miraibio’s masterplex ™ qt webinar series

© MiraiBio Inc., 2004

MiraiBio’sMiraiBio’s

MasterPlexMasterPlex™™ QT QT

Webinar SeriesWebinar Series

“The Calculations”

© MiraiBio Inc., 2003 © MiraiBio Inc., 2004

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?

Preliminary QuestionsPreliminary Questions

www.miraibio.com/products/cat_liquidarrays/view_masterplex/sub_qtdownload /


MasterPlex QT 2.0MasterPlex QT 2.0Advance TopicsAdvance Topics

Allan T. Minn


OverviewOverview

I. General Calibration Process.

II. Interpolation, Background Subtraction &

Interpretation of Results.

III. Heteroscadascity & Weighting.

IV. Treating Standard Replicates.


General Calibration ProcessGeneral 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.


Review on 4PL curveReview 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.


Anatomy of 4PL curveAnatomy of 4PL curve

MFI

Concentrations

A

D

C

B

Based on the standard data given, A is the MFI value that gives 0.0 concentration!

MFI = 0.0, Conc. = 0.0


Parameter CParameter C

MFI

Concentrations

A

D

C

B


Anatomy of 5PL curveAnatomy 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.”


Interpolation & Background SubtractionInterpolation & 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?


Background SubtractionBackground Subtraction

MFI

Concentrations


When is the data “Out of Range?”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.


Out of Range NotationsOut of Range Notations

MFI

Concentrations

MFI > D

MFI < A

Conc. >

Std-m

ax

Conc. <

Std-m

in

Interpolation

Extrapolation

Extrapolation Std-min

Std-max

A

D


Why can’t MFI<A be calculated?Why can’t MFI<A be calculated?

MFI

Concentrations

MFI > D

MFI < A

If Y < A or Y > D, then the second equation is reduced to

C * ( some negative number )^(1/B)

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.


Why is extrapolation dangerous?Why is extrapolation dangerous?

MFI

Concentrations

A slight change in Y(MFI) will result in a huge jump in concentration.


Out of range notationsOut of range notationsMFI

Concentrations

MFI > 21560.6

MFI < 13.5

MFI>MAX

MFI<MIN

Std-Max

Std-Min

Conc. > Std-Max’s Concentration

Conc. < Std-Min’s 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.

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.


What is Heteroscedasticity?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.


Residual PlotResidual Plot

4.572 1.1874.572 0.724.572 0.9534.572 0.4884.572 1.1874.572 0.72

13.717 -0.98613.717 2.31113.717 -1.20513.717 1.42813.717 2.75313.717 0.98841.152 12.73241.152 -11.85641.152 5.47141.152 -2.29641.152 4.83241.152 9.418

123.457 10.249123.457 -18.121123.457 12.42123.457 -2.724123.457 1.976123.457 -0.536

370.37 -9.002370.37 -31.213370.37 -11.672370.37 -23.088370.37 -3.678370.37 -39.393

1,111.111 93.9331,111.111 -26.7041,111.111 49.1061,111.111 20.5711,111.111 67.2111,111.111 48.1943,333.333 -195.4523,333.333 -267.7913,333.333 -33.057

Residual PlotIL-10

Standard-0

Predicted ConcentrationH1 G1 F1 E1 D1 C1 B1 A1

Re

sid

ua

ls

1,6001,5001,400

1,3001,200

1,1001,000

900800700

600500

400300

200100

0

-100-200

-300-400

-500-600

-700-800-900

-1,000-1,100

-1,200-1,300

-1,400-1,500-1,600

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 non-

constant variability.


Visual representation of Visual representation of ResidualsResiduals

Residuals get larger as concentration increases.


Expected concentration


Predicted concentration









Why is this important?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.


How to deal with it.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.


Weighting AlgorithmsWeighting Algorithms

• There are five different ways to assign weights.• 1/Y2 - Minimizes residuals (errors) based on relative

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 WeightingDisadvantage 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.


Results of weightingResults of weighting

• Above is the comparison between weighted and non-weighted 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.

% Recovery = ( Calculated / Expected ) x 100


ReferencesReferences

• 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)


Thank YouThank YouFor Your Time & For Your Time &

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