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© MiraiBio Inc., 2004 MiraiBios MasterPlex QT Webinar 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 Questions www.miraibio.com/products/cat_liquidarrays/view_masterplex/sub_qtdownload /
© MiraiBio Inc., 2004 MasterPlex QT 2.0 Advance Topics Allan T. Minn
© MiraiBio Inc., 2003© MiraiBio Inc., 2004Overview I. General Calibration Process. II. Interpolation, Background Subtraction & Interpretation of Results. III. Heteroscadascity & Weighting. IV. Treating Standard Replicates.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 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.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 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.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 Anatomy 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
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 Parameter C MFI Concentrations A D C B
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 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.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 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 means? How come some concentration values has out of range notation while others that are even lower or higher concentration get calculated properly?
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 Background Subtraction MFI Concentrations
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 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 models calculable range.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 Out of Range Notations MFI Concentrations MFI > D MFI < A Conc. > Std-max Conc. < Std-min Interpolation Extrapolation Std-min Std-max A D
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 Why cant MFI D MFI < A If 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.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 Why is extrapolation dangerous? MFI Concentrations A slight change in Y(MFI) will result in a huge jump in concentration.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 Out of range notations MFI Concentrations MFI > 21560.6 MFI < 13.5 MFI>MAX MFI Std-Maxs Concentration Conc. < Std-Mins 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.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 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.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 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.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 Visual representation of Residuals
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 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., 2003© MiraiBio Inc., 2004 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.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 Weighting Algorithms There are five different ways to assign weights. 1/Y 2 - M inimizes 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/X 2 - Similar to above. 1/Stdev 2 - If you know the exact error distribution and standard deviation for each point you can use this algorithm.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 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.
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 Results 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
© MiraiBio Inc., 2003© MiraiBio Inc., 2004References Weighted Least Square Regression, http://www.itl.nist.gov/div898/handbook/pmd/section1/pmd143.htm 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, 2 nd Edition, Press, Vetterling, Teukolsky, Flannery, (1992)
© MiraiBio Inc., 2003© MiraiBio Inc., 2004 Thank You For Your Time & Participation Today! To reply this webcast (Available 3/17/04) www.miraibio.com/tech/cat_webex/ For copies of todays presentation email email@example.com Further Calculation Information To Contact MiraiBio 1-800-624-6176 firstname.lastname@example.org
© MiraiBio Inc., 2004 Questions & Answers
© MiraiBio Inc., 2004 Thank You Again!
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