# Deming regression & Weighted Deming regression.

Compare analytical methods to determine bias and comparability using Deming regression & Weighted Deming regression.

Analyse-it includes **Deming regression and Weighted Deming regression** so you can compare two analytical methods to determine bias (systematic error). Unlike linear regression, Deming regression allows measurement error (imprecision) in both the X and Y variables so is ideal for comparing clinical methods.

- Useful for robust implementation of CLSI EP9-A2
^{[6]}method comparison guideline. - Supports
**Deming regression**^{[1, 3]}– so you can compare methods with constant precision (constant SD) over the measurement range. - Supports
**Weighted Deming regression**^{[2]}– so you can compare methods with non-constant precision (constant CV%) over the measurement range.

### Flexible experiment design

- Supports any number of observations.
- Supports methods measured in singlicate, duplicate or any number of replicates.
- Specify imprecision (as a SD or %CV or relative ratio) for methods measured in singlicate[4] (imprecision automatically determined for methods measured in replicate).
- Compare methods using the mean of replicates, 1st replicate only, or the 1st replicate of the test method against mean of reference method replicates.

### Statistics and charts you need

**Systematic error as constant and proportional bias**, both with confidence intervals -- easily identify the source of bias so you can then take action to correct it.- Imprecision (repeatability) for methods measured in replicate – essential to get the most accurate estimate of bias on which to make reliable decisions
^{[4]}. - Scatter plot with
**Deming fitted regression line**, confidence bands, identity line and equation – so you can visualise the observations, bias, likely range of bias, and see how well the methods agree. - Standardized residual plot – so you can easily spot outliers, check precision over the range of measurement, and identify non-linearity.
- Syx –an independent estimate of the method’s precision so you can identify whether matrix effects are present, inflating the imprecision.

### Verify bias is within an allowable error goal

- Specify
**allowable error goal**directly or as a percentage of**Total Allowable Error (TAe)**. - Express allowable error goal directly, or Total Allowable Error (TAe), as an absolute concentration (e.g. 5mg/dL), percentage of concentration (e.g. 10%), or combination (e.g. 10%, with minimum of 5mg/dL).
- Scatter plot with allowable error bands – so you can clearly see if, and at what concentration levels, bias exceeds the allowable error goal.

### Determine bias at important clinical decision levels

- Specify up to 3 decision levels
- Calculates bias with confidence intervals – so you can see the bias at clinically important decision points and judge its affect on clinical decision-making.
- Hypothesis test for bias against goal at specified decision levels– tells you if the observed bias at the decision level is outside the allowable error goal.

### Reliable algorithms you can trust

Analyse-it uses the latest algorithms from **widely respected international journals**. **Cornbleet and Gochman**^{[1]} is used to calculate Deming regression, and the latest **iteratively re-weighted procedure** described by Linnet ^{[3]} is used to calculate Weighted Deming regression. Standard errors and confidence intervals use the jack-knife method ^{[3]}.

- Incorrect Least-Squares Regression Coefficients in Method-Comparison Analysis. P. Joanne Cornbleet, Nathan Gochman, Clin Chem. Vol 25 No. 13 1979; 432-437
- Estimation of the Linear Relationship between the Measurements of Two Methods with Proportional Errors. Kristian Linnet, Statistics in Medicine Vol 9 1990; 1463-1473
- Evaluation of Regression Procedures for Method Comparison Studies. Kristian Linnet, Clin.Chem. Vol. 39 No. 3 1993; 424-432
- Performance of Deming Regression Analysis in the Case of Mis-specified Analytical Error Ratio in Method Comparison Studies. Kristian Linnet,Clin Chem. Vol 44 No. 5 1998; 1024-1031
- Necessary Sample Size for Method Comparison Studies Based on Regression Analysis. Kristian Linnet, Clin Chem. Vol 45 No. 6 1999; 882-894
- Method Comparison and Bias Estimation Using Patient Samples; Approved Guideline – Second Edition. CLSI document EP9-A2 [ISBN 1-65238-472-4]