Vol. 14 •Issue 3 • Page 66
Unraveling the Complexities of QC, Part 1

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

Editor’s note:

This is the first in a two-part series. Part 2 will discuss how many laboratory means are needed for a peer comparison.

Quality control (QC) can be a perplexing issue. There are common and related questions frequently asked:

1. How many data points are needed to establish a mean for a new lot of control?

2. Once I have a mean, how do I establish a standard deviation (SD)?

Establishing a Mean for a New Lot of Control

My first serious study of the first question began about 30 years ago when I was working with a short-dated, whole blood-based blood gas control. The customary answer of 20-30 points made it expensive and impractical—the product lasted only 60 days, and one-third to one-half of the life of the material would be depleted before the mean was established and ready to use for quality monitoring.

I worked with laboratory professionals in Miami to examine data from several lots of three levels of blood gas control using a form similar to that shown in Fig. 1. The data in the Cumulative Mean column indicates that by and large the mean for these data becomes stable after some eight data points. This study was published for the American Association for Respiratory Therapy as an abstract for the national meeting in 1978.1

Two Aspects, Two Approaches

There are two aspects of this study that the group felt were important enough to explore in more detail. First, we knew that blood gas instruments, using no true reagents or reactions in the usual sense and calibrated as they were with primary standards, were more precise than most other instruments in the laboratory. Secondly, from the data on the three levels of control for a number of parameters (including oxygen, carbon dioxide and pH) there seemed little, if any, correlation between the SD, coefficient of variation (CV) and the number of replicates to establish the mean.

To pursue how many points are needed to establish a mean, for the new lot of control, we went in two directions. For the first approach, we simply looked at data from chemistry tests, including the routine chemistries such as Glucose, BUN, AST etc., immunoassays such as TSH, as well as protein and LDH isoenzyme electrophoresis. We found that as a rule, eight replicates (often fewer) were all that were needed to obtain a mean. These studies were extended to include other hospitals’ data. Representative data appear in Fig. 2. Our second approach to establishing a new mean was to use the software program, Minitab, which could generate considerable quantities of data quite similar to laboratory data—data that fit a Gaussian (bell-shaped) curve (Fig. 3). Using Minitab, we asked for as many data points that were normally distributed (bell-shaped) as we wished, with whatever mean and SD we wanted, and looked at the cumulative means for the data sets. These data sets were generated hundreds of times with various means and SDs; all returned to the same conclusion that eight is enough.

Your Own Calculations

If you wish to explore these ideas, take your own QC data for the tests you wish to study and set up an Excel sheet (as in Figs. 1 and 2). The formulas are given in the appendix. Enter the raw data in the data point column and the formulas. Should you conclude that eight (or seven or nine) points are sufficient, save the data in case you want to demonstrate it to others (e.g., laboratory inspector). It is easy to generate quite a few means from n = 8 using a set of 30 points.

The second approach is to use a tool available in Microsoft Excel, the random number generator. This algorithm will provide you with as many data points with a given mean and SD. Since these are random (Gaussian) numbers the mean and SD returned will differ slightly from the one you type in.

Establishing an SD

When the mean for the new lot of control has been established using eight replicates, the next task is to establish an SD to set QC limits. Again, the traditional number is 20-30 replicates of the control. In the discussion above we developed the idea that a mean for the new lot of the control can be set with as few as eight data points. Few of us would suggest using eight replicates of any measurement in the clinical laboratory to establish a measurement of the inherent variation (random error) in an analytical system. The list of sources of random error in such measurements include calibration, new lots of reagents and calibrators, maintenance to the instrument, line voltage fluctuations (that would create both temperature fluctuations and lamp fluctuations), and variations between operators, among others. Given this, one has to ask whether even as many as 30 points are sufficient to include all the sources of random error.

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

References

1. Herring K, Matthews H, Pulwer E. Paper presented at the American Association for Respiratory Therapy 1978.

2. Surkin K, Hershberger D. Clinical Chemistry 1997;43(6):S140-141.