biplots applications

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TOXICOLOGY AND APPLIED PHARMACOLOGY 72, 9 I- 10 1 ( 1984)

Application of Biplot Methods to the Multivariate Analysisof Toxicological and Pharmacokinetic Data

JANET S. SHY-M DJESKA, J. EDMOND RIVIERE,~ AND J OHN 0. RAWLINGSLaboratory of Pharmacology and Toxicology, School of Veterinary Medici ne and Interdisciplinary Toxicology

Program, and Department of Statistics, North Carolina State University, Raleig h, North Carolina 27606

Received April 30, 1983; accepted August I, 1983

Application of Biplot Me thods to the Multivariate Analysis of Toxicological and Pharm acokineticData. SHY-M DJESKA, J . S. , RMERE, J . E. , AN D RAWLINGS, J . 0. ( 1984). Toxicol. Appl . Pharmacol.72, 91-101. The biplot technique wa s applied to aminog lycoside renal toxicological and phar-ma cokine tic da ta in beagles. The biplot obtains a two-dimen sional approximation to a ma trixand plots row effec ts and column effe cts ointly, depicting relationships amon g different obse rvedvariables and simultaneo usly showing the relationship of experimen tal units as individuals andas treatme nt g roups to those variables. This graphical representation of the matrix allows inspectionof relationships, trends, clusters, approxima te correlations, and variances existing in the data.Biplots w ere generated from ge ntamicin dosage regimen neph rotoxicity data. Six dogs classifiedas being intoxicated by established indicators of renal to xicity were a distinct cluster. A clusterof nonintoxicated dogs was separated into two groups approximat ing nephrectomized and normaldogs, thus revealing variables signihcant in sep arating toxic and nonto xic as well as nephrectom izedand normal dogs. Biplots from pharm acokinetic data were able to separate different renal diseasestates on the basis of disease- induced changes in gentamicin pharmacokinet ic parameters. Inconclusion, the biplot technique proved to be a very useful tool in exploring this type of databy revealing clear relationships betwee n neph rotoxicity and physiological and pharm acokineticvariables and by separating different disease state s based on these data.

The biplot is a graphical multivariate statisticaltool which displays a two-dimensional ap-proximation to a data matrix of samples andvariables and allows for a visual examinationof the structure of the data. A single graphcan depict relationships among different ob-served parameters, (i.e., clinical pathologicdata, histopathologic scores, and pharmaco-kinetic constants) and simultaneously illus-trate the relationships of experimental unitsas individuals and as treatment groups to eachother and to these parameters. The technique,based on a singular value decomposition of

the data matrix, allows visual inspection ofpatterns existing in the data (e.g., relationships,trends, and clusters) as well as approximatecorrelations and variances (Gabriel, 197 1,1972). Although this technique has been published in some fields (Gabriel, 1972, 198 1;Strauss et al., 1979), it has not been extensivelyutilized in toxicology (Tepper et al., 1982) al-though other multivariate techniques haveproved to be of value (Gad and Weil, 1982).It is the purpose of this paper to demonstratethe application of the biplot technique to tox-icological and pharmacokinetic data throughthe analysis of the nephrotoxic potential and

Laboratory of Pharmacology and Toxicology. pharmacokinetics of the aminoglycoside an-* Address corresponden ce and reprint reque sts to tibiotic gentamicin in dogs with experimen-Dr. J. E. Biv iere. tally induced renal insufficiency. The biplot Department of Stat is t ics. was particularly useful in analyzing a com-

91 0041-008X/84 $3.00Copyright 0 1984 by Academic Press Inc.All rights of reproduction 1 any for? rewned


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92 SHY-MODJESKA, RIVIERE, AND RAWLINGSposite set of data previously reported in in-dependent studies (Riviere and Coppoc,1981a,b; Riviere et al., 1981; Riviere, 1982a).In spite of the complex influence of kidneydisease on the detection of nephrotoxicosisand on the elimination of drugs from the kid-ney, a clear relationship between nephrotox-icity and both physiological and pharmaco-kinetic parameters was seen.

METHODSDescription of Biplot Ana lysis

The technique of biplotting uses the singular va lue de-comp osition (SVD) of a ma trix to give a graphical displayof its two-dimen sional approxim ation. The approximationobtained by using the first and second singular value co m-ponents of a matr ix is the best possible two-dimensionalapproximation in the least-squares sense (Gabriel, 1972).In our analysis, the m X n matr ix Y consist ing of nvariables observed on each of m experimental animalswa s standardized by correcting e ach variable (column) forits mean and dividing by its standard d eviation to givevar iables of uni t var iance. This new matr ix X wa s usedas he input ma trix for Gabriels biplot analysis to com putethe first four singular values (X3 and singular vectors

(yk, Rk ), k = 1, 2, 3, 4. The reader is referred to Gabriel(1972) for the details of these com putation s. The biplotis especially use ful if the first two principal comp onen tsaccount for most of the total variabil ity:

where n = rank of ma trix. Total variabiity is mea suredhere as the sum o f sum of squares for each variable. Sinceall variables we re standardized , the sum o f squares foreach is equal to its degrees of freedom , m - 1, andC xf = n(m - 1) . Row constants, y l r, and column con-stan ts, X~W ~, were then plotted jointly as tlr i vs t)ri and ash,w,- vs X2w2j, respect ively, for i = 1, 2, . . . m and j= 1,2, * - - n. Column vectors were constructed by draw-ing l ines from the origin (0,O) to their end points (Xl Wrj,X,w,) . Row vectors were lef t as points (Ur i , ~r i) . This two-dimensional plot is the best two-dimen sional represen-tation of the original n-dimensional space defined by thedata matr ix , i .e. , a maxim um proport ion of the dispers ionin the original space is retained and the rank two m atrixrepresented by this plot is the best rank two approximat ion,in the least-squares sense, of the original rank n m atrix.The biplot reveals the structure of the data insofar as itcan be represented in tw o dimensions. I f two dimensionsare inadequate, more biplots can be used to study thethird, fourth, e tc. dimen sions.

For i l lustrative purpose s, an idealized b iplot is presentedin Fig. 1. Each plotted vector re presents the projection ofFirst principal component for rows

10.0

First principal component for columnsFIG . 1. Idealized biplot of data ma trix.


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APPLICATION OF BIPLOT TO TOXICOLOGY 93a variables original vector onto this two-space and eachpoini X represents an experimen tal unit. Since all thevecto rs are of equal len gth, m - 1 in n-space , the relativelengths of the plot ted vectors ref lect the c loseness withwhich they fal l in this two-space. Had the var iables notbeen standardized before the analysis, the relative leng thswould include differences in variances. Angles betweenvecto rs represent approxima te correlations with small acuteangles showing high positive correlations betwee n variables(e.g., a and b ), right angles showing correlations of 0 (e.g.,b and c), and large obtuse angles showing high negativecorrelations (e.g., e and b) (- 1 6 r C 1 ). Cluste rs of pointswould represent experimental units with similar parametervalues. Perpendicular projections of the points onto an yvector approxima te the relative values of these . experi-mental units for that variable.

Sample Data Sets

Nephrotoxicity. Twen ty-four adul t female beagles weresubtotally neph rectomized (3/4 or 7/8) and assigned toone of four gentamicin dosage regimens so that meanpretreatment serum creatinine 2 weeks postsurgery wasas balanced as possible among treatments (Table 1). (Ri-viere et al., 1982). All four treatm ent groups containedapproxim ately equal numb ers of high and low serum cre-at inine. A f i f th group of s ix dogs, wi th intact k idneys, w asassigned to the standard dosage regimen.Renal funct ion was assessed n all dogs by the followingmethod s: serum creat inine (SCR), serum urea ni trogen(SU N), 24-hr endogenou s creatinine clearance (CLJ, ureaand free wate r clearances (Cl,,, Cl&, and fractionalsodium and po tassium clearances (CINa, Clx) .Renal c learances of al l substances were calculated ac-cording to the formula:

Clearance = i&V/P, (ml/min)where Ux = ur inary concentration of compound X, P,= serum concen tration of compo und X, and V = urineflow (ml/min ). Fractional electrolyte clearan ces were cal-

TABLE 1EXPERIMENTAL DESIGN

Dosage egimen nD W Interval Nephrec-Treatment h/kg) (hr) tom&d Normal

Standard 3 8 6 6Fixed interval 1.5 or 1.0 8 6 -Fixed dose 3 16 or 24 6 -Control none none 6 -

a Time between successive osesdur ing the 14day treatmentperiod.

culated by dividing the electrolyte clearance by the si-multaneously determined CL, and expressed as a per-centage. Freewater c learance w as calculated by subtractingthe osmo lar clearance from the rate of urine production.All clearances used in the a nalyses were the average oftwo 24-hr determinat ions, normal ized to body weight.During drug dosage , peak (30 min postdosing ) andtrough (imme diately prior to next dose) gentam icin con-centrat ions were determined in al l dogs on D ays 1, 4, I 1.and 14. The daily elimination rate cons tant (Kel) wa sthen calculated according to the formu la:

Kel (hr-) = In peak (&ml) - In trough (&ml)dosing interval - 0.5 hrwhere pe ak and trough are defined as before. In additionthe ratio o f the first and last Kels w as calculated:

Kel( 14) Kel of Day 14 of t reatment-zKel( I ) Kel of Day I of t reatmentFollowing the final asse ssm ent of renal function , dogswere euthanized and necropsied. Renal t issue samples

were collected and prepared for l ight microscopy: histo-logical section s were examine d to quantib the degree ofinterstit ial neph rit is, tubular necro sis, tubular dilatation.and tubular regeneration b y assigning values from 0through 5 for severity of the condition. A histopathologicscore (0 to 20) was def ined for each beagle as the sum ofthese individual score s. Established indicators of genta-mic in toxic i ty were considered to be increased SCR , SU N,CINa,and CIK, decreased CL, and low KeI rat io (Schentag,1982; Cronin et al.. 1980; Brinker et al., 1981; Lufi ctal., 1978).The first biplot (Fig. 2) was based on the 29 dogs havingcomp lete da ta for all variables: histopathologic score, Kelratio, and a transforma tion on the magn itude of changeof the 7 physiological param eters from pre- to postdrugadm inistration. The transforma tion of the data giving thelargest separation amon g dosage regime ns, i.e., the trans-format ion with the highest F ratio for treatments froman analysis of variance of a randomized incomplete blockdesign, was chosen for each variable: log (post Cb,/preC4A pre Cl, , -post Ck , log (post &/pre CIK ), log (postSCR/pre SC R), post SUN /pre SU N, preCI, , -postc l , , .and log (post CI&pre Cl&.The second biplot (Fig. 3) was based on the sam e 29beagles and 9 variables but w ith the 7 physiological pa-rame ters recorded as direction of change from pre to post(+ 1 if post-pre > 0, - 1 if post-pre < 0, and 0 if post= pre). Both data sets were standardized before a nalysis.Correlations among the 9 var iables were computed forboth data setsby Proc CORR in Stat is t ical Analysis System(SAS, 1979), and c lusters among the 29 dogs were com-puted by Proc CLU STE R in SAS to conf i rm relationshipssugge sted in the biplots.

Pharmacokinetics. A second data set consist ing of 8pharmacokinet ic parameters(ClB, @, Vs,, Vd(-), V,, Klz,


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94 SHY-MODJESKA, RIVJERE, AND RAWLINGSFirst principa l comp onent for anim als

0.20 0.40. -0.40 -0.20 0.0

0.60-

0.40

cIK* - 0.40

- 0.20Kek/Kel i

0. 0

-0.40-

- -0.40-0.60-I +I 1 1 1 I r I-0.60 -0.40 0.0 0.40 0.60

First principa l co mpon ent for physiologic 6pharmacologic parameters

FIG . 2. Biplot of transforme d physiologic data, Kel ratio, and histopathologic index. R& = 76%. A, Toxicdogs, 0, nontoxic nephrectomized dogs, l , nontoxic dogs with intact k idneys, * , t ransformat ions of var iables.

K2,, Kel) and Cl, for 23 beagles wa s also analyzed by the The param eters obtained by nonlinear regression analysisbiplot technique . T hese data were obtained from a nalysis were then f i t to a two-compartmen t open pha rmacokinet icof the serum gentamicin decay curve af ter a s ingle iv dose model by methods previously descr ibed (Riv iere and Copof drug was administered; samples were col lected for 6 pot, 1981a; Riviere ef al.. 1983). Six of the dogs whichhr and analyzed for gentamicin by radioimmunoassay. were nephrectomized (7/8,3/4) had received the standard

First prlnclpa l co mpo nent for anhnd r.4a

I

1- 0 .6 0 0 .0 0.60

First principa l comp onent for physiologic Lpharmacokinetic parameters

FIG. 3. Biplot of direction of change of physiologic data, Kel ratio, and histopatholog ic index. R$ , = 69%.A, Toxic dogs, 0, represents nontoxic nephrectomized dogs, 0, nontoxic dogs with intact k idneys.


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APPLICATION OF BIPLOT TO TOXICOLOGY 95dosage regimen and we re part of the previously describedexperimen t (see data above ). Seventee n additional dogs,not part of the previous e xperime nt, were also uti l ized:10 were considered to be normal (Riviere and Copp oc,198 1a; Riviere, 1982a), 4 had glomeruloneph ritis (Riviereet al., 198 I), and 3 had cathete rs surgically imp lanted inthe left lateral ventricle of the brain for determination ofgentam icin concen trations in the cerebral spinal f luid(CSF) (Riviere and Coppoc, 1981b).Because f ive beagles had no Cl, data, this parameterwa s eliminated from the first biplot on this data se t, eavingjust pha rmacokine tic data to be analyzed for all 23 dogs(Fig. 4).

The subse t of 18 dogs containing information on all 9var iables consisted of 8 normal, 6 nephrectomized, and4 glomeruloneph ritis beagles. Biplots were construc ted forthe normal d ogs; normal and nephrectomized dogs; andnorma l, neph rectomized. and glomeruloneph ritis dogswith a subset of the 9 var iables: C&, Vss, Vc, and Cl,(Fig. 5). The se pharm acokinetic variables were selectedbecause they are the model independ ent, primary phar-macokinet ic , parameters.

The four data sets used to generate these biplots werestandardized before analysis, and correlations amon g thefour sets of var iables were again computed with ProcCO RR in SAS for ver i ficat ion of correlat ions shown bythe biplots.

RESULTSNephrotoxicity

The biplot analysis of transformations ofmagnitude of change of physiological param-

eters, Kel ratio, and histopathologic scores hada rank 2 goodness of fit of 76% (I?$) = 76%)(Fig. 2). High positive correlations are seenbetween Kel and Q,, SUN and SCR, andSCR and histopathologic scores (p significantlydifferent from 0 at p < 0.05). The correlationbetween Clk and Cln,o and between CIN, andCl,,, is not significantly different from 0. Cor-relations approaching - I exist between SCRand CL,, histopathologic score and Kel, andbetween Clk and CIN, (Table 2). Vectors fallingon the right-left axis (SUN, SCR, histopath-ologic score, kel ratio, and C&J define a pri-mar-y axis and form a highly correlated set ofvariables. Vectors to the right of center (Kelratio and Cl,,) and those to the left of center(SUN, SCR, and histopathologic score) arehighly correlated among themselves but arenegatively correlated to each other. They ap-pear to separate the dogs into two clusters. Acluster analysis (Proc CORR) grouped thesame six dogs into a distinct cluster and theremaining 23 dogs into another cluster. Thegroup of six dogs had physiological and phar-macokinetic alterations consistent with thosepreviously associated with aminoglycosidenephrotoxicosis and were therefore classifiedas toxic dogs; similarly, the 23 dogs wereclassified as nontoxic (Tables 3 and 4). The

First prmcipal component for animals-0.50 -0.25 0.00 0.25 0.50I I 5 I 1d

4.0-

First principal Componenl for pharmacokmehc parameters*IG. 4. Biplot of pharm acokinetic data. Rc2) 75%. 0, Normal dogs, A, nephrectomized dogs.spinal f luid dogs, X, glomeruloneph ritis dogs . 0, cerebral


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F~rsl prmcipal component for animals

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-2 3. Ci?-

2 2. 0lk iE2c 1.cCL5 0.cF2 -1.czlEx -2.az.a2 -3.c'CP2 4.08fz 3.0

2. 01. 0

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-3.0 -1.0 1 .o 3. 0I I II.40 I I I-0.20 I I I0. 0 I0.20 0.4

C0 xx vs

VXC

T

0000 O CICR

0.60

04 00.20

-0.40-0.60

0.60

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-0.10

-0.30-0.50

-4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4. 0first principa l comp onent for pharmac okinetic parameters

FIG. 5. (A) Biplot of pharmacokinet ic data for normal dogs. R,, -- 83% . 0, Norma l dogs. (B) Biplot ofpharmacokinet ic data for normal and nephrectomized dogs. R& = 93%. 0, Normal dogs, A, nephrectomizeddog s. (C) Biplot of pharm acokinetic data for norma l, n ephrectom ized, and glomeruloneph ritis dog s.R$) = 93%. 0, Normal dogs, A, nephrectomized dogs, X, glomerulonephr it is dogs.96


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APPLICATION OF BIPLOT TO TOXICOLOGY 97TABLE 2

CORRELATION COEFFICIENTS OF TRANSFORMED PHYSIOLOGICAL ANDPHARMACOKINETIC DATA AND HISTOPATHOL~GIC INDEX

SCR CI , SUN Cl , , Cl , , clK Histo Ke lSC R 1.00 -0.76 0.79 0.29 -0.44 -0.70 0.51 0.82 -0.76CL, 1.00 -0.52 -0.3 1 0.54 0.61 -0.47 -0.78 0.63SUN 1.00 0.20 -0.32 -0.69 0.55 0.54 -0.54Cl , 1.00 -0.44 0.02 -0.36 0.32 -0.24Cl,, 1.00 0.16 0.07 -0.59 0.53Ch, 1 oo -0.75 -0.50 0.45 iC l, 1 oo 0.42 0.31Histo b 1 oo -0.83Ke l 1.00

All variables transforme d as defined under Me thods . Histopatho logic score . r significantly different from 0 at p < 0.05.

top-bottom axis (Clx , Cl,,, CIHZO, and Cl,,)is only partially correlated to the right-leftaxis. Correlations among these variables arenear 0 and - 1. The nontoxic dogs are begin-ning to be separated into groups approxi-mating those that were nephrectomized andthose s ix that were not.Direction of change of physiological pa-rameters, histopathologic score, and Kel ratio,when subjected to a biplot analysis, gave awider separation among toxic, nontoxic, ne-phrectomized, and normal dogs and an R$,

TABLE 3PHusro~ocrc, PHARM ACOKIN ETIC, AND HIST~-PATHOLOGIC PARAM ETERS IN TOXIC Dots (n = 6)

Parameter Pre PostCLSC RSU NCl?&ClKKel ratioHistopathologicindex

0.67 (0.11) 0.44 (0.14)1.87 (0.25) 4.27 (1.23)40.83 (7.83) 72.17 (19.77)0.95 (0.10) 1.51 (0.31)27.98 (4.86) 61.32 (22.97)NAb 0.48 (0.07)

NA 10.50 (0.56)a Mean (SE).b NA, Not appropr iate.

= 69% (Fig. 3). The same six dogs stil l groupedtogether in the biplot and the cluster analysesand again were classified as toxic, while mostof the non-nephrectomized dogs fell in anothercluster, and the remaining nephrectomized(nontoxic) dogs fell in a third cluster. (WhenR& is low, the biplot procedure can be ex-tended to include more dimensions.) Highpositive correlations exist between SUN andClx, SUN and CIN,, Clx and CIN,, and Keland C&,. Negative water clearance has a cor-relation not significantly different from 0 withSUN, ClK, and CINa; while both Kel and Cl,,have correlations near - 1 with histopathologicscore. Again, the right-left axis (Kel ratio, Cl,,SCR, and histopathologic score) is made upof two sets of variables highly correlatedamong themselves and negatively correlatedto each other and apparently separate neph-rotoxic and nontoxic dogs. The top-bottomaxis (C1n20, Cl,,, Clx, CIN,, and SUN) ismade up of two sets of variables highly cor-related among themselves and uncorrelatedto each other and separates normal from ne-phrectomized dogs (Fig. 3). This biplot wasused to help generate a nephrotoxicity indexby giving an indication of variables that sig-nificantly separate toxic and nontoxic dogs.


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98 SHY-MODJESKA, RIVIERE, AND RAWLINGSTABLE 4

PHYSIOLOGIC,PHARMACO KINETIC,ANDHISTOPATHOLOGICPARAM ETERSFOR NONTOX~CD OGS(~ = 23)

Parameter

Nephrectomized dogs Normal dogs ( intactreceiving gentam icin kidneys) receiving(n = 11) gentam icin (n = 6)Pre Post Pre Post

Nephrectomized dogsreceiving no gentamicin(n = 6)Pre Post

CL, 0.93 (0.07) 1.11 (0.10) 2.09 (0.23) 2.57 (0.23) 0.66 (0.11) 1.05 (0.17)SC R 1.50 (0.14) 1.46 (0.15) 0.60 (0.03) 0.68 (0.08) 1.72 (0.22) 1.48 (0.17)SU N 32.91 (2.96) 3 1.09 (4.66) 13.50 (0.92) 18.00 (2.08) 34.17 (5.28) 30.83 (4.04)cLNa 0.93 (0.12) 0.64 (0.10) 0.3 1 (0.09) 0.46 (0.10) 1.10 (0.26) 0.70 (0.14)CL, 29.67 (4.91) 20.42 (4.66) 5.68 (0.76) 12.28 (2.35) 35.13 (8.14) 17.12 (4.36)Kel ratio NAb 0.85 (0.04) NA 0.95 (0.11) NA NAHistopathologicindex NA 3.09 (0.44) NA 2.17 (0.60) NA 0.67 (0.33)

Mean (SE).b NA, Not appropr iate.

PharmacokineticsConsidering pharmacokinetic data similarly(Fig. 4), one sees normal dogs near the centerof the biplot, implying little change in their

parameters. Nephrectomized dogs fall to theleft, with low Kel and Cla values. The CSFdogs are within the cluster of normal dogssuggesting that the catheterization did not af-fect the kinetics of gentamicin. The glomer-ulonephritis dogs tend to fall to the right ofthe normal dogs with slightly higher Vc, Vss,Vdc-), and Cln values (R& was 75%).

Positive correlations exist among Vc, Vss,V++ and CIB, between K,z and & , andKel and p. & and K2, have correlations notsignificantly different from 0 with both Keland /3 and have negative correlations with Cle ,V (area)y VSS , and VC (Table 5).The biplot of the eight normal dogs withrespect to CL,, Vc, Cln, and VSSeveals noclusters or relationships, reflecting randomvariation among the dogs (Fig. 5A). Inclusionof nephrectomized dogs gives an entirely dif-ferent biplot. Normal dogs cluster togethermidway up the four vectors while nephrec-

TABLE 5COWLATIONCOEFFKIENTSOFPHARMACOKINETICDATA

B ClB VSS Vd(arca) vc 42 &I Ke lBc& 3VS SVd(Ma)VCKt2K2 1Ke l

1.00 0.70 0.15 0.19 0.321 oo 0.76 0.82* 0.781.00 0.94 0.861.00 0.811 oo

-0.22 -0.18 0.74-0.32 -0.35 0.61-0.15 -0.16 0.13-0.22 -0.31 0.30-0.44 -0.40 0.021.00 0.90 0.131.00 -0.02

1.00B significantly different from 0 at p < 0.0 5.


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APPLICA TION OF BIPLOT TO TOXICOLOGY 99tomized dogs cluster along the vectors in theopposite direction (Fig. 5B). Addition of thefour glomerulonephritis dogs reveals anotherrelationship. Although there is more variabilityamong the glomerulonephritis dogs, they tendto have higher kinetic parameters and lowerCL, readings than the normal dogs. Again, thenephrectomized dogs have lower values forall four parameters when compared to bothglomerulonephritis and normal dogs. Rank 2goodness of fit for those three biplots was 83,93, and 93%, respectively. Vector lengths in-crease (Fig. 5) because degrees of freedom(m - 1) increased as more dogs were includedin the analysis.

DISCUSSIONThis study has shown that the biplot is auseful tool in exploratory analysis of the struc-ture of toxicological and pharmacokinetic

data. Not only does it provide graphic ap-proximations to complex data sets, it also givesinsight into relationships between toxicologicand pharmacokinetic variables as well as be-tween individual treatment responses. Thistechnique replaces the need for multiple two-dimensional scatter plots or tables of corre-lation coefficients; however, in all cases pre-sented in this study, the relationships betweenvariables demonstrated on the biplot wereconfirmed by independent correlation andcluster analyses.

A biplot analysis can determine if clustersof samples exist as a result of specific diseasestates (e.g. nephrectomy) and further, whatvariables separate the clusters. A nephrotox-icity index consisting of variables separatingtoxic and nontoxic dogs was developed byemploying the biplot in this manner. The pri-mary parameters separating toxic dogs, i.e.,SCR, CL,, Kel ratio, and histopathologic in-dex, are similar to those reported by otherinvestigators for aminoglycoside toxic ne-phropathy (Schentag, 1982; Cronin et al.,1980; Brinker et al., 1981; Lufi et al., 1978);

however, such a table of clinical data does notalso show the relationships among toxicologicvariables. The biplot shows both kinds of in-formation simultaneously. This attribute isespecially powerful in the situation abovewhere variables indicative of nephrotoxicosis(i.e., CL,, SUN) may be confounded withvariables indicative of the underlying renalinsufficiency. The biplot was successful in sep-arating these two states of renal insufficiencybecause additional variables specific for eachof the conditions were utilized. It is of interestto note that the high correlation between Cl,,and the Kel ratio implies that changes in drugelimination over time in this study are pri-marily due to the drug-induced decrease inglomerular filtration rate. In this situation thecompound under study, i.e. gentamicin, servesas an excellent marker of glomerular f&ration.The biplot can also discriminate betweenthe effects of different disease states on drugdisposition in animals. For example, normaldogs and nephrectomized dogs differed in allpharmacokinetic variables measured andtherefore appeared as two separate groups inthe biplot (Figs. 4 and 5B). Although nephrec-tomized and glomerulonephritis dogs bothhave renal insufficiency characterized by a lowglomerular filtration rate estimated by lowCL,, differences become apparent in the biplot.Glomerulonephritis dogs have higher Vss, I, ,and C1ii compared to nephrectomized dogswhich have markedly reduced CIB and some-what contracted Vssand Vc compared to nor-mal. In healthy animals aminoglycoside CIBis directly correlated to CL or to other mea-sures of glomerular filtration rate (Chiu et al.,1976; Pechere and Dugal, 1979; Schentag,1980; Riviere, 1982b). The biplot clearly sug-gests an uncoupling of this normal associationbetween Cla and CL,, an event discussed inthe original studies (Riviere et al., 198 1; Ri-viere, 1982a). This uncoupling can be appre-ciated from the clustering evident in the biplots(Figs. 4 and 5C) or from the increased anglebetween the Cl* and Cl, vectors when glo-merulonephritis dogs are added to the input


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100 SHY-MODJESKA, RIVIERE, AND RAWLINGSdata matrix (Fig. 5C vs Fig. 5B). This illus-tration suggests a powerful use for the biplotin pharmacokinetic studies, namely, as agraphical tool to discern the effects of differentpathophysiological states on the parametersof drug disposition by studying the rotationof the parameter vectors induced by the ad-dition of animals with specific disease statesto the overall data matrix. This informationwould be especially beneficial if performed ina real-time environment on a video monitorwhere vector displacement could be quantifiedand highlighted. The above mentioned diseasestates can be compared and contrasted easilyfrom the biplot, conclusions drawn, and out-liers readily noted. Note that when vectors donot fall into the two-space being plotted, theyare short vectors and the angles between themmay not be good reflections of their correla-tions.

dogs in the biplot (Fig. 4), lending support tothe assumption that the surgical procedure in-volved in implanting ventricular cannulas didnot alter drug disposition as compared to his-torical controls. The biplot would be usefulin toxicologic studies utilizing normal animalsto determine relationships between indepen-dent toxicologic parameters. In addition, bygenerating sequential biplots composed ofsubsets of all measured parameters, the op-timal subset which discriminates between toxicand nontoxic animals, i.e., the parameterswhich make up the primary axis, can be se-lected. The use of these parameters in sub-sequent toxicologic studies should increase theefficiency and power of the experiments.

The relationships seen between pharma-cokinetic parameters in Fig. 4 are consistentwith theoretical assumptions (Gibaldi andPerrier, 1982; Wagner, 1975; OFlaherty,1981; Pechere and Dugal, 1979; Schentag,1980, 1982). For example, the K12 and &,distribution rate constant vectors are perpen-dicular to the Kel vector indicating no cor-relation. This is implicit to their derivation.However, note that if only relatively homo-geneous data are utilized as input (Fig. 5A),relationships between parameters may not bevery meaningful. In this case, only the cor-relation structure of homogeneous individualswithin one treatment group is being displayed.Although it is usually evident in a biplot anal-ysis when only random variation is present,techniques such as the cluster analysis can beused to verify such conditions or conclusions.Biological ly significant variation must bepresent if meaningful interpretations are to bemade by this technique.

In summary, the biplot appears to be a use-ful tool in toxicologic and pharmacologic re-search as a graphical device to explore rela-tionships between physiologic or pharmaco-logic variables and individual treatmentresponses to these variables. Biologically sig-nificant variation in the data should be presentbefore the biplot is applied. The biplot is par-ticularly useful as an exploratory tool and isnot intended for statistical test of hypotheses.Its use is analogous to that of scattergramsand residual plots in regression analysis(Chattejee and Price, 1977). Associations orhypotheses suggested by the biplot should beverified with independent sets of data to insurethe results are not unique to that set of data.

ACKNOWLEDGMENTSThe authors thank D r. Gordon L. Coppoc, Dr. Wi ll iamW. Car l ton, and Dr. Edward J . Hinsman of the Schoolof Veterinary Med icine, Purdue U niversity in W est La-faye tte, Indiana, for their supp ort in the original studiesfrom which these data or iginated. We acknowledge Mr.Richard Rogers of the Laboratory of Pharmacology andToxicolog y for assistan ce in graphical preparation of thebiplots. This work was supported in part by the USDA-ES No . 12-05030 0-595. Portions of this work we re pre-sented in abstract form at the Annual Meet ing of the

American Society of Pharmacology and Exper imentalTherap eutics in Philadelphia, Penn sylvania on Aug ust I 1,

Another application for the biplot is in de-termining whether individual animals can beclassif ied as normal in terms of more than oneparameter. For instance, the dogs involved inthe CSF experiment cluster with the normal 1983 (Pharm acologist 25, 232, 1983).


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APPLICA TION OF BIPLOT TO TOXICOLOGY 10 1

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biplots applications

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