Intralaboratory Quality Control of Hematology
Comparison of Two Systems
TERENCE R. J. LAPPIN, PH.D., CHRISTOPHER L. FARRINGTON, PH.D., MAURICE G. NELSON, M.D.
AND JOHN D. MERRETT, PH.D.
Lappin, Terence R. J., Farrington, Christopher L., Nelson,
Maurice G., and Merrett, John D. Intralaboratory quality
control in hematology. Comparison of two systems. Am J Clin
Pathol 72:426-431,1979. Two systems for quality control have
been compared, viz., the whole-blood control preparation
method and the algorithm method using the geometric moving
average X„ and a new estimator Y. The system involving wholeblood controls has the advantage of simplicity of operation, but
the economic cost of commercial preparations is often high.
The algorithm system has the advantage that results of all the
test samples are used in the calculation; to some extent, this
provides a buffer against random variation. The number of
count-outs in a given channel is related to the precision of the
channel, which in turn is a function of the number of
determinations and calculations required for that result. An
error of around 1% is introduced into the result each time a
calculation is performed. A successful quality control scheme
should contain elements of both control preparation and
algorithm methods. (Key words: Algorithm methods; Control
preparations; Geometric moving average; Quality control;
Patient data.)
TO ENSURE THE ACCURACY of hematologic test
results, it is essential to employ quality control procedures to monitor laboratory equipment. Current
methods may be broadly divided into two main
categories. In the first approach, reference or control
preparations of whole blood are used to adjust the
instrument and monitor its performance, usually after
every twentieth sample has been analyzed. Any consistent error or drift may be detected by the operator
either by inspection of the results or by plotting the
cumulative sum of differences between the reference
value and successive observations. 5 In the second approach, the results of analysis of patient samples are
statistically analyzed at various levels of mathematical
sophistication, which range from calculation of the
mean value of batches of results to complex algorithm
methods. Dorsey 6 and Bull and Elashoff2 found that
the data derived from erythrocytic indices of their patient populations showed no significant variation from
Received May 1, 1978; received revised manuscript and accepted for publication July 18, 1978.
Address reprint requests to Dr. Lappin: Department of
Haematology, Royal Victoria Hospital, Belfast, BT 12 6BA,
Northern Ireland.
Department of Haematology, Royal Victoria Hospital,
Belfast, and the Department of Medical Statistics,
Queen's University, Belfast, Northern Ireland
day to day; furthermore, these results were symmetrically distributed and were approximately gaussian
in distribution. A recent advance in this statistical approach to quality control was the introduction of the
algorithm X B by Bull, Elashoff, Heilbron and
Couperus, 3 for monitoring automated analytical instruments using patient erythrocytic indices.
The main purpose of the present investigation was
to compare these two main approaches to quality control. It was hoped that such a comparison would provide information to enable operators of automated
equipment to choose a scheme that would facilitate close
tolerance monitoring of their analytical instruments.
In addition, a further algorithm, Y, which is mathematically closely related to X B and designed to
"amplify" any error caused by drift, was tested in
parallel to X B .
Methods
In order to establish mean values for our hospital
population, 4,535 consecutive routine patient samples
were analyzed on the Coulter® Model S over a 20-day
period. Each morning the Coulter counter was adjusted
by sampling the commercial 4C control preparation
three times, followed immediately by a secondary control, prepared by the method of Carville and Lee, 4
which was then assigned the observed values for the
remainder of the day. Two different batches of secondary standard were used throughout the 20-day test
period, and very little day-to-day variation was found.
When the 4C control preparation was checked against
manual methods a correction for trapped plasma was
applied. Solely for the purpose of this part of the study,
the patient samples were grouped together in batches of
19, according to whether the patients were inpatients,
outpatients, or patients from a maternity hospital.
0002-9173/79/0900/0426 $00.80 © American Society of Clinical Pathologists
426
QUALITY CONTROL IN HEMATOLOGY
Vol. 72 • No. 3
427
Table 1. Hematologic Results from Hospital Patients (Mean Values)
General
Hospital
Outpatients
General
Hospital
Inpatients
Maternity
Hospital
Patients
All Hospital
Patients
Hemoglobin, g/dl
Erythrocyte count, x 106//xl
Hematocrit, %
Mean corpuscular volume (MCV), fl
Mean corpuscular hemoglobin concentration
(MCHC), g/dl
Mean corpuscular hemoglobin (MCH), Pg
13.78
4.83
41.85
86.65
13.15
4.56
40.36
88.46
12.26
4.11
35.88
87.24
13.09
4.52
39.44
87.28
32.94
28.54
32.58
28.82
34.18
29.82
33.20
28.99
No. of patient samples
1,129
2,362
854
4,345
Every twentieth sample tested throughout the day was
either the commercial control or the secondary control.
The rather formidable mathematical expressions for
XB and Y are detailed in the Appendix. Korpman and
Bull9 have outlined the program steps necessary
for X B .
In order to provide data to compare the control
preparation method with the algorithm methods, a
further 1,900 consecutive patient samples were analyzed
by the Coulter S. These patient samples were tested
in the ordinary manner in batches of 18-20, but were
not sorted according to source. For this part of the
study only the 4C control preparation was used, because it was considered more stable than our own secondary control. Therefore, after each batch of patient
samples, the 4C control preparation was analyzed,
and the results were considered "in control" when
they varied by less than 3% from the manufacturer's
asigned mean value. Conversely, they were considered "out of control" when the variation exceeded
3%. When the XB or Y value for a batch of patient
results exceeded a calculated 3% limit, this also was
adjudged to be a loss of control. Loss of control as
defined by either of these criteria is hereafter referred
to as a "count-out." The control preparation and
patient sample data were analyzed and the numbers of
agreements and disagreements recorded.
Results
As can be seen from Table 1, the mean corpuscular
volume (MCV) appeared to be little influenced by the
sample source. However, the mean values for hemoglobin (Hb), erythrocyte count, and hematocrit (Hct)
were lower in the maternity hospital group than in
either of the other two groups. For the mean corpuscular
hemoglobin concentration (MCHC) and mean corpuscular hemoglobin (MCH), the converse was found,
with both these values approximately one unit higher
for the maternity hospital group than for the rest of the
general hospital patients. This last finding is in agreement with that of Holly. 8
Quality Control Trial Based on 1,900 Patient
Samples
Commercial Control Preparation. Table 2 shows the
number of times the instrument was adjudged out of
control when using the commercial control preparation. For this part of the study, 105 batches of samples
were analyzed, but a temporary printing error in the
Coulter S reduced the number of MCH batches avail-
Table 2. The State of Control of the Coulter Model S as Adjudged by Three Different Methods
of Quality Control during Analysis of 1,900 Consecutive Patient Samples
Number of Times 'In Control'
Within Mean ± 3%
Total
Number of
Batches
Channel*
Control
Preparation
Method
105
105
100
105
105
105
MCV
MCHC
MCH
Hb
RBC
Hct
102
80
80
90
95
83
' MCV >= mean corpuscular volume; MCHC = mean corpuscular hemoglobin con-
Number of Times 'Out of Control"
Outside Mean ± 3%
Algorithm
Method
x„
Y
94
98
85
99
99
91
—
—
—
—
—
—
Control
Preparation
Method
3
25
20
15
10
22
centration; MCH = mean corpuscular hemoglobin; Hb
count; Hct = hematocrit.
Algorithm
Method
X„
Y
11
7
15
6
6
9
—
—
—
—
—
—
hemoglobin; RBC
erythrocyte
428
LAPPIN£7"AL.
able for the subsequent statistical analysis to 100. The
three calculated parameters (Hct, MCHC and MCH)
showed a higher number of "count-outs" (outside the
mean ± 3% limits) than the three directly measured
values. Of the six channels, the MCV channel was
clearly the most stable.
Algorithm Data. The XB and Y formulas were applied to the individual patient results in batches of 1820 samples. The figures thus obtained were plotted
on linear graph paper on which the grand mean and
the preset limits (±3%) are indicated for the parameter under consideration.
Table 2 shows the number of times that the analytical
instrument was adjudged out of control by the algorithms
XB and Y. When the instrument was in control, as
adjudged by XB, it was also in control as adjudged
by Y, with only one exception, in the total of 310
batches. On the other hand, the instrument was out
of control on 13 occasions as adjudged by XB when
deemed in control by Y.
This discrepancy between the two algorithms XB
and Y can be explained when the basic differences
between the methods are considered. The algorithm
XB as described by Bull and co-workers3 is essentially
a moving average using the mean of previous batches
to weight the present batch. However, the algorithm
Y was used in a discrete batch mode using the grand
mean instead of the mean of previous batches to
weight each batch of patient results. The effect of this
difference is that XB can indicate a loss of control due
to an accumulation of several batches, whereas Y starts
fresh on each batch and will only indicate whether
an individual batch is out of control. A second difference between the two algorithms is that part of the
equation for Y is raised to the power of 3, which leads
to an ever-increasing Y value for a given deviation
from the mean. The effect is to provide the operator
with a more striking indication of loss of control than is
possible with XB.
Comparison of Control Preparation and Algorithm
Data. The algorithm methods were applied only to
those channels, viz., MCV, MCHC and MCH, which
are known to be relatively stable within the patient
population. The algorithm data were then compared
with the appropriate results obtained from the control
preparations (Table 2).
For the MCHC and MCH channels, loss of control
was indicated more frequently by the control preparation method than by either of the algorithm
methods. In contrast, the MCV was shown to be out of
control more often by the algorithm methods than by
the commercial control method.
A.J.C.P. • September 1979
Percentage Error in Calculations made by the
Coulter S
To investigate the magnitude of the error of the calculations performed by the Coulter S, we analyzed the
data from this trial by performing independently the
calculations for the Hct, MCHC and MCH. It was clear
that each time a calculation is performed by the Coulter
S an error of the order of 1% was introduced into the
result. Therefore, the MCHC determination might be
expected to be less precise than the MCH determination. This trend was confirmed by the results obtained
in an interlaboratory trial involving five separate
Coulter S counters. Our calculations based on the data
of Pinkerton and associates10 gave coefficients of variation of 0.91% for MCV, 0.94% for erythrocyte count,
1.20% for Hb, 1.19% for MCH, 1.22% for Hct, and 1.43%
for MCHC, indicating that the precision of a particular
parameter is in general related to the number of calculations involved.
Relative Costs of the Two Systems
The relative costs of the systems are dependent upon
whether an on-line computing facility is available.
Where such facilities exist for data processing, the
extra cost of running a quality control scheme using
the algorithm approach would be negligible. On the
other hand, where only a desk top calculator is available, it could take one technician VA-2 hours to perform the necessary computations for 300 specimens
on the three channels under consideration. For a
quality control system based on a control preparation
the overall cost is dependent upon several factors. First
is the cost of the preparation, whether commercial or
prepared locally in the laboratory; second, the cost of
analyzing the control samples in terms of technician
time and reagent consumption; third, the cost of any
necessary computations, e.g., a cusum. This last
factor may again be negligible when a laboratory computer is used, but would require 15-20 min for 15 control results (300 specimens, with 1 in 20 a control)
for four channels.
Discussion
Both methods of quality control have inherent advantages and disadvantages. The algorithm methods
generally show fewer "count-outs" than the wholeblood control method, presumably because the large
reservoir of patient results exerted a smoothing effect on the data. As may be seen from Table 1, both
MCHC and MCH showed a higher mean value for
maternity hospital patients than for either the general
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QUALITY CONTROL IN HEMATOLOGY
hospital outpatients or inpatients. It would be expected, therefore, that these two channels would be
susceptible to source weighting. While about half the
MCH count-outs were due to source weighting, only
one of the MCHC count-outs was due to this cause.
There is no apparent reason for this discrepancy. Since
the number of count-outs involved is relatively small,
the problem is easily circumvented by examining any
suspect batches for specimen source. In our experience,
sample source weighting has not been found to be a
serious problem.
A further point worthy of note is that the assay
values supplied by the manufacturers for any batch
of commercial control are not necessarily correct. This
in turn could lead to incorrect setting of the Coulter S.
When an algorithm method is used to monitor the
performance of the instrument, any error in setting
would be reflected in a consistently high or low XB or
Y. During three years' experience of using the algorithm
Y routinely in the laboratory, one such error was detected in the assigned values of one batch of commercial control. In this case the Y values for the MCV,
MCHC, and MCH of each batch of 20 patient samples
were consistently more than 3% above the expected
values. The commercial control preparation was reassayed and new values assigned. When the Coulter S
was reset using these corrected values, subsequent calculation of the Y algorithm for patient sample batches
indicated a return to a satisfactory state of control.
There are two main disadvantages of the whole-blood
control method of quality control. The first is the high
cost of commercial fixed whole-blood preparations, but
this may be partially overcome by the preparation of a
secondary control suspension, albeit with less stability.
The second disadvantage of using a whole-blood control is that a large number of count-outs occur on some
channels when limits of ±3% around the mean are
used. It may be calculated from the data of Pinkerton
and colleagues10 that 2 SD represent a variation of the
order or ±2% or ±3% on all the channels under consideration. A small degree of instrumental drift, say
1.5%, which would not in itself justify resetting, could
by summation with the inherent statistical variation
give an increased number of count-outs.
If it is accepted that the Coulter S results should lie
within ±3% limits, then the essential problem of any
quality control scheme is to detect when these limits
have been reached. The control preparation method
is probably most useful for the directly measured
values. The algorithm methods were directly applied
to the MCV, MCH, and MCHC. However, so long as
one of the primary determinations, e.g., hemoglobin, is
429
checked against a reference method daily, the primary
determinations will remain in control while the
algorithms show the indices to be in control.1
The main advantage of the whole-blood control
method lies in its simplicity. When the error on any
channel is greater than about 5%, it will nearly always
be obvious to the operator from the results of sampling
such a control. Provided that a stable whole blood
suspension is available, and it is sampled regularly
throughout the day, useful statistics about the overall
performance of the instrument may be derived.
The main advantage of the algorithm method is that
the results for all the samples tested are used for the
calculations. In this sense the large amount of patient
sample data available is acting as a buffer against
random variation. In addition to use in daily quality
control, the algorithms have a further advantage of
being able to detect any error in the values assigned
to a commercial control preparation that is used either
for setting or quality control.
The inherent problem with both the algorithm and
control sample methods of quality control is the number of false count-outs. When algorithms only are
used, the problem may be overcome by either rerunning a patient sample previously assayed when the
instrument was known to be in control1 or by using a
whole-blood control sample. When a whole-blood control sample is used for quality control, probably the
simplest method to check a count-out is to reanalyze
the control preparation. In our experience running the
two methods of quality control in parallel prevents any
disruption of the laboratory routine by eliminating the
need to rerun either a patient sample or a control
specimen when a count-out occurs. Thus, the algorithms
provide a cross-check in the event of the control
showing a count-out, and vice versa. With this approach one method can successfully complement the
other to provide a very comprehensive scheme of
quality control for any automated instrument.
During this trial it became increasingly clear that
correct setting of the Coulter S is an essential prerequisite for the production of accurate results. A very
extensive calibration procedure is detailed in Appendix
3 of the Coulter S Operator's Manual; however, this
protocol may prove to be too cumbersome for routine
daily use. Many laboratories may prefer to use a control preparation for setting the instrument. Since no
complete reference material is yet available, the best
substitute for a commercial control preparation may
well be a preparation rigorously analyzed within the
laboratory by the methods suggested by Gilmer and
associates.7 When a control preparation is used for
430
A.J.C.P. • September 1979
LAPPIN£7/AL.
setting the Coulter S, it should be sampled a minimum of three times to allow for the inherent random
variation. Thus, the mean of each parameter can be
calculated and the instrument set accordingly. By use
of a control in this manner the entire operation of
the Coulter S is dependent on the assigned values of
the control. Assuming that the grand mean values of
the algorithm methods were determined over a long
period, covering at least several batches of control
preparation, an independent intralaboratory check for
the instrument is thus available. The algorithms also
serve to ensure not only the within-day accuracy but
also accuracy from day to day and month to month.
On the basis of the results of this trial and our experience over the past three years with the algorithm
methods, we feel that an efficient quality control scheme
for the Coulter S should contain elements of both the
whole-blood control method and an algorithm method.
Where a dedicated computer is available, the calculation of the algorithms in an on-line mode can be
readily accomplished.
Acknowledgment. Mr. A. Lamont, Senior Chief Technician, Department of Haematology, assisted throughout the course of
this work.
References
1. Bull BS: A statistical approach to quality control, Quality Control in Haematology. Symposium of the International-Committee for Standardization in Haematology. Edited by SM
Lewis, JF Coster. London, New York, San Francisco,
Academic Press, 1975, pp 111-121
2. Bull BS, Elashoff RM: The use of patient-derived hematology
data in quality control. Preprint, Proceedings of the San
Diego Biomedical Symposium 13:1-5, 1974
3. Bull BS, Elashoff RM, Heilbron DC, et al: Study of various
estimators for the derivation of quality control procedures
from patient erythrocyte indices. Am J Clin Pathol 61:473—
481, 1974
4. Carville JM, Lee D: Red cell suspension as a working standard.
J Clin Pathol 22:738, 1969
5. Cavill I, Jacobs A: Quality Control in Haematology. Broadsheet
75, Association of Clinical Pathologists, 1973
6. Dorsey D: Quality control in hematology. Am J Clin Pathol
40:457-464, 1963
7. Gilmer PR, Williams LJ, Koepke JA, et al: Calibration methods
for automated hematology instruments. Am J Clin Pathol 68:
(Suppl)185-190, 1977
8. Holly R: The iron and iron-binding capacity of serum and the
erythrocyte protoporphyrin in pregnancy. Obstet Gynecol 2:
119-126, 1953
9. Korpman RA, Bull BS: The implementation of a robust estimator
of the mean for quality control on a programmable calculator or a laboratory computer. Am J Clin Pathol 65:252253, 1976
10. Pinkerton PH, Spence I, Ogilvie JC, et al: An assessment of
the Coulter counter model S. J Clin Pathol 23:68-76, 1970
APPENDIX
Mathematical
Treatment
of
Results
Consider X B , the "robust" geometric moving average described by Bull and Elashoff2:
XB,i = XB,,_, + sgn
( X j ! — X B > 1 _•i ;)
2
V | X J t - XB.,-,1
where XB,,., is the average after i - 1 batches and Xji are
individual patient values, and N is the number of patient
samples considered. To calculate XB.i, a starting value of
X B , i.e., X B 0 must be used.
The rather complex mathematical expression for XB,i is
readily calculated using a desk-top calculator with a program
of about 80 steps. 9
It is possible to simplify equation 1 as follows:
L e t d = Xji — X B ,i_i
i.e., d represents the difference between the individual value
and the mean of the preceding batch for the parameter
under consideration.
Equation 1 can then be simplified to:
XB.i = XB,i-i + sgn
2
2-*VRTJ
-JN2
(2)
We have examined the effect of raising the function
( I d V j d j ) 2 to a higher degree, i.e., ( £ dVTd]) 3 . Instead of
using the mean of the preceding batch as a smoothing
function for X B , as suggested by Bull, 1 we chose to use the
mean value for all patient samples. Thus, for the new esti-
(Xji — XB>i_!)
.
ii
A
V |Xji — XB>1_i I
(1)
N
B,1-1
mator, which we have designated Y,
Y =
m
i
N2
(3)
where d
x „ - XD; XD is the known mean value of the
hospital patient population and N is the number of results
considered. The value of Y has no real meaning in the
physical sense since the higher power in the "cumulative"
function has units of measurement different from X B .
The practical differences between these two algorithms is
best illustrated using the case where the MCV is set one
unit high. The graph for X B rises by one unit and remains
at that level, whereas the value of Y rises with each succeeding sample result (Fig. 1). The X B value may be used to
recalibrate the instrument, whereas that for Y cannot. However, in practice, it is very difficult to reset the potentiometers on the Coulter S by a margin in order of 1%, and
in practice the instrument would be reset only when the
deviation reached 3%. 3
While Y does not allow a decision to be made with respect to the amount of recalibration required, simply by
Vol. 72 • No. 3
QUALITY CONTROL IN HEMATOLOGY
431
20
14
3
>
>
o
CD
IX
15
12
O Y
10 •
01
•
X
B
o
10 •
2
(0
>
00
•
\20
X,
8 •
IX
I
o
o
4 '
N u m b e r of s a m p l e s w i t h r e s u l t s
one u n i t above the mean
FIG. 1. The relationship between the number of samples with
results one unit above the mean and the XB and Y values.
inspection of the plot of the results, it is possible to plot a
graph of Y against percentage deviation (Fig. 2) for 20 sample
results, i.e., a Y20 value. As a linear relationship exists
between Y and the number of patient specimens tested, it is
considered valid to calculate a Y20 when fewer than 20
specimens are analyzed, although for practical purposes an
arbitrary minimum of 18 has been set.
One striking feature of Figure 2 is the rapidly increasing
Y value with increasing deviation of the results from the
mean, resulting in an "amplification" of the error, leading
to easier recognition of a loss of control by the laboratory
staff.
0
1 2
3
4
5
6
D e v i a t i o n from the mean value
FIG. 2. The relationship between the deviation from the mean
value and the Y and XB values.
The use of the patient grand mean for all Y computations
means that Y is not a moving average, yet it still retains
the "robust" element of X B . In practice it means that significant changes (>3%) in the average of a batch of 20 patient
samples will not affect succeeding batches. This means that
a batch of samples with predominantly abnormal results will
not influence subsequent batches.