statistical methods for the blood beryllium lymphocyte proliferation

Statistical Methods for the Blood BerylliumLymphocyte Proliferation TestEdward L. Frome,l Matthew H. Smith,2 L. Gayle Littlefield,2Richard L. Neubert,3 and Shirley R Colyer21Computer Science and Mathematics Division, Oak Ridge NationalLaboratory, Oak Ridge, Tennessee; 2Medical Sciences Division, OakRidge Institute for Science and Education, Oak Ridge, Tennessee;3Consultant, Oak Ridge, Tennessee

The blood beryllium lymphocyte proliferation test (BeLPT) is a modification of the standardlymphocyte proliferation test that is used to identify persons who may have chronic berylliumdisease. A major problem in the interpretation of BeLPT test results is outlying data values amongthe replicate well counts (=7%). A log-linear regression model is used to describe the expectedwell counts for each set of Be exposure conditions, and the variance of the well counts isproportional to the square of the expected count. Two outlier-resistant regression methods are

used to estimate stimulation indices (Sls) and the coefficient of variation. The first approach uses

least absolute values (LAV) on the log of the well counts as a method for estimation; the secondapproach uses a resistant regression version of maximum quasi-likelihood estimation. A major

advantage of these resistant methods is that they make it unnecessary to identify and deleteoutliers. These two new methods for the statistical analysis of the BeLPT data and the currentoutlier rejection method are applied to 173 BeLPT assays. We strongly recommend the LAVmethod for routine analysis of the BeLPT. Outliers are important when trying to identify individualswith beryllium hypersensitivity, since these individuals typically have large positive SI values. Anew method for identifying large Sls using combined data from the nonexposed group and theberyllium workers is proposed. The log(SIl)s are described with a Gaussian distribution withlocation and scale parameters estimated using resistant methods. This approach is applied to thetest data and results are compared with those obtained from the current method. EnvironHealth Perspect 104(Suppl 5):957-968 (1996)

Key words: beryllium, chronic beryllium disease, least absolute value regression, lymphocyteproliferation test, outlier, quasi-likelihood estimation, regression, resistant estimators,statistical methods

IntroductionChronic beryllium disease (CBD), a disorder one of several criteria for diagnosis of thethat mainly affects the lung, occurs in a disease (1). In vitro proliferation ofsmall percentage of persons exposed to bronchoalveolar lavage (BAL) cells whenberyllium dusts. Most investigators require exposed to beryllium is extremely sensitiveevidence of beryllium hypersensitivity as to and specific for the diagnosis of CBD

This paper was presented at the Conference on Beryllium-related Diseases held 8-10 November 1994 in theResearch Triangle Park, North Carolina. Manuscript received 29 April 1996; manuscript accepted 7 May 1996.

Research was supported by the Offices of Occupational Medicine and Epidemiology and HealthSurveillance, Environment, Safety and Health, U.S. Department of Energy under contract DE-AC05-840R2140with Lockheed Martin Energy Research Corp.; and DA-AC05-760R00033 with Oak Ridge AssociatedUniversities. The authors thank BL Gangaware and LR Moore for their assistance in data collection. A draft ver-sion of this report was reviewed by several members of the CABST committee and their colleagues, and byR.L. Schmoyer, JP Watkins, DL Cragle, and two anonymous reviewers. We greatly appreciate their useful com-ments and we will address points that are beyond the scope of the present study in a subsequent report.

The work has been authored by a contractor of the U.S. Government. Accordingly, the U.S. Governmentretains a nonexclusive, royalty-free license to publish or reproduce the published form of this work, or to allowothers to do so for U.S. Government purposes.

Address correspondence to Dr. E. L. Frome, Mathematical Sciences Section, Computer Science andMathematics Division, Oak Ridge National Laboratory, PO Box 2008, Oak Ridge, TN 37831-6367. Telephone:(423) 574-3138. Fax: (423) 574-0680. E-mail: [email protected]

Abbreviations used: BeLPT, beryllium-specific lymphocyte proliferation test; BW, beryllium workers; CABST,Committee to Accredit Beryllium Sensitization Testing; CBD, chronic beryllium disease; ConA, concanavalin A;CV, coefficient of variation; DOE, U.S. Department of Energy; IWLS, iterative weighted least squares; LAV,least absolute value; MAD, median absolute devition; MSI, maximum of the estimated Sls; NE, nonexposedworkers; ORISE, Oak Ridge Institute for Science and Education; PHA, phytohemagglutinin; OL, quali-likelihood;SI, stimulation index.

but is not suitable for screening since it isan invasive procedure (1). A noninvasiveprocedure based on the proliferativeresponse of blood cells to beryllium hasbeen developed and is referred to as theberyllium-specific lymphocyte proliferationtest (BeLPT)(2). This modification of thestandard lymphocyte-proliferation test isused to identify relatively rare individualsamong worker cohorts who display delayedhypersensitivity reactions when exposed toberyllium metal. The BeLPT involves invitro challenge of peripheral blood lympho-cytes with salts of beryllium combinedwith assays for clonal proliferation of sensi-tized subsets of CD4 lymphocytes usingtritiated thymidine uptake as a quantitativemeasure of blastogenesis. The test is con-ducted using 96-well microtiter plates; theamounts of tritiated thymidine incorporatedby replicate wells containing lymphocyteschallenged with beryllium is comparedwith uptake of radioactivity by replicatewells of nonchallenged lymphocytes toestablish stimulation indices (SIs) as a mea-sure of in vitro sensitivity to beryllium. Amajor problem in the interpretation ofBeLPT test results is outlying data values( 7%) among the replicate well counts.

The increasing use of beryllium in severalnew economic sectors emphasizes the needfor medical surveillance in the workplace forCBD (3). In particular, beryllium has beenused in the nuclear industry for a numberof years. Kreiss et al. (4) have examinedthe epidemiology of CBD in a stratifiedsample of workers at a nuclear weaponsplant and discuss the role of the BeLPT inberyllium disease surveillance in thenuclear industry. The U.S. Department ofEnergy (DOE) is operating a screening pro-gram for CBD that will eventually includeapproximately 15,000 current and formerberyllium-exposed workers at 20 DOEsites. Each participating beryllium workerwill have a BeLPT at an approved labora-tory using a standard protocol developed bythe Committee to Accredit BerylliumSensitization Testing (CABST). The resultsof each assay will be evaluated and classifiedas normal, abnormal, or unsatisfactory.

A major concern that was not com-pletely resolved by the CABST was how todeal with outliers that occur in the BeLPTdata. The main purpose of this report is topropose a new statistical approach thatcan be used for analysis of a BeLPT assaythat may contain multiple outlying wellcounts. Given their undue influence on theestimates of the SIs. a method for handling

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-M.",W .. .Rl%*'. POWWWWN 5 i AmNal 4014 S. 11, --Ii-n HIM, .m W WK MD~

957

FROME ET AL.

outliers is needed. The current approach(as described in the July 1993 version ofthe CABST protocol ["Appendix"]) isbased on an ad hoc outlier rejectionmethod. As an alternative we propose usingresistant estimation methods that are not

sensitive to outliers. The BeLPT assay isdescribed with a regression model thatrelates the expected well counts at each ofthe three beryllium concentrations to thecontrol well counts for cells that are har-vested after 5 and 7 days. Resistant fittingmethods are used to estimate the SI foreach of the six beryllium concentrations.The main advantage of this approach isthat estimates of the SIs are calculatedwithout explicitly identifying and deletingthe outlying well counts.

Figure 1. Oak Ridge Institute for Science andEducation BeLPT culture assay. ConA, concanavalin A;PHA, phytohemagglutinin.

A second question considered is theidentification of beryllium-exposed workerswho exhibit beryllium hypersensitivity.Most (over 90%) of the beryllium workerswill have SIs similar to those of a controlgroup with no known exposure to beryl-lium. However, even after the use of resis-tant estimation methods to minimize theeffect of outlying well counts, the BeLPTfor some beryllium workers will yield largeSIs. In this case we want to identify theoutliers (i.e., individuals with large SIs),since they represent beryllium workers whoexhibit beryllium hypersensitivity.

Beryllium LymphocyteProliferation TestA detailed description of lymphocyteculture methods, quality control measures,

and examples of plate maps and printoutsof raw data are included in the Appendix.Following is a brief description (Figure 1)of the protocol for the BeLPT culture assay

as established by CABST and implementedby the BeLPT laboratory at Oak RidgeInstitute for Science and Education(ORISE) as of July 1993. The details ofthis procedure and the equipment usedvary at different laboratories that are

performing the BeLPT.First, a 15-ml blood sample is obtained

from each patient and mononuclear cellsare separated using density gradient cen-

trifugation. Next, lymphocytes are culturedusing standard methods at a final concen-

tration of 2.5 x 105 cells per well in 96-well, flat-bottom microtiter plates. Foreach BeLPT assay, 12 replicate controlwells and four replicates for each experi-

mental condition (i.e., 1, 10, and 100 pMof BeSO4, and mitogen-stimulated posi-tive controls) are set up. Third, cells are

incubated at 37°C for 5 and 7 days and a

Table 1. Well counts for BeLPT assay (AC153 data shown

pulse of tritiated thymidine is deliveredprior to harvest. Cells are harvested on fil-ter paper and counts are measured in a

Packard Matrix 96 gas ionization counter

(Packard Instrument Co., Downer's Grove,IL). Each filter is counted for 30 min andthe results organized as shown in Table 1

for statistical analysis.

Statistical MethodsIn this section we describe three methodsof analyses for the BeLPT assay. The firstmethod is the outlier rejection procedureproposed by CABST. A regression model isproposed to describe the two new methods,which are least absolute value (LAV)regression on the log counts and resistantmaximum quasi-likelihood estimation. Theregression model is motivated by the factthat the SI describes the relative increasesin the proliferative response of beryllium-stimulated cells to control cells. This leadsto the log-linear representation of treat-

ment effects. It is also apparent (Results)that the variability in the well counts

increases approximately in proportion to

the square of the expected count, so thatthe coefficient of variation (CV) is constant(i.e., the standard deviation is proportionalto the mean). This implies that taking logsof the well counts leads to constant vari-ance and additive effects, and the mainparameters of interest are the log(SI)s. Ifthere were no problem with outliers, stan-

dard least squares methods could be usedon the transformed data. This approachwas not considered since the occurrence ofmultiple outliers has been well established.

First Method, Based on OutlierRejection ProcedureAt the time this work was initiated, CABSThad proposed a method for calculating SIs

Culture conditions j Replicate counts

Day 5 Control 1 965 1173 828 862Control 1 1474 7237 1021 976Control 1 1500 1729 1672 1992Be 1 2 1050 706 1434 687Be 10 3 1551 1466 1661 2301Be 100 4 3571 5780 4011 5229

Day 7 Control 5 9202 5253 3786 5212Control 5 2310 2844 1915 3102Control 5 2458 3936 3087 6588Be 1 6 714 1135 6084 1097Be 10 7 786 846 2757 652Be 100 8 6037 8349 6852 10449

Day 5 PHA 9 82425 52954 52669 50487Candida 10 35501 21623 21551 22087

PHA, phytohemagglutinin.


I. Culture methodHeparinized blood (-15 ml)Ficoli-hypaque centrifugationSeparated lymphocytes

RPMI 1640 Medium10% pooled human serum

antibiotics

11. Beryllium challenge2.5 x 105 lymphocytes per well96-well, flat-bottomed microtiter plates

Beryllium No. replicate Day ofsulfate (pM) wells harvest

0 12 5,71 4 5,710 4 5,7100 4 5,7PHA (30 pM/ml) 4 5ConA (10 pM) 4 5

Ill. Harvest method (days 5 and 7)Add tritiated thymidine (-8:00 AM)

(1 pCi/well specific activity 5-7 mCi/mMol)Freeze plates at -200 C (-4:00 PM)Perform 30-min counts on Packard Matrix 96

gas ionization counter

IV. Data reductionControl wells

12 replicates-drop outlierscalculate mean and CV

Be treatments4 replicates-drop 1 outliercalculate mean and CV

Stimulation index = (SI)mean Be treated

SI = mean control

958

STATISTICAL METHODS FOR BeLPT

that used an ad hoc procedure for deletingoutliers based on the value of the CV foreach set of culture conditions. If the CV isgreater than 0.3, the most extreme count isdeleted. This procedure is continued untilthe CV is less than or equal to 0.3, pro-vided no more than one-third of the wellcounts have been deleted. A patient's dataare listed as "acceptable" if the resulting CVis less than 0.3 for both day 5 and day 7control data, and for at least four of the sixsets of beryllium-stimulated quadruplicates.If these conditions are not met, the BeLPTis called "unsatisfactory" due to high vari-ability in the data. A BeLPT is also consid-ered unsatisfactory if the positive-controlresponse is too low (indicating lack of cellviability), or if the control counts are con-sidered to be either too low (relative tobackground) or too high. We assume herethat BeLPTs that are unsatisfactory foreither of the latter two reasons are identifiedbefore further analysis using criteria thatdepend on laboratory experience.

The SIs for the stimulated cells are theratios of the treatment means and thecorresponding control means (after theoutliers have been deleted), i.e.,

SI- mean(treated)mean(control)

The positive control wells are only countedfor 10 min, so the SIs are multiplied by 3to adjust for the counting-time difference.The results of applying this procedure tothe BeLPT data in Table 1 are given inTable 2. These data are acceptable sinceboth of the control CVs are less than 0.3,and all six beryllium-stimulated CVs areless than 0.3. The procedure used to deter-mine if a BeLPT is abnormal is presentedat the end of this section.

Rerssion Model for the BeLPT DataLet Yjk denote the well count for the kthreplicate of the jth set of culture conditions.The expected count in each well is repre-sented by a log-linear regression function:

E(yjk) =Aj = exp(Xj13), [1]

where j = 1. 0 and k = 12 for thecontrols and k = 1,2,3,4 for the beryllium-stimulated cells and the positive controls.In Equation 1, X1 is a row vector of indica-tor variables and / is the vector of regres-sion parameters (below). We furtherassume that the variance of the well counts

is proportional to the square of the In the absence of outliers, ordinary leastexpected count: squares on the transformed data would

yield consistent estimates for the log(SI)parameters (5). The effect of outliers is

Var(Yjk)= (OAj) [2] minimized by using LAV (or some otherrobust method) on the zjk. LAV regres-

Equations 1 and 2 together are referred to sion-also known as LI norm, leastas a generalized linear model with constant absolute deviations (LAD), and minimumcoefficient of variation-as detailed by sum of absolute errors (MSAE)-is wellMcCullagh and Nelder (5). The distinct known to be resistant to outliers and is anvalues of the row vectors of covariates Xj, important particular case of a general classj = 1.10 are shown in Table 3. of robust methods known as M-estimators

With this parameterization, the first (6,7). In general, LAV regression requiresthree ,Bs represent the log of the SIs for the special computational resources to calculatethree concentrations of BeSO4 on harvest parameter estimates (8). In this situation,day 5 and the next three Ps are the corre- however, it is only necessary to find thesponding estimates on day 7. The last two median of the log of the well counts forB s are the log(SI)s for the positive control each set of design conditions (say Z) andwells, and 07 and /8 represent the log of then subtract the control median for eachthe control well counts on days 5 and 7. harvest day from the beryllium-stimulatedrespectively. We have developed two out- medians. Frome et al. present details inlier-resistant approaches for estimating the Appendices A and C of a report for OakSIs and the coefficient of variation, 4. Ridge National Laboratory (9). A resistant

estimate of the coefficient of variation canSe iondMethod, Based on LAV then be obtained asRegression on Log(y)The first approach based on the regression = C X medianJ]Z -model is to take the log of the counts since [jkthis is the variance-stabilizing transfor-mation and leads to a linear model inzjk = log(yjk), i.e., where C = 1.48 x nl(n-p), n = 56, and

p = 10 (when the assay is complete). The2 value of C is chosen to make the estimate

E(zjk) = Xj - and Var(zjk) ~ consistent for the standard deviation for a2 an

Table 2. Results of the current outlier rejection method for Table 1.

Culture conditions n Average CV Si log(SI)Day 5 Control 10 1220 0.28

Be 1 3 814 0.25 0.67 -0.40Be 10 4 1744 0.22 1.43 0.36Be 100 4 4648 0.22 3.81 1.34

Day 7 Control 8 2930 0.24Be 1 3 982 0.24 0.34 -1.09Be 10 3 761 0.13 0.26 -1.35Be 100 4 7921 0.25 2.70 1.00

Day 5 PHA 4 59634 0.25 146.6 4.99Candida 4 25190 0.27 61.9 4.13

Table 3. Distinct rows in the model matrix.

I Xji %x2 Xj3 Xj4 Xj5 Xj6 Xj7 X18 xjg Xj101 0 0 0 0 0 0 1 0 0 02 1 0 0 0 0 0 1 0 0 03 0 1 0 0 0 0 1 0 0 04 0 0 1 0 0 0 1 0 0 05 0 0 0 0 0 0 0 1 0 06 0 0 0 1 0 0 0 1 0 07 0 0 0 0 1 0 0 1 0 08 0 0 0 0 0 1 0 1 0 09 0 0 0 0 0 0 1 0 1 010 0 0 0 0 0 0 1 0 0 1

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FROME ET AL.

Gaussian error model and for consistencywith the usual least squares results, inwhich the estimated variance is multipliedby the correction factor n/(n - p) (10) andS-PLUS function MAD (11), which com-putes the median absolute deviation(MAD) estimate of the standard deviation.Alternative approaches to estimating 4have been discussed in the context of LAVregression (7,12) and there is no consensusas to the best approach. In addition to thefact that 4 is of direct interest, it is alsoneeded to obtain an estimate of the para-meter covariance matrix

(02(X'X)-l

where ()2 = [2f(0)]2 is the asymptoticvariance of the sample median (13).Following the approach of McGill et al.(14) we assume that the underlying errordistribution is Gaussian in the center anduse 6 = ,rI2~P to obtain an estimate of thestandard deviation of the log of the stimu-lation indices. The appropriate diagonalterm from (X'X)-l is 4/12, and conse-quently the estimated standard deviation oflog(SI) is 1.25,L(O.58) = 0.72 4OL Theresults of applying this approach to thedata in Table 1 are shown in Table 4.

Third Method, Based onQuasi-likelihood EstimationIn the second regression model approach,the analysis is done on the original scaleand estimation is based on an iterativeweighted least squares (IWLS) algorithm.The use of IWLS for generalized linear(15) and nonlinear (16) regression func-tions leads to maximum likelihood esti-mates when the dependent variable is inthe regular exponential family. McCullagh

(17) extended this result to quasi-likeli-hood (QL) estimation, which requiresspecification of the mean and variancefunction. Extension of IWLS to resistant/robust regression has been described byGreen (18) and Pregibon (19), and thecomputational approach described byChambers and Hastie (20) is used here.Similar resistant regression methods havebeen applied to the analysis of drug concen-tration-time data encountered in humanbioavailability studies (21).

Consider the following weighted sumof squares,

II jk [Yjk -Ai]i k

until convergence. Frome et al. (9) presentdetails in their Appendix D. The momentestimate of 02 is computed after the finaliteration

A2

02 = Yjk Yjkn-p Yjk

To adjust for the effect of outliers we intro-duce a second weight for each observation,

-=f1 lul<kW kl lul lul>k [5]

[3]

where Ai = exp(Xj,1) and Wjk a l/var(Yk) =l/2. The IWLS procedure starts with aninitial estimate, say ,B°, and A7 in Equation 3is replaced with the first order Taylor series

exp(Xj13') + PjS'

where P = XJ/, and the weights are evalu-ated at ,6 to obtain

SWkYjk_(AO + pja)

The unknown "correction vector," 60, isthen calculated using weighted least squares,i.e. by solving

(P-'WP)j5' =P'W'[Y-K] [4]

for 6'. The estimate of /B is then updated13l = p + &0, and the procedure is repeated

where u = (Yjk -3jk) I4)ik is the standardizedresidual using the current estimates of ,Band 4. This is known as an M-estimatorwith Huber's loss function. The "tuningconstant," k, must be specified and we usek = 1.345, which leads to estimates withapproximately 95% efficiency (19).Therefore, to obtain resistant quasi-likeli-hood estimates we multiply the elements ofthe diagonal matrix Win Equation 4 bythe Huber weights discussed in Equation5; again, details can be found in AppendixD in Frome et al. (9). Following the lastiteration, an estimate of the coefficient ofvariation is obtained using a scaled MADestimate of the standardized residualsUjk= (Yjk-Yjk) jk

4 = 1.48 xmedian{lujIk} xn p

Identification ofBeLPTs with Large SIsThe CABST method for identifyingan "abnormal" BeLPT is based on the

Table 4. Results of LAV estimation for log(y) of data in Table 1, OiL=0.367.Experimental conditions Zjk z1 (Zjk- j)I¢L / exp(f)Day 5 Controls 6.872 7.067 6.719 6.759 7.182 -0.8 -0.3 -1.3 -1.2

Controls 7.296 8.887 6.929 6.883 7.182 0.3 4.6 -0.7 -0.8Controls 7.313 7.455 7.422 7.597 7.182 0.4 0.7 0.7 1.1Be 1 6.957 6.560 7.268 6.532 6.758 0.5 -0.5 1.4 -0.6 -0.423 0.655Be 10 7.347 7.290 7.415 7.741 7.381 -0.1 -0.2 0.1 1.0 0.199 1.221Be 100 8.181 8.662 8.297 8.562 8.429 -0.7 0.6 -0.4 0.4 1.248 3.483

Day 7 Controls 9.127 8.567 8.239 8.559 8.139 2.7 1.2 0.3 1.1Controls 7.745 7.953 7.557 8.040 8.139 -1.1 -0.5 -1.6 -0.3Controls 7.807 8.278 8.035 8.793 8.139 -0.9 0.4 -0.3 1.8Be 1 6.571 7.034 8.713 7.000 7.017 -1.2 0.0 4.6 0.0 -1.122 0.326Be 10 6.667 6.741 7.922 6.480 6.704 -0.1 0.1 3.3 -0.6 -1.436 0.238Be 100 8.706 9.030 8.832 9.254 8.931 -0.6 0.3 -0.3 0.9 0.792 2.207

Day 5 PHA 11.320 10.877 10.872 10.829 10.874 1.2 0.0 0.0 -0.1 4.792 120.50Candida 10.477 9.982 9.978 10.003 9.992 1.3 0.0 0.0 0.0 3.910 49.880



distribution of the maximum SI for agroup of individuals with no known expo-sure to beryllium. First calculate the maxi-mum of the estimated SIs (MSI) for eachperson in the nonexposed group,

MSI(i) = maX[Slij j = 15...6j i = 1.Ne,

[6]

where NA is the number in the nonexposedgroup. The mean and standard deviationof the MSIs are then used to calculate SI* =mean + 2 (standard deviations). A BeLPTfor a beryllium worker is defined as abnor-mal if at least two SIs exceed SI*. Using thecurrent value (SI* = 5.65), we concludethat the BeLPT in Table 2 is normal. Theprobability of obtaining a statistical falsepositive for this procedure is unknown.

We propose an alternative approach thatestablishes a reference database of BeLPTsbased on BeLPTs from nonexposed workersand historical data from beryllium workers.The best way to establish this reference data-base is laboratory dependent and will not bediscussed here. For illustrative purposes wewill use the combined data from the beryl-lium workers and the nonexposed (control)group. The method is based on the assump-tions that the estimates of the log(SI)s areapproximately normally distributed and thatalmost all of the beryllium workers are notsensitized. Resistant methods are then usedto counter the influence of outliers (i.e., theabnormal test results). The first step is tocalculate an outlier-resistant estimate oflocation, ft, and spread, Sr, for each of the sixlog(SI) distributions in the reference data-base. In the results that follow we use

j= median(1,1i, i =1.N), and

i =MAD(13,1i = 1...,N),

where N= 173 and j= 1, . . . 6. The secondstep is to convert the log(SI)s for each indi-vidual into standardized deviates

ui.= - [7]S.

using the values of f1 and sL, from the refer-ence database. The six standardized deviatesfor a BeLPT are compared to the zp quan-tile of the standard normal distribution. Ifat least two of these values exceed zp, the

BeLPT is called abnormal. If the estimatedlog(SI)s are independent, then the bino-mial distribution can be used to calculatean approximate probability of at least k outof six "large" SIs for a given value of zp.The probability of at least one large SIis 1 -p6 = 0.141 (forp = 0.975). The proba-bility of at least two is 1 - [p6 + 6(1 - p)p5]= 0.009 (for p = 0.975). In fact, thelog(SI)s are positively correlated, so thisprobability should be a lower bound on thechance of finding a false positive BeLPT.

ResultsThe regression model and the estimationmethods were obtained through analyticreasoning and limited experience with afew data sets. To evaluate the utility of ourtwo new methods, we applied them to allavailable BeLPT assay results obtained atthe ORISE BeLPT laboratory as of July1993. The outlier rejection method in useat ORISE at that time also was applied toeach BeLPT assay.

As a preliminary step we provide ananalysis of the 12 replicate control wells ondays 5 and 7 for each of the 173 BeLPTs.Estimates of scale and location are com-puted to verify the assumed form of themean-variance relation. We then describethe distribution of estimates of the log(SI)sfor each beryllium concentration. Under thenull assumption that if an individual is notsensitized to beryllium his/her SIs should beone, and the estimates of the log(SI)s will beapproximately normally distributed with azero mean and the covariance matrix indi-cated in "Methods." The true SI for anindividual for any given beryllium concen-tration is, of course, unknown. In a popula-tion of nonsensitized individuals, the truelog(SI)s may differ from zero. Conse-quently, the distribution of estimates of thelog(SI)s presented in this 'section reflectsampling variation, possible differences inresponsiveness among individuals who arenot beryllium sensitized, and the presenceof beryllium-sensitized workers. As a matterof convenience, we may refer to the distrib-ution of estimates of the log(SI)s in thissection as a distribution of log(SI)s.

Description of the DataA total of 173 BeLPTs are used in thisevaluation. There are 133 from a group of120 workers exposed to beryllium; theremaining 40 are from persons who haveno known exposure to beryllium. The dis-crepancy between the number of test resultsand the number of beryllium-exposedworkers is accounted for by the fact that a

second BeLPT was carried out on 13workers. Ideally, there should be 56 obser-vations (well counts) for each assay, but insome cases, well counts are missing due toinsufficient number of cells or technicalerrors ("Appendix"). When an assay isincomplete, parameters are estimated (ifpossible), based on the reduced data set.

Comparison ofMoment and ResistantEstimates ofthe Coefficient ofVariation for Control WellsAn important assumption is that the stan-dard deviation of the well counts is propor-tional to the mean as implied by Equation2. Each of the 173 assays contains 12 repli-cate control wells on both days 5 and 7. Toverify this assumption, location and scaleestimates for the control wells for eachassay on days 5 and 7 were calculated.Figure 2A shows the relationship betweenthe moment estimator of location (y, thesample mean) and the moment estimatorof scale (s, the sample standard deviation)for the day 5 control wells.

The solid line is the least squares fits= 0.448y, and the slope (0.448) is an esti-mate of the coefficient of variation for day

A4000 -,

a0

cc

wco-a

C:

co~

400

Co

EcnCo

0l

3001

B Mean

6- %U~~~~~~~~10

0~~~~~~~~~

o

0-~~~~~~~~~~~~~0 w a

0 '' -XI=0 2000 4000

Median6000 8000

Figure 2. (A) Relationship between the mean, 7, andthe standard deviation, s, for day 5 control wells. Thesolid line indicates the least squares fit, s = 0.448y. 0,beryllium workers (n= 133); A, nonexposed workers(n=40). (B) Relationship between the median, y, andthe MAD, d. The solid line is the LAV fit, d= 0.34y. Thebroken lines indicate the result of applying scatterplotsmoothers to the data.

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FROME ET AL.

5. Figure 2B is a similar plot using resistantestimates of location and scale. The samplemedian (y) replaces the sample mean, theMAD estimate (6) replaces s, and LAV isused to regress & ony. The fit is & = 0.34yand the slope (0.34) is a resistant estimateof the coefficient of variation. The decreasein scatter and slope in Figure 2B reflectsthe use of resistant methods.

Figure 3 shows the relationship betweenthe resistant estimates of location and scalefor the day 5 control wells (Figure 3A) andthe day 7 control wells (Figure 3B) on alog-log scale. The solid line for day 5 inFigure 3 (A) is log& = log(O.34) + log(]),and the solid line for day 7 (Figure 3B) islogd = log(0.36) + log(f). Note that if& isproportional toy (i.e., constant coefficientof variation) then the log-log plot shouldbe linear with a slope of one. The slope ofthe least squares regression of log a onlog(y) for day 5 is 1.04 (standard error =0.04) and for day 7 the slope is 0.96 (stan-dard error = 0.03). Since neither estimate issignificantly different from 1, this supportsthe regression model assumption of con-stant coefficient of variation. The main dif-ference in the day 5 and day 7 results isthat the day 7 results are shifted to theright since the control-well counts are gen-erally higher on day 7 than those on day 5.

A50006

The median of the ys on day 5 is 1247compared with 1840 for day 7. Theseresults are consistent with the laboratoryobservation that day 7 results are generallyhigher and show greater variability thanwell counts on day 5.

Summary ofResults forThe MethodsThe three methods of analysis were appliedto the data described at the beginning ofthis section. For each method, two graphi-cal displays summarized the results. Onlythe results for the LAV method are pre-sented here since the plots for the othertwo methods were very similar in appear-ance and are available elsewhere (9).

The first graphical display (Figure 4) isa series of 12 boxplots (11,14,22) placedside by side for the log(SI)s; the horizontalaxis on the bottom shows the untrans-formed SIs. The ends of the box corre-spond to the 25th and 75th percentile sothat 50% of the log(SI)s are contained inthe box for each group. The vertical dottedlines are drawn to the nearest value notbeyond a standard span-1.5 x (inter-quartile range)-from the quartiles. Theoutlying values are shown individually foreach group of data. There are two boxplotsfor each beryllium concentration on days 5and 7. The first one in each pair is labeled

-6 -4 -2

"BW" for beryllium workers, and the sec-ond one is labeled "NE" for not exposed.Consequently, each pair of boxplots pro-vides a comparison of the distribution ofthe SIs for the beryllium group and thenonexposed group for each of the six cul-ture conditions. Consider, for example, thefirst two boxplots in Figure 4 which are forberyllium concentration 1 on day 5 (BW-D5Bel and NE-D5BeI) for the LAV esti-mates. Both log(SI) distributions arecentered near zero and the nonexposedgroup is a little more spread out in the cen-ter. The beryllium-workers group showsnine outlying values in the positive direc-tion and one in the negative direction. Thenotches (which represent confidence limitsfor the sample median) in the boxplotsoverlap, indicating that the difference inthe location of the two distributions is notsignificant at a rough 5% level. The brokenvertical line corresponds to log(SI) equal tozero and passes through both notches,indicating that both distributions are cen-tered near zero on the log scale. Each of theboxplots in Figure 4 is centered near zeroand is spread out evenly in both directions.As the beryllium concentration increases oneach day the variability (as indicated by thelength of the boxes) increases. On day 7 theSIs for the beryllium workers are generally

Log (SI)6 2 4

o '

a .C

I a y a t0

X 00

CD ° ,

0

. ..D 0. : 0

0

Gk0

. 0

. I.z 01#

0 0

,aOr . & 00

5000 10,000Median

Figure 3. Relationship between the median, y, and theMAD, Cy (C = 0.34y) for the day 5 (A) and day 7 (B)control wells (a= 0.361y) shown on a log-log scale.The broken lines show the results of applying a scat-terplot smoother to the data. 0, beryllium workers(n = 133); A, nonexposed workers (n = 40).

BW-D5Bel

NE-D5Bel

BW-D5BelO

NE-D5BelO

BW-D5BelOO

NE-D5BelOO

BW-D7Bel

NE-D7Bel

BW-D7BelO

NE-D7BelO

BW-D7BelOO

NE-D7BelOO

1/64 1/16 1/4 1 4 16 64

Stimulation index

Figure 4. Boxplots of LAV estimates of the log(SI)s for beryllium workers (BW) and nonexposed (NE) group by dayand beryllium concentration.


1000 -

500 -

100 -

gn

B

a)CDECo

CD,

co

ECo

CD,

5000 -

1000 -

500 -

100 -

50

. ...--.. .

----- ---O -. ---- _......................

..^. .........

.-...---.ct..... ........

.-------.- -

........c.

* ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ....... .........

**... .._._............}

0 500 1000

6

962


Day 5 Be 1

M= 0.066 exp(M) = 1.07S= 0.317

oO 0

o~~~~o

0a

I I

-2 -1 0 1 2

Day 7 Be 1

Day 5 Be 10

-2 -1 0 1 2

Quartiles of standard normal

Day 7 Be 10

0

__o Si

-2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2

Quartiles of standard normal

Figure 5. Normal probability plots of LAV log(SI)s. Solid lines in each plot indicates relation expected if log (SI) values are from a normal distribution with location parameterM(determines intercept) and standard deviation S(determines slope).


4-

2-

Day 5 Be 100

00-i

-2 -

-4 -

Si

Day 7 Be 100

963

FROME ET AL.

smaller that those for the nonexposedgroup, and the median log(SI)s are lessthan zero except for the NE-D7Be1OOgroup. Results on day 7 are more variablethan those on day 5 for each of the threeberyllium concentrations. We have nodefinitive experimental data to explain thelarger variability on day 7. However, con-sidering that we are conducting short-termcultures of lymphocytes without replenish-ing of medium, it is not surprising toobserve greater variability among wellswith increasing time in culture since onewould expect to see some depletion ofnutrients, accumulation of metabolicbyproducts, or scenescence of lymphocyteover time. In beryllium-sensitive persons,increasing divergence of counts betweenreplicate wells would be anticipated toresult from clonal expansion of sensitizedCD4 subsets which would be expected tobecome more pronounced with increasingnumbers of cell replications.

The second graphical display (Figure 5)shows a normal (Gaussian) probability plotfor the combined BW and NE SIs for eachof the three beryllium concentrations ondays 5 and 7 (23). In each of the six plots,the data (ordered values of the log(SI)s) areshown on the vertical axis on the left, andthe quantiles of the standard normal distri-bution are shown on the horizontal scale.Statistical theory indicates that estimates ofthe log(SI)s should be approximately nor-mally distributed, and the large samplestandard deviation should be about 0.28 ifthe coefficient of variation is 0.4 (see"Statistical Methods"). If the relationbetween the empirical and theoreticalquantiles is linear, this indicates that thedistribution is Gaussian. In each plot wehave included the median (labeled M) anda resistant estimate of the standard devia-tion (labeled S) for the log(SI)s. The solidline in each plot shows the relationexpected if the log (SI) values are from anormal distribution with median M (whichdetermines the intercept) and standarddeviation S (which determines the slope).(The values ofM and S are also shown inTable 5). Resistant methods were used toestimate the location and scale parametersfor the combined data from the BW andNE groups. This reflects the assumptionthat most beryllium workers do not showan abnormal response, i.e., they look likethe nonexposed group. For example, con-sider the plot for day 5 Be 1 in Figure 5.The log(SI)s appear to be approximatelynormal in the center. but several values arelarger than expected (these are the points

above the line). These outliers are SIs thatindicate hypersensitivity to beryllium.

The results in Figure 5 indicate that thelog(SI)s are approximately normally dis-tributed. The center of each log(SI) distrib-ution is greater that zero for each berylliumconcentration on day 5 and is less thanzero for each beryllium concentration onday 7. The untransformed SI units areshown on the vertical scale on the rightside of each plot. The estimated standarddeviations increase with beryllium concen-tration on each day, and are larger on day 7than on day 5. The estimates of location(,u) and scale (s) for each method are sum-marized in Table 5. For each berylliumconcentration the estimates from the threemethods are in very close agreement. Theboxplots and normal probability plots for

the current method and the QL methodare not shown here since they are almostidentical to Figures 4 and 5 and are avail-able elsewhere (9).

Comparison of the Current Methodand LAVMethodA direct comparison of estimates of thelog(SI)s obtained using the currentmethod and the LAV method for eachberyllium concentration is given in Figure6. The slope of the line in Figure 6 indi-cates exact agreement between the twomethods. To further compare the currentmethod and the LAV approach we use theaverage difference (avedif) of the log(SI)s.For each BeLPT the LAV log(SI)s are sub-tracted from the corresponding log(SI)sbased on the current method. The result is

Table 5. Median estimates (jY) and resistant estimates (I) of the standard deviation (shown in parentheses) ofIog(SI)s for BeLPT data.

Day 5 Day 7Method Be 1 Be 10 Be 100 Be 1 Be 10 Be 100

Current (Aj) 0.069 0.104 0.280 -0.191 -0.330 -0.163(1j) (0.300) (0.568) (0.802) (0.514) (0.857) (1.066)

LAV (Aj) 0.066 0.152 0.284 -0.211 -0.388 -0.139(1j) (0.317) (0.531) (0.770) (0.599) (0.883) (1.113)

QL (Qj) 0.049 0.102 0.258 -0.211 -0.375 -0.226(1j) (0.337) (0.561) (0.795) (0.665) (0.918) (1.155)

o 2 -

4 -

0Eo4- -

am

0

-2

= -2 -

-4

4.-

-0

E

-4

-2

-4

4-

2 -

0 -

-2 -

-4 -

LAV method

Day 7 Be 10

-4 -2 0 2 4

LAV method

4-

2-

0-

-2 -

-4 -

Day 7 Be 100

I

-4 -2 0 2

LAV method4

Figure 6. Comparison of current outlier rejection method and LAV logSIl)s for each Be concentration.



multiplied by 100 and the average differenceis calculated, i.e.

avedif 12 = mean[100 * (f3cM - 1.6]

For example, for AC147 (Table 6), the cur-rent method day 5 BelOO SI is exp(1.41) =4.10 and exp(1.45) = 4.26 for the LAV pro-cedure. The log percent (L%) difference is100 x log(4.10/4.26) = 100 x (1.41 - 1.45)= - 4L% where L% stands for the logarith-mic percent (24). The SI for the currentmethod is 96% of the LAV SI, i.e., about4% smaller. The average difference betweenthe current method and LAV method forAC117 is -1.7L%. Table 6 comparesAC147s log(SI)s for all three methods.

Figure 7 (left panel) shows a boxplot ofavedifl2 (as defined above) for the 173BeLPTs. The average difference is between

Table 6. Comparison of log (SI)s for patient AC147.a

-3L% and 9L% 50% of the time and themean of the average difference is 3L%. Alarge, positive value of avedifl2 indicatesthat the current method log(SI)s for aBeLPT are greater than the LAV log(SI)s.The results in Figures 6 and 7 and Table 5show that the estimates of the log(SI)s forthe LAV and current method are in veryclose agreement.

Comparison ofResistant Quasi-Likelihood Method and LAV MethodThe plot ( not shown) of the QL and LAVlog(SI)s was almost identical to Figure 6.The close agreement between the twomethods is further demonstrated by theaverage difference

avedif32 =

mean[100 * (lBQL - 'L0 j = 1.6].

Day 5 Day 7Method Be 1 Be 10 Be 100 Be 1 Be lOb Be lOOb

Current 0.33 1.83 1.41 -0.17 1.86 1.81LAV 0.26 1.85 1.45 -0.01 1.81 1.81DL 0.16 1.67 1.39 -0.03 1.72 1.67100 *- CM-LAV) 7 -2 -4 -16 5 0100 * (QL -LAV) -10 -18 -6 -2 -9 -14

aDetails presented in Frome et al. (9), Appendix E. bThe last two rows are in L% units.

60-

40-

20-

=a)

0)

0-J

0-

-20-

-40-

-60-

60-

40-

20-

0-

-20-

-40-

-60-

Current vs LAV OL vs LAV

Distribution of average difference of log(SI)s

Figure 7. Distribution of average difference of log(SI)s.

where a large positive value indicates thatthe QL log(SI)s for a BeLPT are greaterthan the LAV log(SI)s. Figure 7 (rightpanel) shows a boxplot of these values. Theaverage difference is between -6L% and3L% 50% of the time, and the mean of theaverage difference is -0.6L%.

Figure 8 compares the distribution of0 L(the LAV coefficient of variation) andQ (the QL coefficient of variation). For

both methods, the estimated coefficient ofvariation is between 0.25 and 0.40 most ofthe time. The median value of L iS 0.321and the median value of Q is 0.329.

Identification ofBeLPTs with UV SIsThe first step in the alternative method isto convert each log(SI) into a standardizeddeviate (Equation 7) using the values of Ujand ij given in Table 5. These standardizeddeviates are compared with the quantiles ofthe standard normal distribution, i.e. Pr[u< zp] = p. If at least two of these u,s exceedzp that BeLPT is called abnormal. Theresults (i.e. the u11s for the abnormalBeLPTs ) of applying this procedure to the173 assays using zO975 = 1.96 are shown inTable 7. In particular. the standardizeddeviates for the LAV log(SI)s for AC147(Table 6) are given in row 2.

An alternative to calculating standard-ized deviates for each log(SI) is to calculatecritical value for each SI

SI; = exp(,t7i + zp j), j=1.6.

The critical values obtained using fj andfor the LAV method in Table 5 are shownin Table 8. If a patient's SI exceeds the cor-responding critical SI, that SI is consideredlarge. Thus, if any two SIs exceed the cor-responding critical SI, that patient's dataare considered abnormal. For example, theLAV SIs from Table 6 (patient AC 147) are1.27, 6.36, 4.26, 0.99, 6.11, and 6.11.

C ------------ ---------------

0 , W **

0.2 0.4 0.6 0.8

Figure 8. Comparison of QL and LAV coefficients ofvariation (ls).


T

I+

t

I +~~

II

965

FROME ET AL.

Table 7. Values of the standardized deviates (u,js) for BeLPTs with at least two > Z0.975.Day 5 Day 7

Be 1 Be 10 Be 100 Be 1 Be 10 Be 100ID u u2 U3 U4 U5 U6L

AC128 2.10 0.65 2.11 -1.23 -0.63 0.49 0.30AC1479 0.61 3.21 1.52 0.33 2.48 1.75 0.26AC161 u 9.61 6.81 5.95 8.33 5.91 4.74 0.42AC171 u 2.47 2.53 2.22 1.90 2.45 2.21 0.18AC174U -0.13 3.22 2.40 -0.50 1.42 1.07 0.27AC182 0.87 1.20 1.73 3.45 2.17 0.70 0.33AC187 3.74 1.96 -0.61 1.62 0.07 -0.98 0.71AC196U 9.08 5.25 2.07 6.50 3.16 2.08 0.38AC208U 5.76 2.15 0.91 4.38 1.04 0.72 0.42AC209 3.79 0.96 1.99 2.55 1.82 1.63 0.43AC218 5.28 -0.07 -0.72 2.75 -1.16 -1.07 0.40AC225U 4.81 4.75 1.47 4.32 1.73 1.03 0.82AC235t 5.17 2.23 2.62 2.71 -0.27 1.59 0.39AC236t 10.04 6.34 3.70 3.15 1.46 0.73 0.21

lDs marked with t were identified as abnormal by the CABST method (Section 3.5) and those marked with u wereunsatisfactory. One BeLPT (AC149) called abnormal by the CABST method does not appear in this table.

Table 8. Critical SI values.

Day5 Day7Be 1 Be 10 Be 100 Be 1 Be 10 Be 1002.00 3.30 6.00 2.62 3.83 7.72

Since the day 5 Be 10 SI (6.36) and theday 7 Be 10 SI (6.11) exceed their respec-

tive critical SIs, these data are deemedabnormal. Regardless of the formulationused (calculating the standardized deviatesor comparing the SIs to critical SIs) theconclusion is identical.

The CABST procedure currently usedat ORISE to identify workers with largeSIs is based on the distribution of themaximum SI for each individual in thenonexposed group (Equation 6). A BeLPTfor a beryllium worker is defined as abnor-mal if at least two SIs exceed SI* (currentlyequal to 5.65). This leads to the identifica-tion of patients AC147, AC149, AC235,and AC236 as abnormal. Using the outlierrejection method, six BeLPTs that hadtwo or more SIs greater than 5.65 were

found to be unsatisfactory based on thevalues of the within-group CVs. They are

patients AC161, AC171, AC174, AC196,AC208, and AC225. Three of the abnor-mal BeLPTs are listed in Table 7 (onlyAC149 is missing). Table 7 also lists fiveBeLPTs as abnormal that were not identi-fied by the current method as eitherabnormal or unsatisfactory.

In situations in which there may beexcess variability, the CV can be used to

evaluate the quality of the BeLPT. For theLAV approach L is a resistant estimate ofthe "within-group" standard deviation ofthe log well counts. Since L is not inflatedby a few outliers (that could be caused bymeasurement error), it may be reflectingsome intrinsic biological variability associ-

ated with the lymphocyte proliferationresponse in certain cell donors. Figure 9shows a normal probability plot forlog(0 L). The resistant estimates of themean and standard deviation of log(O L) are

-1.136 and 0.285. From this we compute

the 99th percentile O* = 0.623. The fiveBeLPTs in our database that have valuesof L > 0.623 are AC242, AC223, AC187,AC211, and AC225.

ConclusionsThree approaches to the analysis of theBeLPT have been described. The firstmethod is the outlier rejection procedure(in use at ORISE in July 1993), and two

new methods (LAV and QL) are basedon resistant regression techniques. Eachmethod was applied to a database of 173BeLPTs (133 from beryllium workers and40 from individuals with no berylliumexposure). Graphical and numerical sum-

maries show that the three methods are

generally in very close agreement. Both ofthe new methods are highly resistant to

outliers (in the well counts), have well-known statistical properties, and provide a

"pooled" estimate of the coefficient ofvariation (0) for each BeLPT. The QL

-0.5 -

>-1.0 -

-j-1.5 -

-2.0 -

-2 -1 0 1

Quantiles of standard normal

- 0.60

- 0.40

- 0.25

- 0.15

2

Figure 9. Normal probability plot of log ('L)-

method requires an iterative algorithm anddoes not appear to offer any practicaladvantage over LAV. The LAV method isalso easy to understand and compute andis recommended for routine analysis ofthe BeLPT.

Estimates of the log(SI)s are approxi-mately normally distributed. The log(SI)distributions are centered near zero foreach of the three concentrations of BeSO4on harvest days 5 and 7. The variabilityis greater on day 7 than on day 5, andincreases with concentration on each day.Resistant estimates of the location andscale parameters for each of the six log(SI)distributions are used to define large SIs,which are used to identify abnormalBeLPTs. Results of this preliminaryapproach to identify abnormal BeLPTswere compared with results obtained usingthe current method, and the discrepanciesbetween the two methods suggest that a

more detailed evaluation of the procedureis needed.

In a subsequent report further consider-ation will be given to the use of the LAVapproach to address the following ques-

tions: a) How should "abnormal" BeLPTsbe identified? b) Should a BeLPT be con-

sidered unsatisfactory as the result of highvariability? c) How should the resistantestimate of the coefficient of variation (OL)be used in the BeLPT analysis?

The methods developed will beapplied to a much larger database ofBeLPTs obtained from the ORISE BeLPTlaboratory and at least one additional labo-ratory that is currently using this assay to

identify persons who may have CBD. Thedata set used in this report and an elec-tronic version of ORNL-6818 (9) are

available on the world wide web at URLhttp://www.epm.ornl.gov/-frome/


M=-1.136S= 0.285

0

966


Appendix: Detailed Protocol For BeLPT

The ORISE protocol for performinglymphocyte proliferation assays essentiallyadheres to the recommendations of theexpert panel (i.e., CABST) convenedjointly by the U.S. DOE Office of Healthand the Beryllium Industry ScientificAdvisory Committee (BISAC) at a meetingheld in Washington, DC, on February3-4, 1992. We collect approximately 30ml of venous whole blood in sterile vacu-tainers containing sodium heparin for eachassay (Figure 1, text). Tubes are inverted tomix blood with the anticoagulant andtransported to the laboratory for process-ing. Cells are maintained at room tempera-ture overnight. Within 24 hr after bloodcollection. mononuclear cells are separatedusing Ficoll-hypaque density gradient cen-trifugation, carried through three sequen-tial washes and counted in triplicate on anautomated cell counter. Lymphocytes arecultured in RPMI 1640 culture medium(GIBCO Grand Island, NY) buffered withHepes salts, and supplemented with 2 mM/-glutamine, 100 units/ml penicillin, and100 pg/ml streptomycin. Pooled humanserum is added at a final concentration of10%. We are using 96-well, flat-bottommicrotiter plates and a final cell concentra-tion of 2.5 x105 cells per well contained in0.2 ml volume of medium.

Beryllium sulfate ([BeSO4], Brush andWellman, Elmore, OH, 99.9% purity) inconcentrations of 1, 10, and 100 pM isused to evaluate donor lymphocyte hyper-sensitivity to Be metals. As positive con-trols we use concanavalin-A (10 pg/ml) andphytohemagglutinin (30 pg/ml). For eachset of exposures, quadruplicate wells areevaluated to obtain estimates of lympho-cyte proliferation response. Unstimulatedcontrol wells are run in replicates of 12because other laboratories have observedconsiderable variability in rates of tritiatedthymidine incorporated in the controlseries, and extra replicates are needed toachieve the required levels of statistical con-fidence. All cells are incubated at 37 +0.5°C in an atmosphere of 5% CO2 in air.Cells assayed for response to Be are har-vested at 5 and 7 days with a terminal 6-8hr pulse of 1.0 pCi of tritiated thymidine(specific activity 6.7 mCi/mM). We areusing a Packard 96-well cell harvester(Packard Instruments, Downer's Grove,IL) that deposits lymphocytes from eachindividual well on a standard glass filterpaper; the lymphocytes then can be

counted intact on the Packard Matrix 96gas ionization counter, or punched for assayusing a liquid scintillation counter. TheMatrix 96 unit is less efficient in detectingbeta decays than scintillation counters buthas the great advantage of simultaneouslydetecting beta radiation emissions from all96 wells. Statistical accuracy can be achievedquite readily by increasing counting timeusing this instrument.

Quality ControlExcess variability in counts between repli-cate wells within a treatment, i.e., outlierscould result from technical errors in initiat-ing the tests, or possibly from intrinsicbiological variables associated with thecharacteristics of lymphocyte proliferationresponse in certain cell donors. Sources oftechnical error might include mistakes inpipetting, such as failures to add appropri-ate numbers of cells to individual wells,lack of addition or double addition oftritiated thymidine to specific wells, or

improper washing of filters resulting inresidual counts of unincorporated thymi-dine, or smearing of radiolabel across thefilter paper.

Stringent methods for quality controlare used routinely to guard against inadver-tent technical errors. To minimize the riskof pipetting errors, all media and other testreagents are delivered to complete rows orcolumns of the test plate using electronicmicropipetters that deliver up to 8 or 12aliquots simultaneously. Thus, it is notlikely that the operator could "loose herplace" in adding reagents. Cells are har-vested onto the surface of filter paper usingthe 96-well harvester, which simultaneouslyaspirates the cellular contents from eachwell. To ensure complete washings of cul-ture plates, a wash volume of approxi-mately 10 times that recommended by themanufacturer is used. For all tests, we rou-tinely leave all wells in rows A and Hempty as a quality control measure to allowevaluation of background counts on boththe top and bottom of the filter paper.Erratic or high counts in these empty wellswould signal incomplete washing of plates

1 2 3 4 5 6 7 8 9 10 11 12A

B

C

D

E

F

GH

......... ... es X e ;ccc ccl llll llll l

........}......... .: 'i..':....

F!r. ll_

: ===w | ||| , __1 2

A P PHA....... ......

B l4IA .PHAC PHA

D P PHAE | ConA

F 11 13ConAG 'an ConA

H Conk ConA

3 4 5 6 7 8 9 10 11 12

Figure Al. ORISE plate maps for BeLPT assay. *Beryllium sulfate 1, 10, 100 pM solutions.

Environmental Health Perspectives - Vol 104, Supplement 5 * October 1996 967

FROME ET AL.

or "smearing" or radioactivity from onewell to another.

Filter papers are counted intact on theMatrix 96 gas ionization counter, whichsimultaneously records counts and counts-per-minute with attendant errors for eachwell. Because the matrix counter is a gasionization unit, only those beta decays thatare emitted at right angles to the surface fil-ter pad are detected and recorded. Thus,the sensitivity of the instrument in detect-ing counts is considerably less than that ofa liquid scintillation counter (about 20%of emissions are detected using the gas ion-ization unit). For this reason, all plates arecounted for longer periods to accumulateenough counts for statistical accuracy.Routinely, all plates containing controlwells and wells challenged by berylliumsalts are counted for 30 min, whereas mito-gen-stimulated positive controls arecounted for 10 min each.

To allow direct comparisons of lympho-cyte proliferation response between differentblood donors, we routinely initiate 5-dayand 7-day tests on lymphocytes from threeseparate donors on a single test plate. Theplate map that is routinely used at ORISEis shown in Figure Al. Cells from threepersons are cultured on the same microtiter

1 2 3 4 5 6 7 8 9 10 11 12

1-A: 57 47 48 52 126 68 99 69 27 37 36

1-B: 515 881 489 303 191 260 673 382 1300 1451 3353 127

1-C: 535 742 1602 676 310 420 251 669 2850 1368 634 1478

1-0: 923 570 510 568 253 550 333 439 540 1654 1487 1330

1-E: 17700 10749 19080 18855 696 372 270 434 1236 1991 1173 1743

1-F: 19197 27501 27280 31033 286 383 758 1369 1175 1591 1617 1877

1-G: 21083 38090 45938 29685 454 428 366 654 1772 2415 2766 3737

1-H: 41 63 52 75 66 83 91 43 49 44 31 24

Figure A2. Typical printout sheets of data from three individuals.

plate. Cells from patient 1 are pipetted intocolumns 1 to 4; cells from patient 2, intocolumns 5 to 8; and cells from patient 3,into columns 9 to 12. Rows A and H areleft blank to monitor background counts inthe culture system. Rows B, C, and D arereplicate sets of control wells, whereas rowsE, F, and G contain beryllium concentra-tions of 1, 10, and 100 pM, respectively.The lower half of the figure demonstratesthe platemap for initiating cultures withphytohemagglutinin or ConA.

An example of a typical printout ofdata from three different individuals isshown in Figure A2. The test is a 5-day

plate, counted for 30 min. Data are shownas total counts. Patient 1 displays a pro-nounced response to all three levels forberyllium-challenged wells, whereas patient3 demonstrates higher levels of counts incontrol wells but also demonstrates noresponse to beryllium. Direct comparisonsof data among the three persons can bereadily made from a single printout sheet.This approach allows comparisons ofcounts within replicate treatments for lym-phocytes from the same donor, as well ascomparisons of inter-individual variabilityin counts between different subjects.

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968 Environmental Health Perspectives * Vol 104, Supplement 5 * October 1996

statistical methods for the blood beryllium lymphocyte proliferation

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