Vol. 14 •Issue 4 • Page 50
Unraveling the Complexities of QC Part 2

A discussion based on means and peer group data of common questions regarding quality control.

Editor’s Note:

Part 1 of this article (published in the March issue) discussed how many data points are needed to establish a mean for a new lot of control and how to establish a standard deviation (SD) for a new lot of control. Here, we examine how many laboratory means are needed for a group comparison.

From the previous discussion (where we suggested that eight replicates of the new control could be used for the mean of the new control), it should be apparent that the number of lab means needed to find a useful mean for interlaboratory comparisons is probably fewer than expected. In looking for an answer to the question of an actual number, we need to keep in mind one of the prime tenets of statistics—the central limit theorem. This theorem simply says that the distribution of means (98 – 102) is narrower than the distribution of the raw data making up the means (88 – 108, Fig. 1). You also see that the distribution of the five data sets from the five laboratories follows the bell or Gaussian curve (Fig 2.).

It is generally assumed that data on control material run on a stable instrument using a single lot of reagent and calibrator without any major maintenance are distributed in this manner. Fig. 1 illustrates this for five means and their ranges from the CK data where each of the laboratories submitted 30 data points. From these data the low value is 88 and the high value is 108. The mean of the five laboratories is 99 and the 98 percent range is 95 – 103, a smaller range than the range of the raw data as suggested in Fig.2. It can also be shown that the t-value for these means is not different from the group mean.

A True Mean

We will use the same two approaches (discussed in Part 1–looking at raw data from a number of labs for a number of tests and using the random number generating capacity of Microsoft Excel) to examine the question of how many laboratory means are needed for a good estimate of the true mean (without the entire data set we can only estimate any statistic such as the mean, SD or range).

Using a data set from a group of laboratories reporting CK on a control (Fig. 3), I have first presented all the unsorted data, then in the next column calculated the cumulative means as we did for the data when establishing the mean for the control in a lab in Part 1. From the data in the cumulative mean column you note that at an n of 5 the mean is about 2 percent different from the mean after 60 points. This difference is not statistically significant, nor is it beyond what might be seen from the precision of the data for any of the laboratories, nor what might occur after changing reagents or recalibration.

Fig. 4a uses data from an interlaboratory survey where the imprecision was somewhat higher as well as with the data from the Excel tool box. Fig. 4b depicts the individual means of participating laboratories, the group cumulative mean and percentage difference between cumulative mean of the participants and the mean after 30 laboratories were included. Again, the t-test did not detect a significant difference between the cumulative mean after five laboratories were included and the entire set of 30 was used.

When assessing interlaboratory data from a QC program one of the main goals is to pass surveys such as those from CAP by keeping the QC data within the CAP or CLIA limits. Thus, using the new mean and new SD for the new lot of control, only the group mean and CLIA limits as reported in some quality assurance programs are necessary to begin setting QC limits. The group SD is not a necessary component.

Conclusions

From these studies, I have concluded that:

1. to find a working mean for a new lot of control, 5 – 8 points are all that are needed;

2. the working mean can be updated as more data are accumulated. Of course, one’s own mean will change with recalibration and new lots of reagents, making any mean a “working mean;”

3. five laboratory means from a group are all that are needed for a comparison of one laboratory to another in an interlaboratory comparison;

4. to establish an SD for a new lot of control, use cumulative data from the previous lot of control and the formula:

SD (new) = CV (cumulative) * Mean (new from n = 8)

This provides a better estimation of the new SD than 20 or 30 data points.

David Plaut is a clinical chemist and statistician in Plano, TX.