Vol. 17,
0095-1137/83/060975-06$02.00/0
Single-Strain Regression Analysis for Determination of
Interpretive Breakpoints for Cefoperazone Disk Diffusion
Susceptibility Testing
GORANKRONVALL
Departmentof Medical Microbiology, UniversityofLund, Solvegatan23,Lund, S-223 62,Sweden Received1 November1982/Accepted 17 March 1983
Anovel approach forsetting interpretivebreakpointsindisk diffusionantibiotic
susceptibility testing according todetermined minimum inhibitoryconcentration
(MIC) limits is described, using the method ofsingle-strain regression analysis.
The procedure was tested on reference strains Staphylococcus aureus (ATCC
25923), Streptococcus faecalis (ATCC 29212), Escherichia coli (ATCC 25922),
and Pseudomonas aeruginosa (ATCC 27853), using published results from
cefoperazone disk diffusion experiments. The correlation between logarithm of thediskcontentandinhibitionzonediametersquaredwaslinear,excludingthree
endpoint values. Whenconstants AandBin thenewregressionlineequationwere
calculated for the four strains, all four showed different regression lines. Zone
diameterscorrespondingtovarious MICswerecalculatedforadiskcontentof 75
,ug.The values obtained for the four strainswere20.1, 20.9, 24.9, and 25.8 mm,
respectively, for an MIC of 16
jig/ml,
and 15.7, 15.7, 22.3, and 17.9 mm,respectively, foran MIC of 64 ,ug/ml. Thefollowing zone diameterbreakpoints
were determined for the "I" (intermediate) category, using a 75-,ug disk: S.
aureus, 18 to 15 mm; S.faecalis, 23 to 13 mm; E. coli, 20 to 17 mm; and P.
aeruginosa, 20to 17 mm.
Interpretive breakpointsfor thesusceptibility categoriesin the disk diffusion methodare
calcu-lated with regression lines obtained from
mini-muminhibitoryconcentration (MIC)
determina-tions of a large number of strains and
correspondingdisk diffusiontestresults(1-6,8,
13, 15, 20, 21, 24, 25). Theuse of the errorrate
bounding method of Metzler and DeHaan (20)
whensetting breakpoints aimsatminimizing the
occurrence ofinterpretive errors. Toobtain an
adequate accuracy with these breakpoints in
individual laboratories, the disk diffusion test
mustbe well standardized. Interlaboratory
vari-ation in inhibition zone diameter results for
controlstrains has been documentedpreviously
(9, 11, 14). Strict standardization togetherwith
regularproficiency testing in the United States
has led to marked improvements (12). Inother
places, however, the situation is still
unsatisfac-tory, requiring further standardization of the
methodoradjustments ofbreakpoints according
to local regression lines. Unavailability of
rec-ommended media might also call for some
meansofdeterminingzonediameterbreakpoints
inindividuallaboratories. Theapparentneed for
asimplifiedmethod forregression line analysis,
both inindividual laboratoriesandfor individual
bacterial species,canbemetby usingamethod
calledsingle-strain regressionanalysis (16). This
technique offersasimple approach for the
calcu-lation of regression line constants and permits
thesetting of interpretive breakpointsaccording
todetermined MIC limits for disk diffusion
sus-ceptibility testing. Thisreport describes the ap-plicationof this method tothedetermination of breakpoints for cefoperazone disk diffusion
tests.
MATERIALS AND METHODS
Susceptibility testresults. The experimental results usedfor the calculations in this paper were obtained fromapublication byThornsberryetal. (24). Data for four of thestrains shown in their Table 3wereused in the present studies: Staphylococcus aureus (ATCC 25923), Streptococcusfaecalis (ATCC 29212), Esche-richia coli(ATCC 25922) and Pseudomonas aerugino-sa(ATCC 27853).
Single-strain regression analysis. The theoretical background and the equations used in single-strain regression analysis have been presented elsewhere (16). The following equation was derived for the calculations:Z2= Alog Q -Alog MIC + B. Inthis
formula, the inhibition zone, Z, is expressed as the diameter inmillimeters, the disk content of antibiotic, Q, in micrograms, and the MIC in micrograms per milliliter (16). Constants A and B depend on several
factors,including the methodological parameters char-acteristic for individual laboratories. Calculation of theseconstants canbe made fromtestresults by using
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two or morediskcontentsof antibioticsandreference strains withwell-defined MICs.
Computer calculations. Mathematical and statistical calculations were performed with amicrocomputer, Metric model M85-T (Compucorp series 600, model 655; Scandia Metric AB, Solna, Sweden), witha64 kilobyte randomaccess memoryanda2 x 640 kilo-byte floppy disk. The software was obtained from Bioscand HB,Lund, Sweden.
RESULTS
Linearity of inhibition zone diameters versus disk contents. The equation for single-strain
re-gression analysiscanbeused only on one
condi-tion: the correlation between logQ andZ2has to
be linear(16). In suchcases, the two constants A
and B will also be valid for the correlation
between MIC and antibioticinhibition zone size
in thedisk diffusiontest. Theexperimental data
published by Thornsberryet al. (24) were
there-fore first analyzed for linearity. Fig. 1 shows the
results obtained for the four reference strains
testedwith disks containing from5 to 200pugof
cefoperazone. There was good linearity in all
four cases, with only three end values off the
lines. These three valuesweretherefore
exclud-ed from the calculations. Regression analysis
provided the two constants A and B with the
numerical values shown in Table 1. The slopes
of the curves were similar for the two
gram-positive cocci tested, Streptococcus faecalis and
Staphylococcusaureus.E. coli showed the
low-est values for the slope constant A, where P.
aeruginosashowedthehighest values(Table1). Zone diameter values corresponding to MIC limits. As thecorrelation between thelogarithm
of the diskcontentandZ2wasfoundtobelinear
(Fig. 1), the calculatedconstants AandBfor the
fourspeciestestedwerealso validforthe
corre-lation between log MIC andZ2. The inhibition
zone diameter values corresponding to
recom-mended MIC limits could therefore be
calculat-edforthesefour bacterialspecies (Table 1).The
inhibition zone diameter values corresponding
to16, 32, and 64
jig/ml
areshown inTable 1. The16-,ug/ml correlates for the two gram-positive
cocciwereslightlylower than 21 mm,being20.1
and 20.9 mm,respectively. E. coli andP. aeru-ginosa gave larger zone diameter values, 24.9 and 25.8 mm, respectively.
Effectsofdifferent diskpotencies on zone
diam-eters. The equation for single reference strain
analysisalsopermitsthecalculationof inhibition
zone diameters for otherMICs and disk
poten-cies. It was therefore possible to analyze the
effects oninhibition zone sizes ofdifferent disk
contents. Figure 2A shows the inhibition zone
diameter values calculatedforanMIClimit of16
,ug/mland thefourbacterialspeciesfor different
disk contents of cefoperazone. The 16-,g/ml
MIC has beenchosen as thelimit for the
suscep-tible category by the National Committee for
Clinical Laboratory Standards (13, 24). With a 50-,ug disk, the zone diametercorrelates for the
twogram-negative specieswereboth around24
mm,andfor thetwogram-negative specieswere
both around 24 mm, and for the two
gram-positive cocci, around 19 mm (Fig. 2A). At a
diskcontentof75 R,g,the zonesizes for thetwo
gram-negative strainswerequite close, whereas
at higher diskcontents theP. aeruginosa strain
gavelargerzones as compared with those ofE.
coli (Fig. 2A). At no disk potency did the
inhibition zone values for all four strains
coin-cide. Amounts of 100 pug or more of
cefopera-zonein the disksresulted in values that were far
apart. Below 10 ,ug, the zone sizes were too
mm2 Pseudeerug.
1200-1100/
-Coll
1000 /
900-6 X /(o)o) S.aurous
800,
E 700_ .2
40
300-
200-
100-(-)
5 1015 30505 100 200 Disk content of Cefoperazone, log,scale FIG. 1. Analysis of linearity for the correlation between thelogarithm ofdisk contents of cefopera-zoneandinhibitionzonediameterssquared,usingdata fromThornsberryetal.(24).Regressionlines obtained by the least-squares method are shown forthe four reference strains: Staphylococcus aureus (ATCC
25923), Streptococcusfaecalis(ATCC 29212),E. coli (ATCC 25922), and P. aeruginosa (ATCC 27853).
Three valuesexcluded inthecalculationsareshownin parentheses.
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REGRESSION 977
TABLE 1. Single-strain regression line constants of reference strainsa
Cefoperazone A B Productmoment CalculatedMICcorrelate(mm)
Strain MIC vau vle coefficient of
(Sg/ml) v value correlation(r) 16 Lg/ml 324g/ml 641Lg/ml
Staphylococcusaureus 1.0 314.2 226.3 1.0 20.9 18.5 15.7
Streptococcusfaecalis 32 262.6 229.2 0.99 20.1 18.1 15.7
E.coli 0.5 204.9 482.9 0.98 24.9 23.6 22.3
P.aeruginosa 4.0 578.5 280.0 1.0 25.8 22.2 17.9
aRegression line constants and zone diameter correlates for MICs were calculated by using
75-j.g
cefoperazonedisksaccordingtodatafromThornsberryetal.(24).Regression analysiswasperformed by using
theleast-squares method. Theproductmomentcoefficient of correlation(r) is shown forregressionlines.
closetothediskdiametertopermita
discrimina-tion between strains with MICs around 16,ug/ml
(Fig. 2A).
Similarcalculations performed for the
64-j.Lg/
ml MIC at different disk contents for the four
strains provided slightly different curves (Fig.
2B). With 50-,ug disks, three zone diameter
valueswerecloseat14 mm,whereastheE. coli
straingave a separatebreakpointof21.5mm.It
was clear from the breakpoint calculations
shown in Fig. 2Bthatdisk contents lower than
50 ,ug did not permit the regular formation of
inhibition zones at an MIC of 64 ,ug/ml. Such
low-contentdisksthereforecannotdiscriminate
properly between strains with MICs around or
above 64 ,.g/ml.
Settingofinterpretive breakpoints.The
inhibi-tion zone correlates of MICs vary with the
bacterial species tested (Table 1). The correct breakpoints, therefore,oughttobespecies
relat-ed,anopinion recently raised in connection with
certaincombinations of bacteria and antibiotics
(10,19).However, MICsforindividualbacterial
speciesoften showalimitedrange,givingriseto relativelyhomogeneous populations. Therefore,
formanycombinations of antibiotics and
bacte-rial species, general breakpoints will
discrimi-natecorrectly between populations belongingto
different susceptibility categories. A
species-related analysis of MICor zonediameter
distri-butions for routine isolates is thusnecessary to
identifythose combinations which require
spe-cies-related breakpoints. Datafrom the studies
by Thornsberryetal. (24)providedinformation
on the distribution of MICs for some of the
strains tested and therefore served the purpose
ofillustratingthe presentmethod. All 49strains
ofStaphylococcus aureusshowedMICs of less
than 16
,ig/ml
and would therefore giveinhibi-tionzonevalueslargerthan 20.9 mm with 75-,ug
disks, according to Table 1. The zone size
between the 16 and 32
jig/ml
correlates mighttherefore be chosen as the breakpoint for the
susceptible category for this species, e.g. 19
mm. Among 25 strains of E. coli, one strain
showed an MIC of 16
pug/ml
and one strainshowed an MIC of 32 ,ug/ml, all others having
lower MICs. According to the calculations
shown in Table 1, the susceptible breakpoint
might be set at24mm.
Among 82 strains ofP. aeruginosa, as many
as 72 strains showed an MIC of -16 xg/ml, 7
strains hadanMICof 32,g/ml,and1strain had
an MICof 64,ug/ml. Since these valuesseemed
to cluster around and close to the MIC limit
recommended, <16,ug/ml, astrict adherenceto
the correct species-related breakpoint, (25.8 ±
22.2)/2 = 24mm,would leadto ahigh
percent-age of erroneous interpretations of antibiotic
susceptibility asintermediate for statistical rea-sons.Thedistribution, however,seems to repre-sent a homogeneous population with a mean
MIC of 16 ,ug/ml and with a methodological
variation which givesafew values of 32 ,ug/ml.
Thebreakpoint, therefore,hastobe selectedto
include also these strains in the susceptible (S)
category requiringabreakpointbetween 20 and 22mm,tentatively 21 mm.
Streptococcus faecalis presents a different
problem. Among 10 strains analyzed, 2 strains
showed MICsof16,ug/ml,5strains had MICs of
32 ,ug/ml, and 3 strains had MICs of 64 ,ug/ml.
These strains in this limited MIC range also
seemedtorepresent ahomogeneouspopulation,
takingthe variation ofthe method intoaccount
(±one2-log dilution). Insuchacase,thewhole
populationshould beassignedtothe"I"
(inter-mediate)category, using species-specific
break-points. With an inhibition zone diameter of 18
mm corresponding to the MIC of 32 Lg/ml for thisspecies,anintermediatezoneof 18± 5mm, e.g., 23 to 13 mm,wouldgivethe correct
suscep-tibility designation I to such strains of
Strepto-coccusfaecalis.
Single reference strain analysis in
combina-tion with a limited population analysis of the
four individual bacterial species studied thus
suggests the following breakpoints: 19, 24, 24,
and21 mm asthelower limits forthe Scategory
for Staphylococcus aureus, Streptococcus
fae-calis, E. coli, and P. aeruginosa, respectively.
To minimize the number of different
break-VOL.17,1983
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_ mm 2S
0
20-c
CL
0
00
2
15-._
._
20
X
0 CL
E
.2
20-0
A
c
A
1015 3050 100 200 Diskcontentof Cefoperazone,log, scale
B
5 10 15 30 50 100 200
Disk contentofCefoperazone,log. scale
FIG. 2. Calculated inhibitionzonediameter
corre-latesof MICs of 15,ug/ml (A) and 64 ,ug/ml(B)forthe
four reference strains at various disk potencies of
cefoperazone. Thezonediameterswerecalculated by
theequation for single-strain regression analysis(16).
points, the population analysis can be used to
indicate additional possible changes. For E. coli, the 24-mmvalue might be lowered,for example,
toconformtothe 21-mm limit ofP.aeruginosa. Thebreakpoint for the resistantcategory canbe
set at avalue givinga4-mmindeterminate zone
for all species except Streptococcus faecalis,
which requires a range equal to the methodologi-cal variation of the disk diffusion test. The final breakpoints selected for the S, I, and resistant
(R) categories, respectively, on thebasis of the
data available were: Staphylococcus aureus,
.19, 18 to 15, and <14 mm; Streptococcus
faecalis, .24,23to 13, and.12mm;E. coli and
P. aeruginosa, -21, 20 to17, and <16 mm.
DISCUSSION
Interpretive breakpoints recommended for
disk diffusion antibiotic susceptibility testing to assign bacterial strains to the category S, I, or R are determined in reference laboratories (1-6, 13, 24). Thesebreakpointsarerecommended for
all laboratories, with the requirement that the
standardized procedures for the disk diffusion
testhave to beadheredtostrictly. However,the
referenceregressionlines are notalwaysvalid in
individual laboratories orfor the bacterial
spe-cies tested. The breakpoints, therefore, would have to be determined with laboratory- or
spe-cies-specific regression lines, efforts which are
outside the scope of most laboratoriesthat use conventional methods. The obvious need for a
simple method forsuch calculationscanbemet
bytheprinciple of single-strainregression
analy-sis (16). This methodisbased on amodification
ofthe original equations describing the
forma-tion of inhibiforma-tion zonesinthedisk diffusiontest
(7, 16). The calculation of the regression line
constants requires only one strain with a
well-defined MIC and inhibition zone diameters
ob-tained by using at least two disk potencies. In thepresentinvestigations, this novel methodhas
been usedtostudysomerecently published data
on cefoperazone susceptibilityand the
determi-nation ofinterpretivestandards(24).The
experi-mental data include inhibition zone diameter values forreference strains tested against disk contents ofcefoperazonebetween 5and 200 ,ug. The plot of these values (Fig. 1) showed good
linearity, permitting the use ofsingle-strain
re-gression analysis.
With the adoption of the recommended MIC limitof <16,ug/mlfor the susceptible category,
thecorrespondingzonediameterswere
calculat-edfor thefourreference strains and various disk
potencies (Fig. 2). With a 75-,ug disk, the zone
diameters obtained were 20.1, 20.9, 24.9, and
25.8mm,respectively, asshown inTable1,and
with a30-,ugdisk,the zonediameterswere17.3,
17.7, 23.2, and 20.9 mm, respectively. These
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valuesgiveamuchmoreinformative picture of
theMIC correlatesascompared with the 21-mm
value, using the conventional regression
analy-sis (24). It is apparent that the general
break-point recommendedby theNationalCommittee
for Clinical Laboratory Standards as the lower
limit for the susceptible category, 21 mm, is
more generous with respect to the two gram-negative bacteria thanto the twogram-positive
ones. As far as Staphylococcus aureus is
con-cerned, thepresentstudies have indicated thata
lower limit might be preferred for this species.
Taking MIC distributions into account, the
breakpoints chosenwere18to 15, 23to 13, and
20to17 mmfor theI(intermediate)categoryfor
Staphylococcusaureus, Streptococcusfaecalis,
andthe twogram-negativespecies,respectively.
Tominimizeinterpetive errors whendefining
breakpoints in a reference laboratory, the
so-called error rate bounding method of Metzler
and DeHaan has been widely used (20). This
method aims at minimizing interpretive errors
byanalyzingthefrequencies offalse-susceptible
andfalse-resistant results of disk diffusion tests
inrelationtothe MICsfor strains. The method is
currently used together with conventional
re-gressionanalysis forthedefinition ofzone
diam-eterbreakpoints. Itmight, however, be
mislead-ing incertain instances. First, the method does
nottake intoaccount any variability of the disk
diffusion method between differentlaboratories,
although the National Committee for Clinical
Laboratory Standards gives rather wide limits
for accuracy control. Frequencies of
false-sus-ceptible and false-resistantresultsinareference
laboratorymight thereforenot represent the real
figures in individual laboratories. Second, the
method is often applied to panels of bacteria
which do not represent the bacterial species of
the routine diagnostic service and will,
there-fore, not predict true error rates. Histogram
analysis of inhibition zone diameter values of
bacterial species as described by O'Brien and
co-workers (22, 23) might offera more suitable
method for individual laboratories to identify
combinations of bacteria and antibiotics which
are subjecttopossible interpretive errors.
When the use of zone diameter breakpoints
for the interpretation ofthe susceptibility
cate-gories is considered, the methodological
varia-tion ofthe disk diffusion method mightinfluence
the resultsmarkedly (15, 17). A single bacterial strain willgivearange of zone size values of 6 to 10 mmupon repeated tests. MICs in individual
bacterialspecies showabiological homogeneity
formostantibiotics,ahomogeneitywhich is also
apparent fromhistogram analysis of zone diame-ter values (10, 16-19, 22, 23). Such histograms
show a clustering of inhibition zone diameter values which often corresponds to the
method-ological variation ofa single strain in the disk
diffusionmethod. Instrictlyhomogeneous
popu-lations, all strains have the same MIC (18). In
routine MIC testing, his includes ± one 2-log
step variation. When the MICs of a
homoge-neouspopulationofabacterial speciesareclose
to recommended MIC limits, then interpretive
errors canbe minimized only by using
species-relatedbreakpoints. Forexample,Proteus
mira-biliscanbeaccurately assignedtothe I
(interme-diate)category ofchloramphenicol
susceptibili-ty only when species-specific breakpoints are
used(10). P.aeruginosarequires
species-specif-icbreakpoints when tested against carbenicillin
(19). In my clinical microbiology laboratory,
severalcombinations of antibiotics and bacterial
species thatrequirespecies-specificbreakpoints
have been identified. Such alternative
break-points can be used on aroutine basis with few
difficulties in their practical implementation,
therebyimproving theaccuracyofthe
suscepti-bilityreporting (17).
ACKNOWLEDGMENTS
FigureswerekindlydrawnbyAnn-CathrinePetterssonand photographed byAkeChristensson. The secretarial assistance of Anita Hansson iskindlyacknowledged.
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