Statistical evaluation of quality control

Proper interpretation of quality control data requires presentation in a format that makes systematic bias readily apparent. Based on the work of Shewhart, Levey and Jennings, Westgard and co-workers proposed in 1981, an algorithm for monitoring quality control in clinical laboratories (Westgard et al., 1981). 'Westgard's Rules' provide guidance for determining when control values are acceptable or, alternatively, when control measurements reflect changes in the performance of the analytical method (Westgard and Barry, 1986; Burtis and Ashwood, 2001).

In a Levey-Jennings control chart, the x-axis represents time or number of analytical runs and the y-axis represents the control results (Figure 1.1a). Control values are plotted on the Levey-Jennings chart, and should fall within a statistically predicted range, based on a Gaussian distribution. The acceptable range of values is typically indicated by lines on the y-axis representing the upper and lower limits for control results (commonly ±2 standard deviations or defined percentages from the mean control value). Westgard described a multi-rule procedure using the Levey-Jennings chart to detect deviations from Gaussian behavior that reflect analytical bias (Burtis and Ashwood, 2001).

Another way to present control data is the cumulative sum control chart. In this method, the x-axis is either time or number of control observations and the y-axis is the cumulative sum (cusum), or the difference between the measured control value and the predicted mean

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Figure 1.1 Examples of (a) Levey-Jennings and (b) cumulative sum (cusum) control charts using inter-assay quality control data from an alprazolam GC-MS assay. Since the cusum chart persents the cumulative sum of deviations from the mean, it is more sensitive to small biases that develop over time, whereas Levey-Jennings charts are most useful for detecting changes in the precision of the assay

Figure 1.1 Examples of (a) Levey-Jennings and (b) cumulative sum (cusum) control charts using inter-assay quality control data from an alprazolam GC-MS assay. Since the cusum chart persents the cumulative sum of deviations from the mean, it is more sensitive to small biases that develop over time, whereas Levey-Jennings charts are most useful for detecting changes in the precision of the assay concentration of the control material (Figure 1.1b). The cusum is calculated by adding this difference to the differences from previous control observations. Random errors should produce cusum values that cross the zero line (mean value) multiple times. However, if there are other sources of error, then the cusum will deviate from the mean value in one or the other direction. Other quality control charts, such as mean, standard deviation and range charts, are used in industry, but are not common in clinical chemistry and toxicology (Westgard and Barry, 1986).

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