5 Parameter Logistic Parallelism Weighting Curve Fit Comparison PDF Curve Fitting Screening Tests Dilutions Unknown Blanks Applications Overview Statistical QC Interfacing Data Tracking Parallelism Multiplex 21 CFR Part 11

TrueFit™ Weighting normalizes the variance along the curve. In the absence of weighting, the curve fit is biased toward the points with the highest responses.

TrueFit™ Weighting models the actual variance using a pool of your own assays rather than an approximation, such as 1/Y or 1/Y², resulting in the most accurate curve fit.

## StatLIA Weighting Features

Custom Weighting Determined from Historical Set of Assays:

Fixed (Weighting settings fixed unless user initiates change)

No Weighting  (weighting turned off)
StatLIA uses previous assays to calculate the best custom weighting for each test
Separate weighting of standards and unknowns (measures matrix differences)
Weighting models based on observed historical data from laboratory
User-defined weighting models available

## Weighting Method

Choosing proper weights is crucial for obtaining the best curve fit.   According to regression theory, the weights should be set equal to the inverse variance of the responses at that concentration.  When this is done, the best-fitting curve, i.e., the one that minimizes the sum of squared error (SSE), will also be the optimal maximum likelihood estimate of the true curve.  This mathematical result stands to reason: weighting the squared errors in this way causes the fitting procedure to adjust the curve to be tighter around those standard responses with the smallest variance (error), typically those with the smallest responses, and looser around those standard responses with the largest variance, typically those with the largest responses.   By weighting this way, the information from the noisier and less noisy standards is optimally combined, leading to the most accurate estimate of the true curve, and therefore resulting in the most accurate concentration estimates.  That is why sample concentrations computed from unweighted curve fitting procedures can differ from properly weighted curves by hundreds of percent.

## StatLIA’s Custom Weighting

StatLIA computes a custom weighting for each test.  StatLIA uses the data from each test’s previously run assays to compute 16 different weighting models.  Then StatLIA calculates which model best defines the true variance for that test.  The weighting model and coefficients are then saved and used for all future assays for that test.

### Reference

The Five Parameter Logistic:  A Characterization and Comparison with the Four-Parameter Logistic, Gottschalk PG, Dunn JR, Analytical Biochemistry, 2005; 343:54-65.  (Free Reprint Available)

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