Regression analysis Deming

Deming Regression Analysis and Ordinary Least-Squares Regression Analysis (OLR) (Constant SDs)... 

Figure 14-22 In OLR, the sum of squared deviations from the line is minimized in the vertical direction. In Deming regression analysis, the sum of squared deviations is minimized at an angle to the line depending on the random error ratio. Here the symmetric case is displayed with orthogonal deviations. (From Linnet K.The performance of Deming regression analysis in case of a misspecified analytical error ratio. Clin Cbem 1998 44 1024-1031 [Figure I]).

To compute the slope in Deming regression analysis, the ratio between the standard deviations of the random errors of xl and x2 is necessary, i.e.,... 

For the OLR procedure, given that the assumptions are fulfilled (which they almost never are), these SEs are exact. For the Deming procedure, they apply approximately. More correct formulas have been given or they can be conveniently derived by a computerized method (see later in this chapter). For both OLR and Deming regression analysis, the correct interpretation of SDji is important, but quite often it is misinterpreted (see the next section). 

The estimated slope and intercept provide an estimate of the systematic difference or error between two methods over the analytical measurement range. Additionally an estimate of the random error is important. As mentioned above, it is commonplace to consider the dispersion around the line in the vertical direction, which is quantified as SD, ( (here denoted SD21). SD21 has originally been introduced in the context of OLR, but it may as well be considered in relation to Deming regression analysis. 

Figure 14-30 An example of application of weighted Deming regression analysis.The solid line is the estimated regression line, and the dotted line is the line of identity.The estimated 95% confidence bands obtained by the jackknife approach are the curved dashed lines.

TABLE 14-12 Results of Weighted Deming Regression Analysis for the Comparison of Drug Assays Example, N - 65 (xl,x2) Measurements... 

Deming regression analysis given proportional SDs (i.e., constant coefficients of variation) CV. - CV. 

Deming regression analysis is performed with a significance level (Type I error) of 5% and a statistical power of 90%. To get the necessary sample size, we consult Table 14-13 and look under a range ratio of 2 and a standardized slope deviation of 3 and find the sample size N = 70. 

Table 14-14 covers application of weighted Deming regression analysis in situations with proportional SDs (constant CVs) and includes intervals with range ratios extending from 2 to 100. The standardized slope deviation is here ... 

Sample size for weighted Deming regression analysis Equivalent sample size for unweighted Deming regression analysis for slope testing... 

Linnet K. The performance of Deming regression analysis in case of a misspecified analytical error ratio. Clin Chem 1998 44 1024-31. 

However, a simple linear relationship does not usually exist. A clear example is the optimization of the pH in RPLC. The window diagram approach was applied to this problem by Deming et al. [550,551,552]. They measured the retention of each solute at a series of pH values (9 in ref. [550], 4 in refs. [551,552]) and fitted the experiments to eqn.(3.70). This is a three-parameter equation and hence a minimum of three experiments is required for it to be applied as a description of the retention surface. If more data points are available, the equation can be fitted to the data by regression analysis. 

Figure 14-29 Distances from data points to the line in weighted Deming regression assuming proportional random errors in xl and x2.The symmetric case is illustrated with equal random errors and a slope of unity yielding orthogonal projections onto the line. (From Linnet K. Necessary sample size for method comparison studies based on regression analysis. Clin Chem 1999 45 882-94.)...

Example of Application of Regression Analysis (Weighted Deming Analysis)... 

Most published method evaluations fail to apply regression analysis in a rigorous fashion. This section considers both the use of OLR instead of Deming regression and the use of unweighted analysis in the setting of proportional random errors. 

According to current practice in method comparison studies, it is usual to apply unweighted forms of regression analysis (i.e., OLR and the Deming procedure), even though the SDs vary with the measured concentration, as occurs... 

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