MiraiBio’sMasterPlex™ QT Webinar Series “The Calculations”
Preliminary Questions • Is this web seminar being recorded so I or others can view it at our convenience? • Will I be able to get copies of the slides after the presentation? • Will I be able to ask questions to the speaker(s)? • Where can I get a demo/trial copy of the software? www.miraibio.com/products/cat_liquidarrays/view_masterplex/sub_qtdownload/
MasterPlex QT 2.0Advance Topics Allan T. Minn
Overview I. General Calibration Process. II. Interpolation, Background Subtraction & Interpretation of Results. III. Heteroscadascity & Weighting. IV. Treating Standard Replicates.
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.
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.
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 Concentrations MFI = 0.0, Conc. = 0.0
Parameter C D B MFI A Concentrations 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.”
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?
Background Subtraction MFI Concentrations
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 Notations MFI > D D MFI Extrapolation Extrapolation Conc. < Std-min Conc. > Std-max Interpolation Std-max Std-min A MFI < A 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) 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. MFI < A Concentrations
Why is extrapolation dangerous? A slight change in Y(MFI) will result in a huge jump in concentration. MFI Concentrations
Out of range notations MFI MFI > 21560.6 Conc. > Std-Max’s Concentration MFI>MAX 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-Max 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 MFI<MIN Conc. < Std-Min’s Concentration 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.
Residual Plot 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.
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. • 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 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 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 weighting % Recovery = ( Calculated / Expected ) x 100 • 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.
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)
Thank YouFor Your Time & Participation Today! To reply this webcast (Available 3/17/04) www.miraibio.com/tech/cat_webex/ For copies of today’s presentation email firstname.lastname@example.org Further “Calculation” Information To Contact MiraiBio 1-800-624-6176 email@example.com