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Deming & Weighted-Deming regression

This procedure is available in the Analyse-it Method Evaluation edition

Deming compares two analytical methods, a test method against a reference/comparative method, to determine analytical accuracy. Error in both the test and reference/comparative methods are supported because Deming regression is used.

The requirements of the test are:

  • Two methods measured on a continuous scale.
  • Any number of replicates can be observed for each method, though all cases must have the same number of replicates.


Arranging the dataset

Data in existing Excel worksheets can be used and should be arranged in the List dataset layout. The dataset must contain at least two continuous scale variables containing the observations for each method. If replicates are observed then a List dataset with repeat/replicate measures layout should be used to arrange the replicates for each method.

When entering new data we recommend using New Dataset to create a new method comparison dataset.

Using the test

To start the test:

  1. Excel 2007:
    Select any cell in the range containing the dataset to analyse, then click Comparison on the Analyse-it tab, then click Deming
  2. Excel 97, 2000, 2002 & 2003:
    Select any cell in the range containing the dataset to analyse, then click Analyse on the Analyse-it toolbar, click Method comparison then click Deming.

  3. Click Reference/Comparative method and Test method and select the methods or individual replicates to compare.
  4. Click Measured on and select Same scale if methods are measured on the same scale / units, otherwise select Differences scales.
  5. Click Errors in Test method and select whether errors in the test method exhibit Constant SD or Constant CV(weighted Deming regression will be used).
  6. If either method is measured in singlicate the SD or CV (depending on the Errors in Test method setting) must be entered. The SD/CV will be automatically determined if 2 or more replicates are observed.
  7. If the methods contains replicates click Use replicates and select:
  8. 1st Uses only the first replicate of each method.
    Mean Uses the mean of the replicates of each method.
    1st v Mean of Reference Uses the 1st replicate of the test method and the mean of the replicates of the reference method.
  9. Click OK to run the test.

The report shows the number of cases analysed, and, if applicable, how many cases were excluded due to missing values. The name, number of replicates, and repeatability (if measured in duplicate), in terms of SD or CV, depending on the Errors in Test method option, of each method is shown. The range of observations (minimum and maximum) for the reference/comparative method is shown.

The ratio of the error variance of reference/comparative to the test method and Syx, a measure of the dispersion of observations around the fitted linear line, are shown. If the test method was observed in singlicate Syx gives an estimate of the precision of the test method. When test method is measured in replicate, and the mean of the replicates used, Syx does not estimate precision as some random error is removed by averaging the replicates.

Constant and proportional bias are shown next. When two methods produce equivalent results constant bias will be zero and proportional bias will be one. Confidence intervals show the range that likely contains the true constant and proportional bias and a hypothesis test compares constant and proportional against the ideal values. If the p-value is statistically significant then the bias differs from the ideal value.

The scatter plot (see below) shows the observations of reference/comparative method (X) plotted against the test method (Y). The Use replicates option determines how replicates for each method, if available, are plotted.

Beneath the scatter plot is a residual plot (see below) of the differences of the test method from the linear fit (Y) against the estimated true concentration (X). The residuals are standardized (residual / Syx) so any observations outside ±4 indicate possible outliers.

Determining bias at specific decision levels

Bias can be determined for up to three decision levels.

To determine bias at specific decision levels:

  1. If the Deming method comparison dialog box is not visible click Edit on the Analyse-it tab/toolbar.
  2. Enter analyte concentration for up to three Decision levels.
  3. Click OK.

An additional table appears above the scatter plot showing the bias at each decision level, with confidence interval.

Comparing against a bias goal specification

Bias can be compared against a bias performance goal. The allowable bias can be specified in absolute units of the analyte, as a percentage of analyte concentration, or as a combination of the two in which case the larger of the absolute and percentage concentration is used.

To compare bias against a goal:

  1. If the Deming method comparison dialog box is not visible click Edit on the Analyse-it tab/toolbar.
  2. Click Compare against and select Bias specification.
  3. Enter Allowable bias as an absolute value, as a percentage of analyte concentration, or enter both values for a combination.
  4. Tick with Allowable Error bands checkbox to show the bias specification on the scatter plot.
  5. Click OK.

If decision levels are specified the bias goal at each decision level is shown for comparison against the observed bias.

If the Allowable Errors bands option is checked the scatter plot shows the allowable bias (see below). The confidence interval around the fitted linear line should fall within the allowable bias band if the methods are comparable within allowable bias.

Comparing against a TEa and Systematic Error%

Bias can be compared against a systematic error% of a total allowable error goal. The total allowable error can be specified in absolute units of the analyte, as a percentage of analyte concentration, or as a combination of the two in which case the larger of the absolute and percentage concentration is used.

To compare bias against a systematic error% of total allowable error:

  1. If the Deming method comparison dialog box is not visible click Edit on the Analyse-it tab/toolbar.
  2. Click Compare against and select TEa , %SE specification.
  3. Enter TEa (total allowable error) as an absolute value, as a percentage of analyte concentration, or enter both values for a combination.
  4. Enter % for Systematic error, that is the percentage of the TEa to allow bias to vary within.
  5. Tick with Allowable Error bands checkbox to show the bias specification on the scatter plot.
  6. Click OK.

If decision levels are specified, the bias goal at each decision level is shown for comparison against the observed bias.

If the Allowable Errors bands option is checked the scatter plot shows the allowable bias (see above). The confidence interval around the fitted linear line should fall within the allowable bias band if the methods are comparable within allowable bias.

References to further reading

  1. Evaluation of Regression Procedures for Method Comparison Studies
    Kristian Linnet, Clin.Chem. Vol. 39 No. 3 1993; 424-432
  2. Incorrect Least-Squares Regression Coefficients in Method-Comparison Analysis
    P. Joanne Cornbleet, Nathan Gochman, Clin Chem. Vol 25 No. 13 1979; 432-437
  3. Estimation of the Linear Relationship Between the Measurements of Two Methods with Proportional Errors
    Kristian Linnet, Statistics in Medicine Vol 9 1990; 1463-1473
  4. Performance of Deming regression analysis in case of misspecified analytical error ratio in method comparison studies
    Kristian Linnet,Clin Chem. Vol 44 No. 5 1998; 1024-1031
  5. Necessary Sample Size for Method Comparison Studies Based on Regression Analysis
    Kristian Linnet, Clin Chem. Vol 45 No. 6 1999; 882-894