222222 
5 
Standard 
4 
16.51111111111 
6.25 
Standard 
5 
17.22222222222 
7.8125 
Standard 
6 
15.52222222222 
5 
Sample 1 
Validity of Assay
Due To 
Sum of Squares 
DoF 
Mean Square 
FStat 
Prob 
Constant 
1472.319 
1 
1472.319 


Preparations 
0.024 
1 
0.024 
3.699 
0.1502 
Linear Regression 
6.276 
1 
6.276 
951.408 
0.0001 
Nonlinearity 
0.020 
3 
0.007 


Treatments 
6.320 
5 
1.264 


Residual 
0.000 
0 



Total 
6.320 
5 
1.264 


Potency
0 residual SSQ and DoF replaced by nonlinearity SSQ and DoF.

Estimated Potency 
Lower 95% 
Upper 95% 
DoF 
Sample 1 
0.9529 
0.8789 
1.0321 
3 

Relative Potency 
Lower 95% 
Upper 95% 
Sample 1 
95.29% 
87.89% 
103.21% 

Percent CI 
Lower 95% 
Upper 95% 
Sample 1 
100.00% 
92.23% 
108.31% 