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Deming regression

Command:    

 Statistics
Next selectMethod comparison
Next selectDeming regression

Description

Allows to perform method comparison using the Deming regresson model (Combleet & Gochman, 1979).

Whereas the ordinary linear regression method assumes that only the Y measurements are associated with random measurement errors, the Deming method takes measurement errors for both methods into account.

Required input

Select the variables for the two techniques you want to compare.

For each of both techniques you can either enter 2 variables (which contain repeated measurements) or you can enter only one variable, in which case you will have to enter an already established Coefficient of Variation (CV, expressed as a percentage).

As an option, you can create 2 graphs:

  • A scatter diagram with the regression line
  • The residuals plot.

Use the Subgroups button if you want to identify subgroups in the scatter diagram and residuals plot. A new dialog box is displayed in which you can select a categorical variable. The graph will display different markers for the different categories in this variable.

Results

The results are displayed in the following text window:

  • Mean and Coefficient of Variation (%) for both methods
  • Sample size: the number of (selected) data pairs
  • Variance ratio: this is the ratio of the measurement errors of X and Y.
  • The regression equation, Intercept and Slope with 95% confidence interval
  • The Intercept and Slope are calculated according to Combleet & Gochman, 1979. The standard errors and confidence intervals are estimated using the jackknife method (Armitage et al., 2002).

The 95% confidence interval for the Intercept can be used to test the hypothesis that A=0. This hypothesis is accepted if the confidence interval for A contains the value 0. If the hypothesis is rejected, then it is concluded that A is significant different from 0 and both methods differ at least by a constant amount.

The 95% confidence interval for the Slope can be used to test the hypothesis that B=1. This hypothesis is accepted if the confidence interval for B contains the value 1. If the hypothesis is rejected, then it is concluded that B is significant different from 1 and there is at least a proportional difference between the two methods.

Graphs

The first graph window displays the scatter diagram with regression line (solid line) and identity line (x=y, dotted line)

The second graph windows displays the residuals:

Literature

  • Cornbleet PJ, Gochman N (1979) Incorrect least-squares regression coefficients in method-comparison analysis. Clinical Chemistry, 25:432-438. [Abstract]
  • Armitage P, Berry G, Matthews JNS (2002) Statistical methods in medical research. 4th ed. Blackwell Science.

See also