Variation and Information in White Blood Cell ... - CiteSeerX

Variation and Informationin White Blood CellDifferential CountsSvend Juul, M.D.,Joseph S. Pliskin, Ph.D.,and Harvey V Fineberg, M.D., Ph.D.

The magnitude and sources of variation in the white blood cell (WBC) count and dif-ferential count affect their information content and clinical value. This studydescribes components of variation in the WBC count and differential, estimates themagnitude of each component, and uses computer simulations to compare the infor-mation conveyed by the total WBC count and by the WBC differential count,expressed as the number of each type of cell and as the percentage of each cell type.

Biologic variation is much greater than statistical sampling variation in differen-tial WBC counts, even when a relatively small number of cells is classified. The com-monly reported neutrophil percentage is inferior both to the neutrophil count and tothe total WBC count in its ability to detect neutrophilia and to detect recovery fromelevated levels. This conclusion holds for single as well as for sequential WBC differ-ential determinations and regardless of the level of test result at which the clinicianconsiders disease to be present. The total WBC count and the neutrophil count differlittle in performance, so a neutrophilic patient’s return to normal levels can safely bedetected and monitored by relying on the less expensive total WBC count and for-going repeated requests for differential counts. (Med Decis Making 4:69-80, 1984)

Introduction

The total white blood cell (WBC) count and the WBC differential count arefrequently-used clinical tests. The information conveyed by a single differ-ential count or by a series of counts depends on the origin and magnitude ofvariation in reported results. Since a differential count is more labor-

This research was supported in part by grants from the Robert Wood Johnson Foundationand the National Center for Health Services Research (HS 03314-03).

From the Institute of Social Medicine, Umversity of Aarhus, Denmark; the Department ofIndustrial Engineering and Management and University Center for Health Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel; and the Institute for Health Research, Ajoint program of the Harvard Community Health Plan and Harvard University, HarvardSchool of Public Health, Boston. Please address requests for reprints to Dr. Fmeberg, Institutefor Health Research, Harvard School of Pubhc Health, 677 Huntington Avenue, Boston, Mas-sachusetts 02115, USA.

at PENNSYLVANIA STATE UNIV on September 18, 2016mdm.sagepub.comDownloaded from

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intensive and expensive than a total WBC count, it would be of practicalvalue in specified clinical conditions to know what amount of additionalclinical information is conveyed by a differential count as compared to atotal WBC count.

Typical uses of the WBC differential count are to detect infection and tomonitor the effects of treatment. Though the WBC count-in particular theneutrophil count-tends to increase during bacterial infection, the clinicalusefulness of the WBC count as an aid to diagnosis may be controversialeven in a common problem like appendicitis [1,2]. Such disagreement maybe based on differences in the performance of the test in different popula-tions and settings, on differences in expectations for test performance, andon differences in the form for expressing results.

The WBC differential count is typically performed in two stages. Firstthe total concentration of white blood cells is determined as cells/mm3.Then the differential distribution is obtained by estimating the relative fre-quency of each cell type in a random sample of cells. The proportion ofeach cell type can be multiplied by the total count to obtain an estimate ofthe differential concentration (cells/mm3). In most laboratories the differ-ential distribution is reported as the percentage of each cell type, rather thanas separate cell counts.

This paper describes five principal components of variation in the WBCdifferential, assesses statistical sources of variation, and compares the mag-nitude of statistical variation to that of interindividual and intraindividual

biologic variation. Computer simulations examine the abilities of the totalwhite blood cell count, the neutrophil percentage, and the neutrophil countto discriminate among patients with and without bacterial infection. In par-ticular, this paper assesses the extent to which the type of test (total WBCcount or differential count) and the form of reporting the differential (as apercentage or as a count) affect the amount of information conveyed by thetest.

Sources of Variation

Table 1 summarizes five sources of variability in WBC differentials: inter-individual variation (among individuals), intraindividual variation (withinan individual), statistical sampling, inconsistent cell classification, andinconsistent sample preparation. The table shows how these sources affectthe cell counts from different types of specimens.

The source of greatest variability is interindividual variation, i.e., varia-tion in the WBC differential counts among different, apparently healthyindividuals [3]. The distribution around the population mean value for acell type reflects the interindividual variability in that cell type. Typically,clinical results of WBC differentials are interpreted in relation to a referenceinterval based on samples drawn from a population of healthy individuals.Though some studies have shown differences in average cell counts by age,sex, and racial characteristics, these differences are much smaller than the



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interindividual differences in a healthy population [3] and are of little con-sequence in evaluating the test results in single patients.

The second largest source of variability is physiological variability withina single patient, or intraindividual variation [3]. In the short term (hours tomonths) this variability is partly diurnal, and it is also related to activity,diet, medication, and other stimuli [4]. The intraindividual variation is ofgreatest concern in the interpretation of a series of examinations in one indi-vidual.

The third source of variability is statistical sampling [5], which comesfrom the two independent steps in performing a differential: estimating thetotal number of white blood cells per mm3 and estimating the proportion ofeach cell type. From these the concentration of each cell type can beobtained by multiplying the total WBC count by the proportions.

Figure 1 illustrates these three components of variation in the distributionof a cell count in a healthy individual. The population mean is representedby point A, around which there is considerable interindividual variation.The average value for one member of the population is represented by B,around which there is some intraindividual variation. C represents theactual concentration of that cell type in that individual at a given point intime. Due to statistical sampling variation there is some variation in therecorded value d that estimates the actual concentration C.

Figure 1. Sources of variation in the determination of white blood cell concentration.A = Population meanB = Individual mean

C = Actual individual value at a given timed = Measured value at the same point in time

The area under each curve equals unity. The curves may be viewed as having differ-ent vertical scales.



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The final two sources of variation, inconsistent sample preparation andinconsistent cell classification, bear on the evaluation and comparison ofvarious technologies to perform differential counts. The term analytic vari-ation includes these two sources, as well as the variation due to statistical

sampling. The magnitude of variation due to inconsistent cell classificationhas been examined by Bacus [6] and by Winkel et al. [7]. Inconsistent cellclassification typically contributes very little to observed variation, and forthis reason inconsistent sample preparation and cell classification will notbe separately quantified in the subsequent analysis.

Measures of Variation. The probability distribution of a variable x maybe characterized by its mean value X, and by its standard deviation SD(x).In ratio scales (scales with a natural zero, e.g., length, counts) variation in xis sometimes expressed as the coefficient of variation, CV(x) = SD(x)lX. CVis a dimensionless measure, and particularly useful when the SD variesdirectly with the mean. CV is often used in hematology to describe variabil-ity in cell counts.

In biologic measurements a logarithmic transformation frequentlyimproves the correspondence of an empirical distribution to a normal distri-bution. The standard deviation of a log transformed distribution is denotedSD(log x). Like CV, SD(log x) is dimensionless. SD(log x) can be approxi-mately calculated from CV(x) by the formula

SD(log x) = log [CV(x) + (CV(X)2 + 1)112].A justification for this approximation is available from the authors.When two independent sources of variation are combined, the combined

variation can be calculated as CV(x) = CV(xl)2 + CV(X2)2 , and correspond-ingly for the log transformed distribution:

[SD(log X)]2 = [SD(log xl)]2 + [SD(log X2)]2.This applies, for example, when combining the total white blood cell countwith the differential distribution to calculate the differential count.

REFERENCE VALUES IN HEALTHY INDIVIDUALS. Medical textbooks pro-vide different ranges for the levels of white blood cells in healthy individuals[8-11]. One inconsistency in the figures given by one text is that the sum ofthe lower ranges of all cell types is higher than the lower range given for thetotal WBC count [9]. A key study by Orfanakis et al. [12] demonstrated thatthe counts of individual cell types in 291 healthy subjects were log normallydistributed. Orfanakis’ main findings are summarized in the first threecolumns of Table 2. The fourth column shows the geometric mean, i.e., theretransformed value of the mean in a logarithmic transformation. The geo-metric means are close to the median values reported in the second column,supporting the assumption of a log normal distribution. The standard



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Table 2. Reference Values and Ranges of White Blood CeHs______

[Counts of cells(x) per mm 3 1

&dquo; From Orfanakis et al. [12].

b Geometric mean = antilog [log x2 5% +log X97 s%)~2].‘SD(log x)=(log x9~s%-log X2 5oy,,)/3.92. For eosinophils and basophils, SD(log x)=(log xso% -log x2 5 %) /1.96.

deviation of the log normal distribution is shown in the fifth column of thetable. In a normal distribution the central 95 percent of the distribution isencompassed within 1.96 standard deviations on either side of the mean,yielding the figures in the fifth column.

The following sections on sampling variation and biologic variationdescribe the breakdown of the total variation of the last column into its sta-tistical and biological components. The latter will be further dissected intointerindividual and intraindividual components.

SAMPLING VARIATION. Both the total WBC count and the determinationof the proportion of each cell type involve sampling variation. We calculatethe variation from these two sources separately.

Sampling Variation in the Total WBC. Most contemporary total WBCcounts are performed by machines such as the Coulter S counter. Variationin the total WBC count depends on statistical properties of sampling and onmachine imprecision. Typically, 10 000 cells are counted, giving rise to aPoisson variation corresponding to a CV of 0.01. The analytic variation of atotal WBC count performed on a Coulter S counter has been empiricallyestimated to correspond to a CV of 0.04 [13], indicating some degree ofmachine imprecision. We will use 0.04 to represent the coefficient for varia-tion attributed to the total WBC count.

Statistical Sampling Variation in the Differential Count. Sampling varia-tion in the count for each cell type is due in part to statistical variation in thedifferential classification of cells, and in part to variation in the total WBCcount.

The differential count is calculated by multiplying the total WBC countby the proportion of the cell type of interest. If k of n cells are identified as agiven cell type, the estimated proportion of that cell type is p = kln. The



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standard deviation of the estimate is SD(p)=[p(I-p)lnl 1/2 , based onthe binomial distribution. The corresponding CV is given by CV(P)=[(1- p)/np]l/2.As can be seen from the above formula, the coefficient of variation for

the proportion of cell types depends on both the proportion of the cell typeand the number of cells counted. For example, if 200 cells are counted (forthe differential) and the observed proportion is p = 0.2,

CV(p) _ [0.8/(0.2)(200)] 1/2 = 0.141.

The coefficient of variation of the concentration of a cell type CV(x) incor-porates the sampling variation in the total WBC (CV = 0.04):

[CV(x)]Z - [CV(p)]2 + [0.04]2 = 0.0216;

hence CV(x) = 0.147.Table 3 presents for each cell type the assumed proportion p, the coeffi-

cient of statistical sampling variation of the proportion CV(p), the co-efficient of total sampling variation CV(x), and the standard deviation ofthe log normal distribution SD(log x) in a classification of 200 cells. Thesecalculations yield estimates of the sampling variation of the cell countsreported by Orfanakis et al. [12].

BIOLOGIC VARIATION. The sampling component of variation can be sub-tracted from total variation to yield an estimate of biologic variation. Bio-logic variation includes two components, interindividual variation andintraindividual variation. Table 4 summarizes these components of varia-tion for each of the five major types of white blood cells. Biologic variationis much larger than sampling variation for neutrophils and lymphocytes;these cell types are the most important clinically and typically constitutemore than 90 percent of the circulating WBC population.

Information Value of the WBC Differential:

Computer Simulation of Changes During Infection

We examined the abilities of WBC counts and WBC differential counts, assimulated by a computer, to identify patients with bacterial infection and tomonitor recovery from infection. We compared the information conveyedby the WBC differential when expressed as proportions and as cell counts,and we compared these expressions with the information conveyed by thetotal WBC count. We proceeded in three steps to simulate results in a popu-lation of 1000 individuals without infection (healthy). Then we proceeded ina similar way to estimate results in a population of 1000 individuals withinfection (sick).

As a first step we simulated the average counts for each individual in the

healthy population, using the mean counts of each cell type in the secondcolumn of Table 2 and the interindividual variation in the fourth column of



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Table 3. Estimated Statistical Sampling Variation of White Blood Cells,by Classification of 200 Cells

a

Proportions according to the relative distribution of median values in Table 2, second column.bCV(p) = [(1- p)/200pI1l2c [CV(x)l2 = [CV(p)]2 + [O.04¡2. CV(x) = Coefficient of variation for the cell~ SD(Iog x) = log [CVM + (CV (X)2 + 1)1121

Table 4. As a second step we simulated the concentration of each cell type inan individual at a point in time by applying the intraindividual variation ofthat cell type (Table 4, column 5) to the individual average values obtainedin the first step. Finally, we simulated in each patient the classification of100 randomly selected cells, assuming no errors in cell classification.We followed the same approach to simulate cell counts in the population

with infection. We considered the five major white blood cell types (neutro-phils, lymphocytes, monocytes, eosinophils, and basophils) as coming fromfive independent cell populations. (This assumption would not apply to thesubgrouping of neutrophils according to maturity, i.e., band versus seg-mented forms.) We assumed the mean neutrophil count in a sick individualwas double the level for that individual when healthy. We further assumedthat the levels of nonneutrophil cells do not change with infection.

Table 4. Components of Biologic Variation in White Blood Cells

a From Table 2, column 5.

b From Table 3, column 4.c (Col. 3)2 = (Col. 1)2 - (Col. 2)2(Col. 3)2 = (Col. 4)2 + (Col. 5)2.Allocations to the last two columns are proportional to the interindividual and intra-individual variation found by Statland et al. [3].



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To judge whether these assumptions are reasonable, we examined therecords of 56 patients at Mt. Auburn Hospital, Cambridge, Massachusetts,with primary or secondary diagnosis of gram-negative sepsis. The reviewconfirmed that an increase in the neutrophil count to twice the usual level ormore is a typical occurrence during that type of infection. The assumptionthat other cell types are unaffected during infection was not directly con-firmed, as lymphocytes tended to decrease and monocytes to increase dur-ing gram-negative sepsis. These changes were, however, much smaller thanthe change in the neutrophil count, and they tended to balance each other,so that the total count of nonneutrophil cells remained approximatelyunchanged during infection. To avoid unnecessary complexity of the com-puter model we did not introduce changes in lymphocyte and monocytelevels at the time of infection.

The analysis addresses two types of clinical problems: the ability of asingle white blood cell differential to distinguish sick from healthy individ-uals, and the ability of repeated WBC differentials to identify individualswith changing clinical conditions.

Figure 2. ROC curves showing the abilities of the neutrophil count, neutrophil per-centage, and total WBC count to distinguish neutrophilic from nonneutrophilic indi-viduals.



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The neutrophil count, total WBC count, and neutrophil percent inpatients with and without infection were used for calculating points onROC curves. The ROC curves in Figure 2 describe the ability of the neutro-phil count, the total white blood cell count, and the neutrophil percentageto distinguish between sick and healthy individuals under the conditionsdescribed above. The location of curves nearer to the upper left corner indi-cates superior performance. The area under the ROC curve was used as anindex of test performance, an area of 1.0 indicating a perfect test and anarea of 0.5 indicating a test without informative value. The area was com-puted by the method described by Swets [14].

The location of ROC curves in Figure 2 indicates that the neutrophil per-centage is inferior for distinguishing healthy from sick individuals, as com-pared to the neutrophil count, which in turn is slightly better than the totalWBC count. This conclusion holds regardless of the level of test result atwhich the clinician considers disease to be present. The areas under the threecurves are listed in the first row of Table 5, confirming the visual impressionfrom Figure 2.We examined the ability of the white blood cell differential to indicate

recovery from disease, by simulating results for two hypothetical popula-tions, each of 1000 individuals. For each individual in the &dquo;recovery&dquo; popu-lation the assumed neutrophil level shifted from double the assumed healthylevel back to the healthy level. In the &dquo;no recovery&dquo; population each individ-ual’s average neutrophil count was simulated to remain double the healthylevel for that individual. The underlying intraindividual variation and theanalytic sampling variation remained in effect.

Changes from one determination to a second can be examined by meansof the ratio or by means of the difference between the determinations. Weexamined the abilities of the ratio and the difference to distinguish membersof the recovery group from the no recovery group by constructing ROCcurves for the neutrophil count, total WBC count, and neutrophil percent-age.

The test performances are summarized in the second and third rows ofTable 5. The ratio between determinations was superior to the differencebetween determinations. The neutrophil count and the total white blood cellcount were superior to the neutrophil percentage. Successive WBC countswithin an individual can discriminate disease better than a single determina-tion because successive counts in an individual are not influenced by inter-individual variation.We also simulated a succession of five determinations in the recovery and

no recovery populations, the recovery population being subject to a gradualreduction in neutrophil level. In both groups cell counts were subject tointraindividual variation. We calculated the regression coefficient and thecorrelation coefficient for the changes in neutrophil count, total whiteblood cell count, and neutrophil percentage over time, and used these



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Table 5. Performance (Area under the ROC curve)of the White Blood Cell Differential

results to construct the ROC curves summarized in the last rows of Table 5.

The correlation coefficient seems to be a slightly better predictor ofrecovery than the regression coefficient for sequential neutrophil and totalWBC counts.

Conclusions

Compared to biologic sources, statistical sampling makes a relatively smallcontribution to variation in the white blood cell differential count, evenwhen only 100 cells are classified. The origin and magnitude of variationdetermine the potential performance of any technology to count and clas-sify white blood cells. The relatively small statistical component of variationlimits the potential added precision of counting large numbers of cells, asdone, for example, by automated differential counters.

Based on simulated determinations of white blood cell counts under stan-dard conditions, we conclude that the neutrophil percentage is inferior tothe total WBC count and to the neutrophil count in ability to identify indi-viduals with elevated neutrophil concentrations. The neutrophil percentageis also inferior in ability to identify individuals in whom the neutrophil levelchanges over time. Laboratory reports of the WBC differential countshould prominently show the numerical counts of each cell type, perhapsindicating percentages in parentheses. The total WBC count and the neutro-phil count based upon a classification of 1000 cells differ little in perform-ance. This conclusion is consistent with the findings of Brecher et al., whoanalyzed 415 sequences of WBC and differential counts in hospital patients



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and found only four in which the neutrophil count had changed without aconcomitant change of comparable magnitude in the total WBC count [15].The clinician who wishes to detect and monitor a neutrophilic patient’sreturn to normal levels can safely rely on the total WBC count and forgorepeated requests for differential counts.

References

1. Raftery AT: The value of the leukocyte count in the diagnosis of acute appendi-citis. Br J Surg 63:143-144, 1976

2. Bolton JP, Craven ER, Croft RJ, Menzies-Gow N: An assessment of the valueof the white cell count in the management of suspected acute appendicitis. Br JSurg 62:906-908, 1975

3. Statland BE, Winkel P: Physiological variability of leukocytes in healthy sub-jects. In, Koepke JA, ed: Differential Leukocyte Counting. Aspen, Colo: CAPConference, 1977, pp 23-37

4. Boggs DR: Response of blood leukocytes to common stimuli. In, Koepke JA,ed: Differential Leukocyte Counting. Aspen, Colo: CAP Conference, 1977, pp47-52

5. Rumke CL: The statistically expected variability in differential leukocyte count-ing. In, Koepke JA, ed: Differential Leukocyte Counting. Aspen, Colo: CAPConference, 1977, pp 39-45

6. Bacus JW: The observer error in peripheral blood cell classification. Am J ClinPathol 59:223-230, 1973

7. Winkel P, Statland BE, Harris SC, et al: A study of variation of concentrationvalues of leukocyte type 2. Analytical considerations. Manual vs. automated cellcounting. Advances in automated analyses. Technicon International Congress.Tarrytown, New York: Mediad Incorporated, 1977

8. Rumke CL, Bezemer PD, Kuik DJ: Normal values and least significant differ-ences for differential leukocyte counts. J Chronic Dis 28:661-668, 1975

9. Cecil RL, Loeb RF: Textbook of Medicine (13th ed). Philadelphia: Saunders,1971

10. Harrison TR: Principles of Internal Medicine (9th ed). New York: McGraw-Hill, 1980

11. Wintrobe MM: Clinical Haematology (7th ed). Philadelphia: Lea and Febiger,1974

12. Orfanakis NG, Ostlund RE, Bishop CR, Athens JW: Normal blood leukocyteconcentration values. Am J Clin Pathol 53:647-651, 1970

13. England JM: Total and differential leukocyte count. Br J Haematol 33:1-7, 197614. Swets JA: ROC analysis applied to the evaluation of medical imaging tech-

niques. Invest Radiol 14:109-121, 197915. Brecher G, Anderson RE, McMullen PD: When to do diffs. How often should

differentials be repeated? Blood Cells 6:431-439, 1980



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