Linear Method comparison
Linear method comparison compares two analytical methods, a test method against a reference/comparative method, to determine analytical accuracy. The procedure uses ordinary leastsquares linear regression so does not account for error in the reference/comparative method. This limitation is not a concern when errors in the reference method are very small or are minimised by replicate measurements.
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:
 Excel 2007:
Select any cell in the range containing the dataset to analyse, then click Comparison on the Analyseit tab, then click Linear fit.
Excel 97, 2000, 2002 & 2003:
Select any cell in the range containing the dataset to analyse, then click Analyse on the Analyseit toolbar, click Method comparison then click Linear fit.
 Click Reference/Comparative method and Test method and select the methods or individual replicates to compare.
 Click Measured on and select Same scale if methods are measured on the same scale / units, otherwise select Differences scales.
 Click Errors in Test method and select whether errors in the test method exhibit Constant SD or Constant CV (weighted linear regression will be used).
 If the methods contains replicates click Use replicates and select:
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. 
 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, with the correlation coefficient r to test if the range is adequate (adequate when r > 0.975) for ordinary linear regression.
S_{yx} is a measure of the dispersion of observations around the fitted linear line. If the test method was observed in singlicate S_{yx} gives an estimate of the precision of the test method. When the test method is measured in replicate and the mean of the replicates used, S_{yx} 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 pvalue 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.
(click to enlarge)
Beneath the scatter plot is a residual plot (see below) of the differences between the test method and the linear fit. The residuals are standardized (residual / S_{yx}) so any observations outside ±4 indicate possible outliers.
(click to enlarge)
Determining bias at specific decision levels
Bias can be determined for up to three decision levels.
To determine bias at specific decision levels:
 If the Linear method comparison dialog box is not visible click Edit on the Analyseit tab/toolbar.
 Enter analyte concentrations for up to three Decision levels.
 Click OK.
An additional table appears above the scatter plot showing the bias at each decision level, with confidence intervals.
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:
 If the Linear method comparison dialog box is not visible click Edit on the Analyseit tab/toolbar.
 Click Compare against and select Bias specification.
 Enter Allowable bias as an absolute value, as a percentage of analyte concentration, or enter both values for a combination.
 Tick with Allowable Error bands to show the bias specification on the scatter plot.
 Click OK.
If decision levels are specified the bias goal at each decision level is calculated and a hypothesis test is shown to test if the observed bias is outside goal bias. If the pvalue is statistically significant the observed bias is outside the goal.
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.
(click to enlarge)
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:
 If the Linear method comparison dialog box is not visible click Edit on the Analyseit tab/toolbar.
 Click Compare against and select TEa , %SE specification.
 Enter TEa (total allowable error) as an absolute value, as a percentage of analyte concentration, or enter both values for a combination.
 Enter % for Systematic error, that is the percentage of the TEa to allow bias to vary within.
 Tick with Allowable Error bands checkbox to show the bias specification on the scatter plot.
 Click OK.
If decision levels are specified the bias goal at each decision level is calculated and a hypothesis test is shown to test if the observed bias is outside goal bias. If the pvalue is statistically significant the observed bias is outside the goal.
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.
Comparing against a performance claim
Bias can be compared against a manufacturer's performance claim to demonstrate a method is operating correctly.
To compare bias against a manufacturers claim:
 If the Linear method comparison dialog box is not visible click Edit on the Analyseit tab/toolbar.
 Click Compare against and select Performance claim.
 Enter up to 3 Decision levels and their corresponding Claimed bias. The claimed bias must be entered as an absolute value.
 Click OK.
Bias and claimed bias at each decision level is shown, with a confidence interval and a hypothesis test to test if the observed bias is different from the claimed bias. If the pvalue is statistically significant the observed bias is significantly different from the claimed bias.
References to further reading
 EP9A2 Method Comparison and Bias Estimation Using Patient Samples; Approved Guideline (2nd edition)
CLSI, ISBN 1562384724 2002;
 Evaluation of Regression Procedures for Method Comparison Studies
Kristian Linnet, Clin.Chem. Vol. 39 No. 3 1993; 424432
 Validity of linear regression in method comparison studies: is it limited by the statistical model or the quality of the analytical input data?
Dietmar Stöckl, Katy Dewitte, Linda M. Thienpont, Clin Chem. Vol 44 No. 11 1998; 23402346
 Points of Care in Using Statistics in Method Comparison Studies
Editorial, Clin Chem. Vol 44, No. 11 1998; 22402242
 Use and Interpretation of Common Statistical Tests in MethodComparison Studies
James O. Westgard, Marian R. Hunt, Clin Chem. Vol 19 No.1 1973; 4957
 Necessary Sample Size for Method Comparison Studies Based on Regression Analysis
Kristian Linnet, Clin Chem. Vol 45 No. 6 1999; 882894
(click to enlarge)