Bull’s Averages

Commercial controls tell only part of a quality story. While they detect analytical drift and estimate precision, they are often run when an instrument is in a pristine, “ready” state (after maintenance, before sample runs, etc.). And because they are not fresh whole blood samples, they don’t react quite the same as your daily workload.

Many laboratories also run patient sample controls as a cost-effective way to check instrument performance throughout the day. A previously analyzed sample is run on the same or different analyzer, or in a different sampling mode. But tracking a moving average of red blood cell indices (MCV, MCH, MCHC) of all samples is another approach in hematology. One algorithm, proposed by Dr. Brian Bull of Loma Linda University of California in 1974, does just that.

Red Cell Indices

Red blood cells are biconcave disks able to squeeze, bend and twist through blood vessels. Mature RBCs lack nuclei, mitochondria and other organelles but are packed with hemoglobin, a complex protein containing iron. Hemoglobin picks up oxygen across diffuse membranes in lung sacs called alveoli.1

RBC survival rates range from 15 days (abnormal) to 2-3 weeks (donor transfusion) to normal life span (120 days).2 A four-month life span means a stable population of cells in the blood stream. Thus, physiological ratios (e.g., the amount of hemoglobin in a red cell) do not vary significantly in patients without anemia or hemoglobin variants. The most commonly measured ratios are RBC indices.

RBC indices classify anemias by how red cells are structurally altered. Too little hemoglobin, for example, results in smaller than normal cells (decreased MCV, or microcytic appearance). Microcytic anemias can be caused by iron deficiency, thallasemia, chronic infection, etc. RBC indices are an important part of a differential diagnosis.3

On the bench, they can identify analytical error. RBC indices are described in Table 1, along with suggested action if change is observed, in Table 2. A change in MCH alone, for example, suggests a problem in hemoglobin measurement.

RBC indices are not the only ratios in use to differentiate anemias (see Table 3).

Bull’s Moving Averages

“Smoothing” is a statistical technique used by financial forecasters to remove short-term market fluctuations.4 In the laboratory, fluctuations are abnormal patient results (anemia, polycythemia, microcytosis, macrocytosis, etc.). Smoothing algorithms include truncation (arbitrarily discarding low or high values), logarithmic transformation, reducing the weight of a small sample mean by a multiplier, or a combination of these. Software such as Microsoft Excel can perform smoothing with added functions (Excel’s “smoothed line” option creates a Bezier curve for aesthetic purposes).5 6

Bull designed a weighted moving average for the Coulter Model S, starting with expected population normals (90 fL for MCV, etc.). His smoothing algorithm, designed to track normal patients, is described by Dr. Roy Barnett in his book Clinical Laboratory Statistics.7

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Bull’s algorithm manipulates 20 consecutive patient samples into positive and negative values around a running mean designated XB (written with a bar over the X and pronounced “X bar B”). The square roots of these differences is averaged, preserving their signs, and added to XB. Values are plotted on a chart as a timed series (called a power function). Unless a batch of 20 samples contains a significant number of abnormals (e.g. a chemotherapy clinic) deviation represents analytical error.

Levy et al proposed standardized multirules in 1986 using a computer approach of Cembrowski and Westgard to reject a batch: the Bull’s mean of one batch is outside 3% OR the average of three consecutive Bull’s means is outside 2% limits. This allows significant shifts to be detected sooner.8

It also links analytical performance to a biological standard: the physiology of human red blood cells. If your daily runs are less than 50 samples, batches of 15 can be used; check with your accrediting agency.

Bull or Bear

How does Bull’s algorithm stack up? Early computer simulation demonstrated its effectiveness in detecting significant population shifts with greater sensitivity depending on the size of the batch included in the algorithm.9 A comparison of multiple control samples to a single XB using a multirule approach showed the two to be equally sensitive quality indicators.10

However, instrument error affecting several values simultaneously can effectively null the algorithm. This is demonstrated in a 1991 study using a Technicon H6000 analyzer, in which RBC and hemoglobin drift while MCV is unaffected, canceling out the effect on the MCH and MCHC indices. In this instance, Bull’s algorithm failed to detect an out of control situation 38%, 15%, and 13% (MCV, MCH, MCHC, respectively) of the time compared to 2 SD limits on commercial controls.11

But in another study on a Coulter STKS seasonal shifts in Bull’s algorithm were observed depending on ambient reagent temperature. Samples were reanalyzed with reagents at 15ø, room temperature, and 30ø C. A change of 5øC was associated with a 1% drift in MCH and MCHC values; a small complimentary shift in RBC caused the moving average to exceed control limits.12

One article cautions that since the current batch is compared to a previous batch, it may take a while for the power function graph to “rebound” back to normal after corrective action.13

Future Trends

Microcomputer technology has proliferated Bull’s algorithm (e.g. indices or all CBC parameters) on Sysmex14, Beckman-Coulter15 and Cell-Dyn16, to cite three. Applying it to labile white blood cell differential measurement adds a significant layer of patient quality control.

At least one author suggests that a moving averages approach, while traditionally used in hematology, could be efficacious in chemistry. Patient controls obviate matrix effects and reduce cost; tracking calculated parameters (anion gap, etc.) could suggest differential troubleshooting as seen in hematology. The author cautions that control limits need to be established.17 But the possibility is intriguing.

The use of patient data moving averages, including Bull’s algorithm, is a useful part of a total quality system, recognized in literature and regulated by accrediting agencies. It can help you save cost on control materials, troubleshoot real time, repeat samples before they degrade, and provide better patient care.

Scott Warner is lab manager at Penobscot Valley Hospital in Lincoln, ME.

See References on page 3…


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12. Cembrowski GS et al. Strict Use of Moving Averages for Quality Control of Multichannel Hematology Analyzers Requires Optimal Control of Ambient Temperature (abstract). Available at: http://cardenjennings.metapress.com/app/home/contribution.asp?referrer=parent&backto=issue,4,10;journal,32,42;linkingpublicationresults,1:104952,1. Last accessed: 11/6/10.

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