MiraiBio’s
MasterPlex™ QT
Webinar Series
“The Calculations”
© MiraiBio Inc., 2004
Preliminary Questions
1. Is this web seminar being recorded so I or others
can view it at our convenience?
2. Will I be able to get copies of the slides after the
presentation?
3. Will I be able to ask questions to the speaker(s)?
4. Where can I get a demo/trial copy of the software?
www.miraibio.com/products/cat_liquidarrays/view_masterplex/sub_qtdownload/
© MiraiBio Inc., 2004
2003
MasterPlex QT 2.0
Advance Topics
Allan T. Minn
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Overview
I. General Calibration Process.
II. Interpolation, Background Subtraction &
Interpretation of Results.
III. Heteroscadascity & Weighting.
IV. Treating Standard Replicates.
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2003
General Calibration Process
• To interpolate unknowns from a set of
known standard values.
• Generally accepted models are 4 and 5
parameter logistics curves.
• Extrapolation is possible but use with
caution.
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2003
Review on 4PL curve
• In order to understand the calculation
process one should be familiar with the
curve model used to represent standard
data.
• Therefore, we shall review on the basic of
4PL curve.
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2003
Anatomy of 4PL curve
D
B
MFI
Based on the standard data given, A is the MFI value
that gives 0.0 concentration!
A
C
MFI = 0.0, Conc. = 0.0
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2003
Concentrations
Parameter C
D
B
MFI
A
Concentrations
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2003
C
Anatomy of 5PL curve
• 5PL curve is identical to 4PL except the extra
asymmetry correction parameter E.
• In this model upper and lower part of the
standard curve need not be symmetric
anymore.
• 5PL model fits asymmetric standard data better.
Next “Interpolation & Background Subtraction.”
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2003
Interpolation & Background Subtraction
• Interpolation is a process of using a standard data to
read unknown values. In this section we will cover some
of the most commonly asked questions.
 Why are there negative MFI values?
 Why are negative MFI values giving positive concentration
results.
 What does MFI < Concentration or MFI > Concentration
means?
 How come some concentration values has out of range notation
while others that are even lower or higher concentration get
calculated properly?
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2003
Background Subtraction
MFI
Concentrations
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When is the data “Out of Range?”
• There are two different “Out of Range”
scenarios.
• The first scenario is when an MFI value is out of
“Standard Range” where “Standard Range” is
defined between the highest and lowest
standard points.
• The second condition is when MFI value falls
out of an equation model’s calculable range.
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2003
Out of Range Notations
MFI > D
D
MFI
Std-max
Std-min
Extrapolation
Conc. > Std-max
Extrapolation
Conc. < Std-min
Interpolation
A
MFI < A
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2003
Concentrations
Why can’t MFI<A be calculated?
MFI > D
MFI
If Y < A or Y > D, then the second
equation is reduced to
C * ( some negative number )^(1/B)
MFI < A
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2003
This is not mathematically
possible and therefore Y
(MFI) values less than A or
greater than D is regarded to
be out of equation range.
Concentrations
Why is extrapolation dangerous?
A slight change in Y(MFI) will result in
a huge jump in concentration.
MFI
Concentrations
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2003
Out of range notations
MFI
MFI
Conc.
> 21560.6
> Std-Max’s
MFI>MAX
Concentration
Concentration for this sample cannot be
calculated because it is out of equation model
range. The best conclusion we can make about
this sample is that it is lower than the
concentration for the lowest standard point.
Std-Min
Horizontal lines A and D are called asymptotes
meaning, the curve will never reach or intersect
these lines. Therefore, it is not possible to
extrapolate the overall maximum and minimum
concentration from this curve.
MFI
< 13.5
Conc.
< Std-Min’sMFI<MIN
Concentration
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2003
Std-Max
Concentrations
What is Heteroscedasticity?
• Nonconstant variability also called
heteroscedasticity arises in almost all
fields.
• Chemical and Biochemical assays are no
exceptions.
• In assays, measurement errors increase
as concentrations get higher and therefore
the variability of a measurement is not
constant.
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2003
Residual Plot
Residual Plot
IL-10
Standard-0
1,600
1,500
1,400
1,300
1,200
1,100
1,000
900
800
700
600
500
400
300
200
100
0
-100
-200
-300
-400
-500
-600
-700
-800
-900
-1,000
-1,100
-1,200
-1,300
-1,400
-1,500
-1,600
H1
G1
F1
E1
D1
Pre d i cte d Co n ce n tra ti o n
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2003
C1
B1
A1
4.572
1.187
4.572
0.72
4.572
0.953
4.572
0.488
4.572
1.187
4.572
0.72
13.717 -0.986
13.717
2.311
13.717 -1.205
13.717
1.428
13.717
2.753
13.717
0.988
41.152 12.732
41.152 -11.856
41.152
5.471
41.152 -2.296
41.152
4.832
41.152
9.418
123.457 10.249
123.457 -18.121
123.457
12.42
123.457 -2.724
123.457
1.976
123.457 -0.536
370.37 -9.002
370.37 -31.213
370.37 -11.672
370.37 -23.088
370.37 -3.678
370.37 -39.393
1,111.111 93.933
1,111.111 -26.704
1,111.111 49.106
1,111.111 20.571
1,111.111 67.211
1,111.111 48.194
3,333.333 -195.452
3,333.333 -267.791
3,333.333 -33.057
Residuals are
difference between
expected
concentrations and
calculated
concentrations.
The higher the
residual the further
the standard curve
is away from the
sample.
Funnel or wedge
shape residual
plots usually
indicate nonconstant variability.
Visual representation of
Residuals
Predicted
Predicted
concentration
concentration
Expected
Expected
concentration
concentration
get
Residuals
Residuals get
as
larger
larger as
concentration
concentration
increases.
increases.
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2003
Why is this important?
• Curve fitting algorithms used to analyze assay data are based on
probability theories.
• One of those theories assumes that all data points are measured
the same way.
• This means all data points are assumed to have similar
measurement errors.
• During curve fitting all standard samples are given equal freedom to
influence the curve.
• The only problem is that those points with higher errors (variance)
are given the same freedom as those that are more accurate.
• So those points pull the curve to their ways leaving more accurate
points near the lower end relatively further from the curve causing
lack of sensitivities in lower part of the curve or concentration.
© MiraiBio Inc., 2004
2003
How to deal with it.
• One way to counterbalance nonconstant
variability is to make them constant again.
• To do this weights are assigned to each
standard sample data point.
• These weights are designed to
approximate the way measurement errors
are distributed.
• By applying weighting, points in lower
concentration are given more influence on
the curve again.
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2003
Weighting Algorithms
• There are five different ways to assign weights.
• 1/Y2 - Minimizes residuals (errors) based on relative
•
•
•
•
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2003
MFI values.
1/Y - This algorithm is useful if you know errors
follows Poisson distribution.
1/X - Minimizes residuals based on their
concentration values. Gives more weights to left part
of the graph.
1/X2 - Similar to above.
1/Stdev2 - If you know the exact error distribution and
standard deviation for each point you can use this
algorithm.
Disadvantage of Weighting
• In practice, we almost never know the
exact values of the weights.
• That is because we almost never know
the nature (distribution) of the errors.
• So we have to guess these weights.
• And results are as good as this initial
guess.
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2003
Results of weighting
% Recovery = ( Calculated / Expected ) x 100
• Above is the comparison between weighted and nonweighted analysis.
• The last three columns on the right were produced by
weighting.
• The accuracy increases dramatically at the very low end
without sacrificing over all accuracy of the curve.
• Also, QT 2.0 has more overall accuracy than previous
version 1.2.
© MiraiBio Inc., 2004
2003
References
•
•
•
•
•
Weighted Least Square Regression,
http://www.itl.nist.gov/div898/handbook/pmd/section1/pmd143.htm
General Information for regression data analysis,
http://www.curvefit.com
Transformation and Weighting in Regression, Carroll & Ruppert (1988)
Intuitive Biostatistics, Harvey Motulsky (1995)
Numerical Recipes in C, 2nd Edition, Press, Vetterling, Teukolsky, Flannery,
(1992)
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2003
Thank You
For Your Time &
Participation Today!
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Further “Calculation” Information
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2003
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Questions
&
Answers
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Thank You Again!
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