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Variance Analysis For Multiplexed
qPCR Samples: A System Approach
Designed by Geoffrey Dennis and
Concept Proofed by Hugo DiGiulio
Variance Analysis of Multiplexed
Systems: Individual vs. Whole
• Multiplexing ≥ 2 gene targets for quantitation in single
well format
• Typical basic analysis of individual amplisets includes
CV (RSD), CI, relevant t-test
• Comparison between systems can be done by ANCOVA,
t-test, χ test, etc.
• By use of dilution series, the multiplex can be set up as a
matrix and the system variance can be analyzed as a
single unit
– This is done by calculating a %CV based on frequency of
particles
– using %CV calculated by frequency of particles provides clarity
on the decision to accept or not accept the outcome of a sample
Example of Variance Analysis of
Individual Parts
Gene 1 Gene 2 Gene 3 DCt Gene 1 Gene 2 Gene 3
1000000 19.97 19.68 19.95 -3.91 -3.60 -3.71 Slope
300000 21.38 21.15 21.60 1.65 43.13 40.99 42.01 Intercept
100000 23.50 22.71 23.44 1.83 0.253 0.22 0.14 Error
30000 25.72 24.58 25.09 1.66 0.142 0.105 0.174 ANCOVA
10000 27.69 26.76 27.14 2.04
3000 29.13 28.23 28.88 1.75
1000 31.17 30.22 30.87 1.98
300 33.43 31.85 32.80 1.93
100 35.55 34.01 34.72 1.92
NTC Neg Neg Neg
Gene 1 Gene 2 Gene 3
Sample dilution 1 24.03 23.28 23.83
Sample dilution 2 27.52 26.94 27.40
Sample dilution 1 3.10E+09 3.30E+09 3.18E+09
Sample dilution 2 3.96E+09 3.17E+09 3.47E+09
17.4% 2.7% 6.1% %CV
Resulting Cq
Resulting
c/mL
Example of Variance Analysis of System
as Whole
%CVWhole = 2 – Σ(λ1 + λ2)
Gene 1 Gene 2 Gene 3
Sample dilution 1 24.03 23.28 23.83
Sample dilution 2 27.52 26.94 27.40
Sample dilution 1 3.10E+09 3.30E+09 3.18E+09
Sample dilution 2 3.96E+09 3.17E+09 3.47E+09
17.4% 2.7% 6.1% %CV
Sample dilution 1 0.32 0.34 0.33
Sample dilution 2 0.37 0.30 0.33
0.7 0.7 0.7
0.0 0.0 0.0
5.5% %CV
Resulting Cq
Resulting
c/mL
Frequency of
Particles
Calculated
Lambdas
Example of Variance Analysis of System
as Whole: Accept or Reject?
• While 36% is typically
acceptable in c/mL for qPCR,
calculating %CV by using
frequency of particles in a
matrix may result in a need to
repeat the sample
• Observed acceptance tolerance
was at a maximum of 10% CV
compared to controls
Sample A Gene 1 Gene 2 Gene 3
Sample dilution 1 3.10E+09 3.30E+09 3.18E+09
Sample dilution 2 3.96E+09 3.17E+09 3.47E+09
17.4% 2.7% 6.1% %CV
Sample dilution 1 0.32 0.34 0.33
Sample dilution 2 0.37 0.30 0.33
0.7 0.7 0.7
0.0 0.0 0.0
5.5% %CV
Sample B Gene 1 Gene 2 Gene 3
Sample dilution 1 1.88E+09 2.07E+09 3.00E+09
Sample dilution 2 3.12E+09 3.48E+09 3.46E+09
35.0% 36.0% 10.1% %CV
Sample dilution 1 0.27 0.30 0.43
Sample dilution 2 0.31 0.35 0.34
0.6 0.7 0.7
0.0 -0.1 -0.1
12.7% %CV
Resulting
c/mL
Frequency of
Particles
Calculated
Lambdas
Resulting
c/mL
Frequency of
Particles
Calculated
Lambdas
Variance Analysis of a System as a Whole
• For each additional ampliset,
– %CV = (2+N additional sets)- Σ(λ1 + λ2)
∀± CV indicates direction of inconsistency in
system (but remember, since 2+N used, the
result indicates the inverse of the direction!)
Variance Analysis System Dynamics
-0.08
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.6 0.62 0.64 0.66 0.68 0.7 0.72 0.74
Series1
Series2
Series3
Series4
Series 1 0.06
Series 2 0.13
Series 3 -0.02
Series 4 -0.18
System CV
The arrows show how signal changes are reflected with this analysis
Rating Complex Systems
5`
5`
Capped RNA
miRNA
For 1 Probe
Rev
For 2
RT Primer
For Probe
Rev
Rating Complex Systems Continued
RNA Cap Detection Set 1 Set 2
Sample dilution 1 3.10E+09 3.30E+09
Sample dilution 2 2.88E+09 2.07E+09
Sample dilution 3 3.12E+09 3.48E+09
Sample dilution 4 3.96E+09 3.17E+09
Sample dilution 1 0.48 0.52
Sample dilution 2 0.58 0.42
Sample dilution 3 0.47 0.53
Sample dilution 4 0.56 0.44
1.00
-0.10 1.00
1.00 0.11
-0.08 9.9% %CV
Lambdas
Resulting
c/mL
Frequency
of Particles
Rating Complex Systems Continued
miRNA Evaluation miRNA 1 miRNA 2 miRNA 3 miRNA 4
Sample dilution 1 3.10E+11 3.30E+11 3.18E+11 4.64E+11
Sample dilution 2 3.96E+11 3.17E+11 3.47E+11 4.59E+11
17.4% 2.7% 6.1% 0.7%
Sample dilution 1 0.22 0.23 0.22 0.33
Sample dilution 2 0.28 0.22 0.24 0.32
0.5 0.5 0.5 0.6 0.6 0.6
0.0 0.0 0.0 0.0 0.0 0.0
3-sum λ's -2.2% %CV
Conclusion
• In conclusion, using %CV based on
matrices calculated by frequency of
particles provides clarity on the decision to
accept or not accept the outcome of a
sample

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A System Approach

  • 1. Variance Analysis For Multiplexed qPCR Samples: A System Approach Designed by Geoffrey Dennis and Concept Proofed by Hugo DiGiulio
  • 2. Variance Analysis of Multiplexed Systems: Individual vs. Whole • Multiplexing ≥ 2 gene targets for quantitation in single well format • Typical basic analysis of individual amplisets includes CV (RSD), CI, relevant t-test • Comparison between systems can be done by ANCOVA, t-test, χ test, etc. • By use of dilution series, the multiplex can be set up as a matrix and the system variance can be analyzed as a single unit – This is done by calculating a %CV based on frequency of particles – using %CV calculated by frequency of particles provides clarity on the decision to accept or not accept the outcome of a sample
  • 3. Example of Variance Analysis of Individual Parts Gene 1 Gene 2 Gene 3 DCt Gene 1 Gene 2 Gene 3 1000000 19.97 19.68 19.95 -3.91 -3.60 -3.71 Slope 300000 21.38 21.15 21.60 1.65 43.13 40.99 42.01 Intercept 100000 23.50 22.71 23.44 1.83 0.253 0.22 0.14 Error 30000 25.72 24.58 25.09 1.66 0.142 0.105 0.174 ANCOVA 10000 27.69 26.76 27.14 2.04 3000 29.13 28.23 28.88 1.75 1000 31.17 30.22 30.87 1.98 300 33.43 31.85 32.80 1.93 100 35.55 34.01 34.72 1.92 NTC Neg Neg Neg Gene 1 Gene 2 Gene 3 Sample dilution 1 24.03 23.28 23.83 Sample dilution 2 27.52 26.94 27.40 Sample dilution 1 3.10E+09 3.30E+09 3.18E+09 Sample dilution 2 3.96E+09 3.17E+09 3.47E+09 17.4% 2.7% 6.1% %CV Resulting Cq Resulting c/mL
  • 4. Example of Variance Analysis of System as Whole %CVWhole = 2 – Σ(λ1 + λ2) Gene 1 Gene 2 Gene 3 Sample dilution 1 24.03 23.28 23.83 Sample dilution 2 27.52 26.94 27.40 Sample dilution 1 3.10E+09 3.30E+09 3.18E+09 Sample dilution 2 3.96E+09 3.17E+09 3.47E+09 17.4% 2.7% 6.1% %CV Sample dilution 1 0.32 0.34 0.33 Sample dilution 2 0.37 0.30 0.33 0.7 0.7 0.7 0.0 0.0 0.0 5.5% %CV Resulting Cq Resulting c/mL Frequency of Particles Calculated Lambdas
  • 5. Example of Variance Analysis of System as Whole: Accept or Reject? • While 36% is typically acceptable in c/mL for qPCR, calculating %CV by using frequency of particles in a matrix may result in a need to repeat the sample • Observed acceptance tolerance was at a maximum of 10% CV compared to controls Sample A Gene 1 Gene 2 Gene 3 Sample dilution 1 3.10E+09 3.30E+09 3.18E+09 Sample dilution 2 3.96E+09 3.17E+09 3.47E+09 17.4% 2.7% 6.1% %CV Sample dilution 1 0.32 0.34 0.33 Sample dilution 2 0.37 0.30 0.33 0.7 0.7 0.7 0.0 0.0 0.0 5.5% %CV Sample B Gene 1 Gene 2 Gene 3 Sample dilution 1 1.88E+09 2.07E+09 3.00E+09 Sample dilution 2 3.12E+09 3.48E+09 3.46E+09 35.0% 36.0% 10.1% %CV Sample dilution 1 0.27 0.30 0.43 Sample dilution 2 0.31 0.35 0.34 0.6 0.7 0.7 0.0 -0.1 -0.1 12.7% %CV Resulting c/mL Frequency of Particles Calculated Lambdas Resulting c/mL Frequency of Particles Calculated Lambdas
  • 6. Variance Analysis of a System as a Whole • For each additional ampliset, – %CV = (2+N additional sets)- Σ(λ1 + λ2) ∀± CV indicates direction of inconsistency in system (but remember, since 2+N used, the result indicates the inverse of the direction!)
  • 7. Variance Analysis System Dynamics -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.6 0.62 0.64 0.66 0.68 0.7 0.72 0.74 Series1 Series2 Series3 Series4 Series 1 0.06 Series 2 0.13 Series 3 -0.02 Series 4 -0.18 System CV The arrows show how signal changes are reflected with this analysis
  • 8. Rating Complex Systems 5` 5` Capped RNA miRNA For 1 Probe Rev For 2 RT Primer For Probe Rev
  • 9. Rating Complex Systems Continued RNA Cap Detection Set 1 Set 2 Sample dilution 1 3.10E+09 3.30E+09 Sample dilution 2 2.88E+09 2.07E+09 Sample dilution 3 3.12E+09 3.48E+09 Sample dilution 4 3.96E+09 3.17E+09 Sample dilution 1 0.48 0.52 Sample dilution 2 0.58 0.42 Sample dilution 3 0.47 0.53 Sample dilution 4 0.56 0.44 1.00 -0.10 1.00 1.00 0.11 -0.08 9.9% %CV Lambdas Resulting c/mL Frequency of Particles
  • 10. Rating Complex Systems Continued miRNA Evaluation miRNA 1 miRNA 2 miRNA 3 miRNA 4 Sample dilution 1 3.10E+11 3.30E+11 3.18E+11 4.64E+11 Sample dilution 2 3.96E+11 3.17E+11 3.47E+11 4.59E+11 17.4% 2.7% 6.1% 0.7% Sample dilution 1 0.22 0.23 0.22 0.33 Sample dilution 2 0.28 0.22 0.24 0.32 0.5 0.5 0.5 0.6 0.6 0.6 0.0 0.0 0.0 0.0 0.0 0.0 3-sum λ's -2.2% %CV
  • 11. Conclusion • In conclusion, using %CV based on matrices calculated by frequency of particles provides clarity on the decision to accept or not accept the outcome of a sample