COAGULATION AND TRANSFUSION MEDICINE
Original Article
Estimation of the Lower Limits of Manual
and Automated Platelet Counting
EDGAR HANSELER, P H D , 1 JORG FEHR, M D , 2 A N D HERBERT KELLER, M D , P H D 1
Most evaluators of automated or manual methods for platelet counting
focus on characteristics such as imprecision, linearity, and carry over.
The limits of the analytical procedure are usually not assessed. The
limits of the different techniques are neither discussed in the literature
nor do manufacturers of analytical systems supply these data.
A new procedure is presented to assess the performance of the manual as well as the automated platelet count. This procedure allows, with
defined statistical confidence (eg, 95%), the determination of (1) the
limit of platelet detection (LD) at which signals of platelets can be discriminated from the system noise; (2) the lower limit of quantification
(LLQ), at which a certain imprecision is not surpassed; and (3) the
power of definition (PD) that defines the number of values that can
be discriminated in a certain interval. For each value, the PD allows
calculation of the two adjacent (lower and higher) values that are significantly (P 2:0.95) different.
For the manual count, LD was found to be 1.6 X 109 plt/L and the
LLQ 6.9 X 109 plt/L. For the automated count with the Technicon H1,
LD was 4.3 X 10' plt/L and LLQ 13.8 X 10' plt/L (CVmn, = 15%).
The PD in the range 20 to 100 X 10' plt/L is 8 for the automated and
7 for the manual count. (Key words: Platelet count; Measuring interval;
Limit of detection; Lower limit of quantification; Power of definition)
Am J Clin Pathol 1996; 105:782-787.
The determination of the number of leukocytes, erythrocytes, and platelets in blood is of great importance in
many diagnostic processes. Two analytical procedures
are commonly used for blood cell counting: the manual
and the automated count. Manual methods for cell
counting are known to be time consuming and tedious.1
It is common knowledge that manual cell counting is
burdened with high imprecision.2 Nevertheless, these
techniques are still used as routine methods in the laboratories of many practitioners or if low or high cell count
ranges or atypical cells are present also in specialized hematology laboratories.
The introduction of electronic cell counters permit a
more precise enumeration of erythrocytes, leukocytes,
and platelets and has reduced these drawbacks significantly. Coefficients of variation (CV) <3% can be obtained.3
The precision and accuracy of electronic cell counters
is better compared to manual counting mainly because a
much higher number of cells is counted.2 This fact might
lead to the assumption that this superior performance
can be observed over the entire measuring range. Few
authors have stressed the fact that this assumption is
valid only for a limited measuring interval.4 In the past,
neither the LD nor the LLQ have been determined.
When describing the analytical performance of an instrument, manufacturers of cell counters and evaluators
of new instruments pay much attention to international
committee recommendations.5 These include issues
such as linearity, imprecision, and carry over,67 but only
a few authors ask what the limits of cell counting are at
various platelet count levels.6,8 At low platelet numbers,
because fewer cells are counted, observed CVs are expected to be increased and even the use of automated
cell counters may be inappropriate.5 For very high cell
numbers, it is mainly the inaccuracy of the cell count
that has to be critically evaluated.4
It is common practice to use manual counting
methods if platelet numbers are low. The decision to use
manual rather than electronic counting is based more on
subjective impressions than on a solid statistical basis. In
1986, Hackney and coworkers9 pointed out that there is
a need for improvement in instrument and kit evaluations and stated that in contrast to clinical chemistry
evaluations, evaluations of quantitative hematology and
coagulation methods are generally lessrigorous.This less
rigorous approach is unsatisfying because clinical decisions with significant clinical consequences are also
based on eg, very low platelet counts, such as in patients
undergoing chemotherapy.
Our goal was to develop a statistically well-defined
procedure that allows us to describe the performance of
From the 'Instillite of Clinical Chemistry, and 2Department of Internal Medicine, Hematology, University Hospital, Ziirich, Switzerland.
Manuscript received March 20, 1995; revision accepted November
29, 1995.
Address reprint requests to Dr. E. Hanseler: Institute of Clinical
Chemistry, University Hospital Zurich, Gloriastr. 29, 8091 Zurich,
Switzerland.
782
HANSELER, FEHR, AND KELLER
783
Determination of the U rits of Platelet Counting
the manual as well as the automated platelet count methods. This procedure describes (1) the lower limit of detection (LD), the lowest signal or number of platelets that
can be discriminated from the background noise with a
defined probability (eg, 95%); (2) the lower limit of quantification (LLQ), the limit for which a defined maximal
imprecision (eg, 15%) will not be surpassed; and (3) the
power of definition (PD) that defines the number of values that can be differentiated in a certain interval with a
predefined statistical confidence (eg, 95%). The PD also
allows determination of the next adjacent value (lower
or higher) that can be discriminated from the actual
value with a defined statistical confidence. Thus, the
mathematical procedure presented here allows us to determine, in each interval of the measuring range, if the
difference of two consecutive platelet counts represents a
significant change.
To demonstrate the validity and usefulness of this procedure the platelet count is an appropriate parameter to
investigate because there is a large dynamic range of the
platelet count for patients. In addition, low platelet
counts are of special diagnostic and therapeutic importance in thrombocytopenic patients with leukemia or on
cytotoxic therapy and in the management of many other
diseases.
MATERIALS AND METHODS
Platelet counts of 120 patient samples (K 3 EDTA
blood) selected for platelet counts ^100 X 109/L have
been determined in triplicate using a Technicon H1 flow
cytometer (Bayer/Technicon, Tarrytown, NY). In another 120 patient samples, also selected for platelet
counts s, 100 X 109/L, platelets have been counted manually and independently in a Neubauer improved counting chamber by three technicians, (each technician sampled the specimen separately). Two different batches of
samples had to be used because there was not enough
sample material available to perform a triplicate manual
as well as a triplicate automated count.
The mathematic procedure to determine the variance
function has been described in detail in previous publications.10"13 Using the computer program by Sadler and
Smith, 14 the variance was calculated for each triplicate
measurement and the variance profile was constructed
out of the individual variances. The parameters of the
variance function were defined by an iterative procedure.
The general formula of the variance function is s2(N) =
(j3, + j82 X N) J , where N is the number of platelets and 0,,
ft, and J are the parameters.
The determination of the critical limit (LC), LD, and
PD were performed as described earlier.10 By setting the
platelet number to "zero" in the variance function, the
variance or standard deviation of a blank sample can be
calculated [s20 = G8|)J]. This standard deviation was used
to construct a normal distribution representing the random error of the blank (ie, the background noise of the
instrumental system). The adjacent normal distribution,
overlapping the first by a defined amount (eg, 5%) was
constructed using an iterative procedure (Newton Raphson) (Fig. I).' 5 The projection of the intersection of the
two normal distributions to the x-axis represents the LC.
At this point, the odds that a measuring signal is derived
from platelets or from system noise equals 1:1. The peak
of the second normal distribution represents the LD,
which means that a certain number of platelets is present
with a defined probability (eg, 95%).
The PD was determined by constructing adjacent normal distributions overlapping the previous by a defined
amount (eg, 5%).
The LLQ was determined as the platelet number
where a predefined CV line intersects with the upper
limit of the confidence interval in the precision profile
(CV versus platelet number).
RESULTS
Manual Counting
The variance function for the manual counts was assessed as:
s2(N) = (0.207 + 0.094 X N) 1 4 2 8
where N represents the platelet count X 109/L. The normal distribution of the random error of the blank and
the adjacent normal distribution are shown in Figure 1 A.
The LC was 0.7 X 109 plt/L, and the LD 1.6 X 109 plt/L.
From the variance function the precision profile for the
range <100 X 109 plt/L, shown in Figure 2, could be derived.
Accepting a CV of 15%, the LLQ was determined to
be 6.9 X 109 plt/L for the manual count (Fig. 2). The
lower limit of quantification for a maximal CV of 10% is
17.6 X 109 plt/L.
The power of definition or "sensitivity profile" in the
interval 0 to 100 X 109 plt/L for the manual count is
shown in Figure 3A. This profile illustrates the limited
number of values that can be differentiated from each
other in a certain interval. In the range < 100 X 109 plt/L
the PD for the manual count was 13.
Two examples are given in Figure 3A to illustrate the
meaning of the PD. Assuming a value (A 1) of 11.0 X 109
plt/L, the first lower value (Bl) that could be differentiated from A1 with P ;>0.95 was 6.9 X 109 plt/L. The first
higher value (C1) that could be differentiated from A1
with P >0.95 was 16.0 X 109 plt/L. The corresponding
values for the second example were: A2: 65.0 X 109 pit/
L, B2:51.5X 109 plt/L, and C2: 80.9 X 109 plt/L.
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COAGULATION AND TRANSFUSION MEDICINE
Original Article
784
FIG. 1. Normal distribution of the random error of the blank and the adjacent normal distribution, overlapping
the first normal distribution by 5%. A,
manual counting. B, automated counting (H1 flow cytometer) LC = critical
limit, LD = limit of detection.
Platelets |107L|
Platelets 1107L|
Automated Counting
The variance function for the automated platelet
counts was determined to be:
s2(N) = (0.997 + 0.098 X N)' 087
The normal distribution of the random error of the
blank of an automatically counted sample is shown in
Figure IB. The LC was 2.0 X 109 plt/L and LD 4.3
X 109 plt/L. The precision profile for the automated
counting is shown in Figure 2 for the range < 100 X
109 plt/L. The variance function for the automated
and the manual count cross at 26 X 109 plt/L and
their respective confidence intervals intersect at 30 X
109 plt/L. This means that below this intersection, the
reliability of the manual method is higher (Fig. 2). Assuming a maximal (acceptable) CV of 15% the LLQ
was determined to be 13.8 X 109 plt/L for the automated count (Fig. 2). For a maximal CV of 10%, LLQ
was21.7X 109 plt/L.
In the range 0 to 100 X 109 plt/L, the PD for the automated count was 12. In Figure 3B, two examples are
given to illustrate the PD for the automated count. The
first lower value (Bl) that could be differentiated from
Al (9.5 X 109 plt/L) with P >0.95 was 4.3 X 109 plt/L.
The first higher value (CI) different from Al with P
>0.95 was 15.5 X 109 plt/L. The corresponding numbers
for the second example were: A2: 71.0 X 109 plt/L, B2:
59.4 X 109 plt/L, and C2: 83.6 X 109 plt/L.
DISCUSSION
The significantly improved precision of modern automated cell counters might lead to the misunderstanding
A.J.C.P.'June 1996
HANSELER, FEHR, AND KELLER
Determination of the Limits of Platelet Counting
manual
automated
20
9 3 _»
40
60
Platelets |x 109/L|
FIG. 2. Precision profiles and confidence intervals for the range < 100 X
10' plt/L for the manual as well as for the automated counting. The lower
limit of quantification (LLQ) was set where a CV line (10%, 15%, respectively) intersects with the upper limit of the confidence interval, m | 5 : manual count, CVmax = 15%; LLQ = 6.9; a,5: automated count, CVmax =
15%; LLQ = 13.8; m, 0 : manual count, C V ^ = 10%; LLQ = 17.6; a,0:
automated count, CVmax = 10%; LLQ = 21.7, (all values X 10' plt/L).
that the performance of these instruments is superior to
manual counting over the entire measuring interval. The
question of what are the measuring limits of an analytical
procedure is fundamental and relevant whenever quantitative measurements are made (eg, in analytical chemistry, clinical chemistry, forensic chemistry, as well as in
hematology).
However, the topic of the analytical measuring limits
in hematology is discussed in only a few articles6,8 and
little or no room is given to this issue in modern hematology textbooks. There are at least two possible explanations for limited studies in this area. First, the scientific
community does not consider it an analytical, diagnostic, or scientific problem worthy of discussion. Second,
there is no obvious solution to the problem, and therefore, it is easier not to address it!
Contrary to other medical disciplines such as microbiology, toxicology, or oncology, in hematology, the limit
of detection itself is more a theoretical limit. The mere
detection of cells or platelets is not the issue, but rather
to determine a precise quantitative number of cells or
platelets in the low range.
As is evident from the precision profile (Fig. 2), quantitative determinations at the LD are burdened with a
high CV.16 Therefore, a second limit has to be set for the
platelet count as well, which defines the limit at which
the imprecision of the analytical procedure is equal to
or smaller than a threshold that can be tolerated from a
diagnostic point of view. This limit is called the lower
limit of quantification (LLQ). To use the intersection of
the CV-line with the upper limit of the confidence interval as the LLQ rather than with the curve itself17 is a
785
conservative approach, but it provides additional certainty that a maximal CV is not surpassed at this point.
Three elements contribute to the total variance of an
analytical measurement in a human sample: (1) random
analytical; (2) interindividual; and (3) intraindividual
variance [CVtol = V(CVanal2 + CVjmer2 + CVintra2)].18 Data
can be found in the literature for the interindividual and
the intraindividual variance for most of the analytical
parameters for healthy individuals.19 For patients, these
data are usually not known. Consequently, for the patient with disease, only the analytical variance can be
taken into account, despite the fact that other sources of
variation contribute to the total variance.
Which CV can be tolerated from a diagnostic point of
view is controversial. (Reviews for chemical and hematological parameters are given in refs. 20 and 21). For
practical purposes, it might be assessed by the formula:
CVtot = 2.6 X CVana,.22 An example illustrates what the
practical consequences are of assuming a CVanai of 10%
and 15% and a lower limit of the reference interval of 125
X 109 plt/L. With a CV of 10%, the analytical span would
be 92.5 to 157.5 X 109 plt/L. With a CVana, of 15%, the
analytical span would be 86.3 to 173.8 X 109 plt/L. This
broad zone demonstrates the urgent need for a more precise analytical determination of platelets.
The knowledge of the variance function allows the determination of PD (analytical sensitivity) of an analytical
procedure in a specified interval as shown in Figures 3A
and 3B. In the diagnostically important interval of 20100 X 109 plt/L only 8 (7 with manual counting) values
(or steps) can be differentiated with a probability of
2:95% with these techniques. This number of discriminating intervals may be a too optimistic estimation if biologic variations are added. This means that two analytically different values of a patient do not have to be
different because the actual biologic variation is unknown. When the difference between two consecutive
values is smaller than the PD in a certain interval, we
know that these values can not be discriminated with an
acceptable degree of confidence.
The decision to count a sample manually or by automation is usually based on the experience of the hematologist or on a flagging system incorporated into the instrument.23 However, this decision is usually made
without knowing exactly the performance of the manual
or the automated counting methods. Manufacturers of
the most frequently used automated counters do not give
information on the imprecision at varying counting levels (imprecision profile) or indications to the analytical
limits of their instruments. Obviously these limits are not
taken into account by the integrated flagging systems.
It has been described in the literature that low as well
as high platelet counts are "not always reproducible"24
Vol. 105'No. 6
786
COAGULATION AND TRANSFUSION MEDICINE
Original Article
i
FIG. 3. Power of definition (sensitivity
profile) of the manual (A) and the automated counting (B) in the range
<100 X 109 plt/L. The peak values of
the individual normal distributions
can be discriminated from each other
with a confidence of 0.95. Two examples are given for each counting procedure to illustrate the meaning of the
power of definition. Assuming a first
value A, B is the first lower and C the
first higher value, that can be differentiated from A with a confidence of
P^0.95.
Platelets 1107L|
10
20
30
40
60
50
Platelets [107L|
and that special emphasis should be given to the lower
part of the measuring range.23 Lacking a well-defined
mathematic procedure investigators have not evaluated
this question further.
The procedure presented here for the assessment of the
performance of the platelet count can be applied not
only to the platelet and different cell counts in hematology, but also to clinical chemistry and toxicology for the
determination of tumor markers, drugs, and drugs of
abuse.10"13 This procedure is based on a clearly defined
mathematic procedure that can be adapted on a personal
computer and implemented in every laboratory to assess
the performance of an analytical system or procedure.
From one set of data, the LC, LD, and LLQ can be determined. In addition, PD allows one to determine in
every interval of the measuring range, whether or not a
value is significantly different from the previous one.
70
80
90
100
Concluding Considerations and Recommendations
1. A comparison of the analytical performance of the
manual and of the automated counting procedure of
platelets showed, that the automated count is more
precise because of the higher number of platelets
counted in the range >30 X 109 plt/L.
2. The differences found in the LD of 1.6 X 109 (manual) and 4.3 X 109 plt/L (automated) is of limited
practical relevance, because these values are both in
the clinically critical low range.
3. The differences in the analytical performance at <
30 X 109 plt/L has practical consequences for the
LLQ of the two procedures studied. As a result of
this study our recommendations to users of the
Technicon H1 are:
• below counts of 30 X 109 plt/L, the automated
A.J.C.P.-June 1996
HANSELER, FEHR, AND KELLER
Determination of the Limits of Platelet Counting
counting should be replaced by the manual procedure, and
• results <7 X 109 plt/L (the lower limit of manual
quantification) should not be reported to the
physician because the imprecision below LLQ is
too high (>15%). The statement "platelets <7 X
109 plt/L" is recommended.
4. In the interval from 20-100 X 109 plt/L, only 8 values (and 7 for the manual procedure) can be discriminated with a confidence of >95%. This fact should
be considered when presenting and interpreting results. Assuming a biologic variation, the number of
PD intervals may be even lower.
Determination of the PD in the low range of the platelet count is important to give the physician statistical information to decide if differences of subsequent platelet
counts represent a significant change or reflect the limited analytical performance of the procedure used. Ideally, each test result produced by the laboratory should
be accompanied by this information.
In accordance with Mayer and colleagues,6 we summarize that those who order platelet counts or other hematologic or chemistry tests should have full understanding of the capabilities and of the limitations of the
methods and instruments currently available.
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