Assessing in vitro combinations of antifungal drugs

Medical Mycology March 2005, 43, 133 /152

Assessing in vitro combinations of antifungal drugs against yeasts and filamentous fungi: comparison of different drug interaction models JOSEPH MELETIADIS*, PAUL E. VERWEIJ*, DEBBIE T. A. TE DORSTHORST$, JACQUES F. G. M. MEIS$ & JOHAN W. MOUTON$ *Department of Medical Microbiology, Nijmegen University Center for Infectious Diseases, and $Department of Medical Microbiology and Infectious Diseases, Canisius-Wilhelmina Hospital, Nijmegen, The Netherlands

Med Mycol Downloaded from informahealthcare.com by Radboud Universiteit Nijmegen on 12/09/12 For personal use only.

Non-parametric and parametric approaches of two competing zero-interaction theories the Loewe additivity and the Bliss independence were evaluated for analyzing the in vitro interactions of various antifungal drugs. Fifty-one data sets, derived from three drug combinations, tested in triplicate against 17 clinical yeast and mold isolates with a two-dimensional checkerboard microdilution technique, were selected to span from strong synergy to strong antagonism. These were analyzed with the standard FIC index model and modern concentration-effect response surface models: the fully parametric model developed by Greco et al. and the 3-D analysis developed by Prichard et al. The FIC index model is subjective, sensitive to experimental errors and resulted in approximated results and variable conclusions depending on the MIC endpoints determined and interpretation endpoints used. By using the MIC-2 endpoint (lowest drug concentration showing 50% of growth) for calculating the FIC indices, problems due to trailing phenomena were reduced and weak interactions could be detected; higher levels of reproducibility and agreement with the other models were achieved using the MIC-0 and MIC-1 (lowest drug concentration showing 10 and 25% of growth, respectively). High reproducibility was achieved in interpreting the FIC indices when the cutoffs of 0.25 and 4 (for single experiments) and the cutoff of 1 (for replicates) were used for defining the limits of additivity/indifference. Although the fully parametric Greco model did not describe precisely the entire response surface of all antifungal drug interactions, it was able to differentiate synergistic from nonsynergistic interactions with a non-unit, reproducible, concentration-independent interaction parameter, including its uncertainty, without requiring replication. The Bliss independence based models resulted in mosaics of synergistic and antagonistic combinations, raising questions about the concentration-dependent nature of antifungal drug interaction. The sum of all statistically significant interactions were used as a summary interaction parameter for the entire response surface, concluding synergy or antagonism when it was positive or negative, respectively. The cutoffs of 100% and 200% were used to distinguish weak and moderate interactions, respectively in 12 16 8 12 checkerboard formats. Semi-parametric approaches need particular care as experimental errors are not eliminated from the entire response surface. /

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Received 22 October 2003; Accepted 25 March 2004 Correspondence: Paul Verweij, Department of Medical Microbiology, University Medical Center Nijmegen, PO Box 9101, 6500 HB Nijmegen, The Netherlands. Tel: /31-24-3619627; Fax: /31-243540216; E-mail. [email protected]

– 2005 ISHAM

DOI: 10.1080/13693780410001731547

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Keywords antifungal susceptibility testing, in vitro combination of antifungal drugs, synergy and antagonism, drug interaction modeling


Introduction Although antifungal drugs may interact differently under different conditions in in vitro systems [1,2], variable results can be obtained even when the same in vitro methodology is used depending on the way that the nature and the intensity of drug interactions are assessed [2 /5]. The standard approach in the field of medical microbiology is the calculation of the fractional inhibitory concentration (FIC) index [6,7]. Synergy or antagonism is concluded when the concentration of the drugs in a combination showing the same effect as the minimal inhibitory concentration (MIC) are lower or higher, respectively, than the MIC of the single acting drugs for more than 1 dilution step of the assay. Despite the simplicity of this model, there are several drawbacks in being able to describe correctly, reliably and precisely the multi-variate phenomenon of drug interaction. These include: (i) the choice of the MIC endpoints, particularly with the combination of fungistatic and fungicidal drugs and when trailing phenomena are present; (ii) the choice of endpoints for the interpretation of the FIC indices; (iii) the sensitivity to intra-experimental errors, particularly when a twofold dilution scheme is followed; (iv) the imprecise approximation of the real FIC index when off-scale MIC are present; (v) the lack of a good summary of the interactions; and (vi) the difficulty to interpret the results statistically [8]. The multi-variate nature (drugs/effect) of the drug interactions has led to the development of new models based on the response surface [9 /11]. One is a fully parametric model described by Greco et al . This is a sigmoidal Emax based model and fits to the entire data set with a non-linear regression analysis [1]. Many of the above-mentioned problems of drug interaction modeling will be overcome as the nature and the intensity of an interaction is summarized with a nonunit, concentration-independent interaction parameter that included the uncertainty of the estimate [12]. Both models rely on the Loewe additivity (LA) zero-interaction theory. This theory is based on the simple idea that a drug, by definition, cannot interact with itself; therefore a combination of a drug with itself is additive, and its effect is that which would be expected from concentration-effect curves [12]. Opponents claim that the LA theory is limited to drugs that act similarly or

that have similar concentration-effect curves. Although many zero-interaction theories can be found in the literature, the major competitor of LA for a reference theory is the Bliss independence (BI) theory. This relies on the idea that two drugs that act independently follow the law of probability: the probability that either or both of two independent events (i.e. the action of a drug which, in the case of susceptibility tests, corresponds to percent inhibition) will occur is the sum of the probabilities that each event will happen alone, minus the two probabilities multiplied [12]. Opponent arguments of this theory are based on paradoxical cases derived when sham combinations of the same drug are analyzed with the BI as zero-interaction theory. Furthermore, given the complexity of systems like cells equating drug actions with independent events, as it is assumed in the BI theory, is questionable. Several models based on BI have been described elsewhere [2]. One of these is the non-parametric model described by Prichard et al . [13,14] and the semiparametric approach of the latter model, which assumes that the concentration-effect relationship of each drug follows the Emax model [2,15]. Both models emphasize the multidimensional nature of drug interactions and determine the interactions, including the statistical significance. Furthermore, they enable the presence of mosaics of synergistic and antagonistic combinations within a data set, which the Greco model does not. However, both models lack a good summary, although various summary measures have been previously described [2,14,16]. Controversial results on the nature and intensity of in vitro interactions can be obtained using each of the above-mentioned models [2]. Given the increasing interest in combination antifungal therapy, an unbiased and comprehensive analysis tool for the assessment of the in vitro combination of antifungal drugs is warranted. Although the above-mentioned drug interaction models were previously used to analyze antifungal drug interactions, a head-to-head comparison of these models, which would explore advantages and disadvantages, similarities and differences, for the whole range of in vitro interactions is lacking. In order to compare all of these models, 51 twodimensional, checkerboard data sets, selected based on the FIC indices, were analyzed. The collection thus consisted of 18 data sets (six strain-drug combina– 2005 ISHAM, Medical Mycology, 43, 133 /152


Drug interaction modeling of antifungals

tion pairs /three replicates) classified as synergistic interactions (FICi: 5/0.5), 18 data sets (six strain-drug combination pairs /three replicates) classified as additive/indifferent interactions (FICi: /0.5, 5/4) and 15 data sets (five strain-drug combination pairs /three replicates) classified as antagonistic interactions (FICi: /4). Data obtained from previous in vitro interaction studies [8,17,18] where the combination of various antifungal drugs (three different drug combinations) were tested in triplicate against 11 yeast and six mold clinical isolates using two dimensional checkerboard microdilution techniques based on a spectrophotometric (for yeasts) and a colorimetric (for molds) modification of the NCCLS standard for antifungal susceptibility testing [17,18]. Results concerning the parameters of concentration-effect curves of the drugs, the nature and the intensity of the interactions, as well as the drug concentrations, which showed the interactive effects estimated with each model, were compared to each other.

Materials and methods Isolates and drugs Six clinical isolates of filamentous fungi [three Scedosporium prolificans, AZN7901 (SP1), AZN7902 (SP2) and AZN7906 (SP3), and three itraconazole-resistant Aspergillus fumigatus, AZN5241 (AF1), AZN58 (AF2) and AZN59 (AF3)] and 11 yeast clinical isolates [three Candida albicans, AZN574 (CA1), AZN2308 (CA2) and AZN4518 (CA3), three C. krusei , AZN1-27 (CK1), AZN1-31 (CK2) and AZN1-32 (CK3), and five C. glabrata, AZN608 (CG1), AZN1143 (CG2), AZN1-28 (CG3), AZN2-50 (CG4) and AZN2-57 (CG5)] were used in this study. The isolates were stored in 50% glycerol in water at /708C. C. parapsilosis (ATCC 22019) and C. krusei (ATCC 6258) were used as quality control (QC). Six antifungal drugs belonging to different classes of antifungal agents, namely the azoles miconazole (MZ) (Janssen Research Foundation, Beerse, Belgium), itraconazole (IZ) (Janssen), and fluconazole (FZ) (Pfizer, Capelle aan den IJssel, The Netherlands), the allylamine terbinafine (TB) (Novartis, Basel, Switzerland), the polyene amphotericin B (AB) (BristolMyers Squibb, Woerden, The Netherlands) and the pyrimidine 5-flucytosine (FC) (ICN, Pharmaceuticals, Zoetermeer, The Netherlands) were tested. In order to obtain stock solutions miconazole, itraconazole, terbinafine and amphotericin B were dissolved in 100% dimethylsulfoxid at concentrations of 25 600, 12 800, 25 600 and 6400 mg/l, respectively, and fluconazole and – 2005 ISHAM, Medical Mycology, 43, 133 /152

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5-flucytosine were dissolved in water at concentrations of 512 mg/l.

Interaction studies The interaction of antifungal drugs against fungi was previously tested [8,17,18] with a two-dimensional microdilution checkerboard technique using modifications of NCCLS M-27A and M-38P protocols for the in vitro antifungal susceptibility testing of yeasts and filamentous fungi, respectively. Based on these experiments, data sets were chosen in such a way as to have interactions that spanned from strong synergy to strong antagonism (Table 1) based on the definitions of the fractional inhibitory concentration index (FICi) model [13].

Drug interaction modeling Data obtained as described above were analyzed using four different models, used previously to analyze antifungal drug interactions [8,17,18]. The models were parametric and non-parametric approaches of the following two zero-interaction theories: Loewe additivity and Bliss independence.

Loewe additivity Loewe additivity (LA) is described by the following equation: 1 dA =DA dB =DB ; where dA and dB are the concentrations of the drugs A and B in the combination that elicits a certain effect, and DA and DB the iso-effective concentrations of the drugs A and B when acting alone.

FIC index model The non-parametric approach is based on the fractional inhibitory concentration index model expressed with the following equation, SFIC FICA FICB

Ccomb A MICalone A

Ccomb B MICalone B

where MICalone and MICalone are the concentrations of A B the drugs A and B when acting alone and Ccomb and A Ccomb are the concentrations of the drugs A and B at B the iso-effective combinations [7]. As each replicate experiment yields several SFIC, among all SFIC calculated for each replicate, the SFICmin and SFICmax were determined corresponding to the lowest and the highest SFIC, respectively. The reported SFIC (FIC index) was the SFICmin in all

Spectrophotometric 43 16/12 3 5 C. glabrata 48 h

Spectrophotometric 43 16/12 3 3 C. krusei 48 h

42 MTT colorimetric 12/12 3 3 A. fumigatus 48 h

MTT colorimetric 26 Spectrophotometric 43 3 3 S. prolificans 3 C. albicans 3 72 h 48 h

/4 5 Antagonism

4 Additive/indifferent 0.5 /4

3 Additive/indifferent 0.5 /4

miconazole (64 /0.06)/terbinafine (64 /1) 5-flucytosine (64 /0.004)/fluconazole (128 /0.125) amphotericin B (16 /0.015)/itraconazole (16 /0.015) 5-flucytosine (64 /0.004)/fluconazole (128 /0.125) 5-flucytosine (64 /0.004)/fluconazole (128 /0.125) 5/0.5 5/0.5 1 Synergy 2 Synergy

No. of strains Replicates Checkerboard Method format Time Species FIC indices Drug combination (concentration range in mg/l) Interaction

Characteristics of drug combination-strains pairs used in the interaction studies Table 1


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cases unless the SFICmax was higher than 4, in which case the SFICmax was reported as the FIC index (FICi). In order to determine the larger departure from additivity, the SFICmax was also reported as the FIC index for data sets where the latter was smaller than 4 but the SFICmin was greater than 1. If for a data set the SFICmin was lower than 0.5 and the SFICmax was higher than 4, both SFIC were reported [7]. Three MIC endpoints were used, namely MIC-0, MIC-1 and MIC-2 defined as the lowest drug concentration showing 10, 25 and 50% growth, respectively, compared to the growth control. Thus the following FIC indices were determined for each replicate, FICi-0, FICi-1 and FICi-2, respectively. Off-scale MIC were converted to the next highest or lowest twofold concentration. As the FICi are not normally distributed, the median and the range of FICi among the replicates was calculated. Furthermore, the drug concentrations of the combination, which was corresponded to the FICi, were determined. This combination was actually the combination with the strongest interaction (Imax).

Greco model The fully parametric surface approach described by Greco et al . [1] was used based on the following equation: 1 IC50;A

DA E

1=m A

Emax E

a IC50;A IC50;B

IC50;B

DB E

1=m

B

Emax E

DA DB 0:5(1=m 1=m ) A B E

Emax E

where E is the percentage of growth (dependent variable) at the drug concentrations DA and DB (independent variables), Emax is the maximal percentage of growth observed in the drug-free control, IC50,A and IC50,B are the drug concentrations producing 50% of the Emax, mA and mB are the slopes of the concentration-effect curves (Hill coefficient) for the drugs A and B, respectively, and a is the interaction parameter that describes the nature of the interaction. This model was fitted directly to all experimental data of a data set (percentages of growth for all concentrations of the two drugs alone or in combination) with a non-weighted, non-linear regression analysis using the MODLAB program (MEDIMATICS, Maastricht, The Netherlands, www.medimatics.nl). When the estimate of a was positive and its 95% confidence interval (95% CI) did not include 0, statistically significant synergy – 2005 ISHAM, Medical Mycology, 43, 133 /152



was claimed, while when a was negative without its 95% CI overlapping 0, statistically significant antagonism was concluded. In any other case Loewe additivity/ indifference was concluded. Goodness of fit criteria included the 95% CI of the estimated parameters, the R2, the sum of the squares (SumSq), correlation and covariance matrices. In order to check for any systematic deviation of the model from the data, residual plots were constructed and deviation from the normal distribution was tested with the Kolmogorof/Smirnof (KS) test. In order to determine the drug combination that produced the strongest interaction (synergistic or antagonistic), the additivity surface was simulated by fixing all parameters of the Greco model to values obtained after the model was fitted to experimental data except, a which was fixed at 0. This surface was then subtracted from the fitted surface calculated by the Greco model. The drug concentrations of the combination with the highest percentage of synergy or antagonism were reported.

Bliss independence Bliss independence (BI) is described by the equation: Iind IA IB IA IB ;

where Iind is the predicted percentage of inhibition of an non-interactive theoretical combination, calculated based on the experimental percentages of inhibition (IA, IB) of each drug acting alone, respectively [12]. The equation is equivalent to Eind /EA /EB (as E /1 /I), where Eind is the predicted percentage of growth that describes the effect of a combination where the drugs are acting independently and EA, EB are the experimental percentages of growth of each drug acting alone, respectively. The difference (DE) between the predicted percentage of growth (Eind) and the experimentally measured percentage of growth (Eexp) describes the interaction at each combination of the drug concentrations. A three dimensional plot can then be constructed resulting in a surface plot. In the non-parametric response surface approach described by Prichard et al . [19], the EA and EB are obtained directly from the experimental data, but in the semi-parametric response surface approach [15] these values are derived from fitting the Emax model to the concentration-effect curves of each drug alone. Thus, for the latter approach, the Eind was calculated with the following equation: – 2005 ISHAM, Medical Mycology, 43, 133 /152

A

Eind

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B

(DA =IC50;A )m (DB =IC50;B )m A B (1 (DA =IC50;A )m )(1 (DB =IC50;B )m )

where DA, DB, IC50,A, IC50,B, mA and mB are the same parameters as described above for drugs A and B in the Greco model. The parameters of the model were obtained by a non-weighted non-linear regression analysis of concentration effect curves of each drug alone using GraphPad Prism Software (San Diego, CA). Data were normalized by using the percentages. The maximum and the minimum of the Emax model were kept constant during the fitting procedure at 100 and 0%, respectively. Goodness of fit was interpreted using the 95% CI of the estimates, the run tests and the R2 values. The estimated parameters for each drug generated were subsequently used to calculate the zerointeraction surface for each experiment. For each combination of drugs in each of the independent replicate experiments, the Eexp was subtracted from the Eind, calculated with the non-parametric or the semi-parametric model. When the mean difference was positive and its 95% CI did not include 0, statistically significant synergy was claimed for that specific combination of drug concentrations. When the mean difference was negative without its 95% CI overlapping 0, statistically significant antagonism was claimed for that specific combination of drug concentrations. In any other case Bliss independence was concluded. In the three-dimensional plots, peaks above and below the 0 plane indicate synergistic and antagonistic combinations, respectively, whereas the 0 plane itself indicates no statistically significant interactions. As the plots only show the interaction for each separate combination of concentrations, a value is needed to summarize the whole interaction surface for each strain. This was done in two different ways. In the first, the percentages of all statistically significant interactions were summed (SSSI) [17]; in the second, all statistically significant interactions were averaged and the mean percentage (MSSI) as well as its 95% CI was calculated. When the MSSI was positive and its 95% CI did not include 0, statistically significant synergy was claimed for the entire data set. When the MSSI was negative without its 95% CI overlapping 0, statistically significant antagonism was concluded for the entire data set. In addition, the SSSI and the MSSI were calculated only for the statistically significant synergistic (SSYN and MSYN, respectively) and antagonistic (SANT and MANT, respectively) separately. Finally, the drug concentrations of the combination that yielded the highest synergistic or antagonistic interaction (Imax) were determined.

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Comparison of models In order to compare the four models various parameters were chosen such as (i) the single drug parameters MIC-0, MIC-1 and MIC-2 of the FIC index model, and the IC50 and the slope, m , of the Greco and the semi-parametric BI-based model; (ii) the summary interaction parameters FICi-0, FICi-1 and FICi-2 of the FIC index model, a interaction parameter of the Greco model and SSSI and MSSI of the non-parametric and semi-parametric BI-based models; and (iii) the highly interactive (Imax) drug concentrations that yielded the most potent interaction as determined with each model. The range (R ) and the geometric mean (GM) of the single drug parameters [for the slopes m the median (M) was reported] and the Imax concentrations among all strains were calculated. The relationship between the interaction parameter a and the FIC index was further examined. Hypothetical FIC indices calculated at the level of 50% of Emax (i.e. FICi-2) were plotted against the interaction parameter a according to the following equation: FICi-2 1aFICA FICB ; and assuming that FICA /FICB. This is derived after rearrangement of the Greco model given that the term [E/(Emax /E)]0.5 (1/mA1/mB) at 50% of effect equals 1 independent of the value of the slopes m , and the sum of the first two terms on the right part of the Greco equation thus is the FICi-2 [2]. In addition, the FICi-2-a relationship was studied for an alternative model, introduced first by Finney et al . [20], which is described by the following equation: 1 IC50;A

DA E

Emax E

1=mA

IC50;B

DB E

1=mB

Emax E

DA DB a (1=mA 1=mB ) E IC50;A IC50;B Emax E

1=2

The Finney model [20] is exactly the same as the Greco model except for the coefficient of the interaction parameter a, which is squared [2], and the corresponding a-FICi-2 relationship when FICA /FICB is described by FICi-2 /1 /a /(FICA /FICB)1/2. The concentrations of the drugs were transformed logarithmically in order to approximate the normal distribution. The differences between the single drug parameters and Imax concentrations determined with each model for all drug-strain pairs were analyzed with analysis of variance (ANOVA) for matched observa-

tions followed by Bonferroni’s multiple comparison tests. The summary interaction parameters determined with each model were correlated with each other with Spearman rank correlation analysis and the correlation coefficients (rs) were reported. In all comparisons, differences and correlations with P B/0.05 were considered statistically significant. Furthermore, different endpoints were used to determine synergy, zero-interaction (additivity, indifference, independence) and antagonism for each model. For the FICi model the endpoints 0.25, 0.5, 1, 2, and 4 were used, and for BI-based models 50, 100, 150 and 200% SSSI were used to determine interactions. The percentage of agreement was calculated and the results were analyzed with the weighted kappa test.

Results FIC index model The summarized results obtained with the FIC index model are presented in Fig. 1 for each species-drug combination. FIC indices varied from as low as 0.02 for S. prolificans strains with terbinafine and miconazole, to as high as 32.5 for C. glabrata stains with 5flucytosine and fluconazole, indicating strong synergy and antagonism, respectively. The results of the median FICi-0, FICi-1 and FICi-2 were consistent for three of the five combinations (S. prolificans, C. krusei and C. glabrata ). In contrast, for C. albicans and A. fumigatus the value of the FICi was dependent on the MIC endpoint chosen. For instance, using the FICi-0 for C. albicans one could conclude synergy (median FICi 0.17) but if using the FICi-2 additivity/indifference would be concluded (median FICi-2 1.03) and vice versa for A. fumigatus. As some of the variation of the results might be due to experimental errors, we looked at the variation between replicate experiments. Most of the differences among the FIC indices of the replicates were within 3 log2. High reproducibility among replicates was found when the cutoffs 0.25 and 4 were used for the lower and upper limit of additivity/indifference for interpreting the results of the FICi-1 (100%) and FICi-2 (94%). Because these indices seldom ranged from B/1 to /1 among the replicates, interactions could be classified as synergistic or antagonistic when all replicates resulted in indices lower or higher than 1, respectively, and additive/indifferent when the range of FIC indices included 1.

Greco model The fully parametric model was fitted to the entire data set of each replicate. The results of the interaction – 2005 ISHAM, Medical Mycology, 43, 133 /152



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Fig. 1 Graphical representation with analytical results of the Loewe additivity based models. (A, B, C) Fractional inhibitory concentration (FIC) index model. The minimum, median and maximum among the replicates are presented for each strain with the three horizontal lines, respectively, for the FICi-0 (A), FICi-1 (B) and FICi-2 (C). For all data sets for which the reported FICi corresponded to the SFICmin (Seedosporium prolificans, Candida albicans and Aspergillus fumigatus with FICi-1 and FICi-2), the SFICmax were lower than 2.5, while for all data sets for which the reported FICi corresponded to the SFICmax (Aspergillus fumigatus with FICi-0, Candida glabrata and Candida krusei ), the SFICmin were greater than 0.5. The difference between the SFICmin and SFICmax within a data set was less than 4 log2 for the majority (90%) of the data sets analyzed and they never ranged from B/0.5 to /4, respectively, which indicates that for a certain level of effect there were not both synergistic and antagonistic combinations within the same data set. (D) The Greco model. The interaction parameter a with its 95% confidence interval (95% CI) is presented for each replicate of each strain. Squares and triangles correspond to positive and negative a values, respectively. Regarding goodness of fit, narrow 95% CI ( B/1 log10) of the fitted parameters were obtained and the R2 and the sum of squares of all fits ranged from 0.75 to 0.95 (median 0.91) and from 0.3 to 7.4 (median 1.3), respectively.

parameters a are presented in Fig. 1. Statistically significant synergistic interactions were found for S. prolificans and C. albicans strains. Statistically significant antagonistic interactions were found for A. fumigatus, C. krusei and C. glabrata strains. No additive interactions were found with the Greco model. As can be seen in Fig. 1, the model showed excellent reproducibility (100%) among the replicates because the results of all replicates were concordant. When the residuals of each fit were tested with the KS test, statistically significant deviation from the normal distribution was found for all strains (P B/0.05) except the S. prolificans strains and two replicates of AF1. The residual plots, together with the threedimensional graphs of the response surface constructed by plotting the experimental data (experimental response surface) and data predicted with the Greco model (predicted response surface), revealed the areas – 2005 ISHAM, Medical Mycology, 43, 133 /152

where the model deviated from the data (Fig. 2). For all fits with negative interaction parameters, observed mainly with C. glabrata strains, the model deviated from the data at high concentrations of fluconazole and low concentrations of 5-flucytosine (Fig. 2Ai,ii). For this area of concentrations, the model yielded higher percentages of growth compared to the data at relatively lower concentrations of 5-flucytosine, whereas the opposite was observed at relatively higher concentrations (Fig. 2Aiii), with the two groups of residuals above and below the 0 plane. For the fits with positive interaction parameters, two patterns of deviation were found. In yeasts (i.e. C. albicans strains), the model deviated at intermediate concentrations as well as at low and high concentrations of fluconazole (Fig. 2Bi,ii), where the predicted response surface was above and below, respectively, that of the experimental data (Fig. 2Biii). In molds (i.e. S. prolificans strains),


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Fig. 2 Response surfaces of the experimental data (i) and the data predicted with the Greco model (ii) as well as the residual plots (iii). (A) Combination of fluconazole and 5-flucytosine against a Candida glabrata strain (CG2) for which the FICi-0 (fractional inhibitory concentration index 0), FICi-1 and FICi-2 were 8.5. The interaction parameter a9/95% confidence interval (95% CI) derived with the Greco model was /0.239/0.10, indicating antagonism. The normality test of the residuals resulted in systematic deviation of the model (KS /5.376; P B/0.0001). (B) Combination of fluconazole and 5-flucytosine against a Candida albicans strain (CA2) for which the FICi-0, FICi-1 and FICi-2 were 0.09, 0.09 and 1.03, respectively. The Greco model resulted in an interaction parameter of 37.089/10, indicating synergy. The normality test of the residuals resulted in systematic deviation of the model (KS/3.659; P B/0.0001). (C) Combination of miconazole and terbinafine against a Scedosporium prolificans strain (SP3) for which the FICi-1 and FICi-2 were 0.13 and 0.02, respectively. The interaction parameter a9/95% CI derived from the Greco model was 2719/120 indicating very strong synergy. The normality test of the residuals resulted in non-systematic deviation of the model (KS/0.854; P /0.46).

despite the fact that the residuals did not deviate statistically significantly from the normal distribution, the Greco model deviated from the data at high concentrations of the two drugs where the fitted response surface did not follow the same pattern of curvature as the experimental response surface resulting in higher percentages of growth (Fig. 2C).

Bliss independence based models The results for all strains are summarized in Fig. 3, where the sum and the mean of all statistically

significant interactions for each strain (SSSI and MSSI, respectively) are presented. Although the SSSI and MSSI were used for each strain as summary parameters of the BI-based models, both models resulted in a mosaic of synergy and antagonism at different concentrations of the two drugs, as depicted in Fig. 4, where the amphotericin /B-itraconazole interaction surface for an A. fumigatus strain (AF1) is presented. The sum and mean of all statistically significant synergistic (SSYN and MSYN) and antagonistic (SANT and MANT) interactions are therefore presented separately in Fig. 3. – 2005 ISHAM, Medical Mycology, 43, 133 /152



Between the two approaches, the non-parametric approach resulted in stronger interactions for S. prolificans and C. glabrata strains, whereas the semiparametric approach did this for the remaining strains. Although the absolute values of the SSSI were different between the non-parametric and semi-parametric approach, the nature of the interaction determined with these two models was the same for most strains, with the exception of one C. krusei strain. When the MSSI was correlated with the SSSI, the former became statistically significant (P B/0.05) / positive and negative / when the SSSI was higher that 100% and lower than /100%, respectively, with the non-parametric approach. With the semi-parametric approach, the

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same was found for the levels of 150% and /150% SSSI, respectively. For both approaches the MSSI was statistically significant at P /0.01 level when the SSSI was higher or lower than 200% or /200%, respectively. Based on the non-parametric approach, S. prolificans strains showed the largest SSYN (600 /1800%) and the C. glabrata strains showed the largest SANT (300 /800%) without showing both types of interaction. The remaining strains showed both SSYN and SANT, with the former being higher than the latter in most of the cases, as shown in Fig. 3Ai. Using the MSYN and MANT, the same results were obtained, with the MSYN being statistically significant higher than the MANT for the S. prolificans strains and vice versa

Fig. 3 Graphical representation with the analytical results of the non-parametric (A) and the semi-parametric (B) Bliss independence (BI) based models. The (i) sum and the (ii) mean with the 95% confidence interval (95% CI) of all (gray), synergistic (right-diagonal lines) and antagonistic (left-diagonal lines) statistically significant interactions are presented separately for each strain. Regarding goodness of fit of the Emax model for the parametric approach, the R2 ranged from 0.88 to 1 (median 0.98) and the sum of squares ranged from 0.01 to 0.27 (median 0.06) for the concentration-effect curves of 5-flucytosine. For the concentration-effect curves of fluconazole for all Candida strains except C. albicans, the R2 ranged from 0.85 to 1 (median 0.97) and the sum of squares ranged from 0.01 to 0.35 (median 0.05). Low R2 (0.47 /0.98, median 0.64) and high sum of squares (0.04 /0.31, median 0.22) were found for C. albicans strains. For miconazole, terbinafine, amphotericin B and itraconazole, the R2 and sum of squares ranged from 0.72 to 1 (median 0.86) and from 0.01 to 0.2 (median 0.05), respectively. Low R2 (0.43 /0.57) and high sum of squares (0.17 /0.32) were found for itraconazole against the AF2 strain. Run tests resulted in non-statistically significant deviation of the Emax model for the concentration-effect curves of all drugs.

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for the C. glabrata strains, as shown in Fig. 3Aii. Although the same conclusions were inferred with the semi-parametric approach, the latter model resulted in some, but weak, SANT for S. prolificans strains (Fig. 3Bi) and MSYN, that was not statistically significantly different from the MANT in absolute values (Fig. 3Bii). However, the 95% CI of MSYN and MANT could not be calculated in some cases as only one combination showed the effect.


Comparison of the models Single drug parameters Among the three MIC endpoints calculated with the FIC index model, statistically significant differences were found between the MIC-2 (R : 0.03 to /64 mg/l; GM: 2.8 mg/l), and the MIC-0 (R : 0.03 /256 mg/l; GM: 8.2 mg/l) and MIC-1 (R : 0.03 /256 mg/l; GM: 7.3 mg/l). These differences were observed mainly with the azoles and particularly with fluconazole tested with the C. albicans strains where a 10- and ninefold difference between the median MIC-0 and MIC-1, respectively, and the MIC-2 was found. Overall, the IC50 estimated with the Greco model (R : 0.03 /4 /104 mg/l; GM: 4.2 mg/l) and semi-parametric BI-based model (R : 0.01 /2.9 /104 mg/l; GM: 2.1 mg/l) were not statistically significant different from each other, although relatively higher IC50 were obtained with the former. The differences between the median IC50 of each drug-species combination were within two twofold dilutions, with the exception of the S. prolificans strains. For these strains the IC50 of terbinafine obtained with the Greco model were higher than those obtained with the semi-parametric BI-based model. The IC50 estimated with the Greco model were not statistically significant different from the MIC endpoints, whereas the IC50 estimated with the semiparametric BI-based model were statistically significant from MIC-0 and MIC-1, but not from MIC-2. The slopes estimated with the Greco model (R :/0.07 to /300; M: /1.6) and the semi-parametric BI-based model (R : /0.1 to /20; M: /1.8) were not statistically significant different (data not shown). Summary interaction parameters Statistically significant correlation was found among all summary interaction parameters (Table 2). All correlation coefficients between the FIC index model and the other models were negative. Between the FIC index and the Greco model, the strongest correlation was found between the interaction parameter a and the FICi-0 (rs / /0.745) followed by FICi-1 (rs / /0.736). To determine

whether the value of the a interaction parameters could predict the magnitude of the FIC indices, combinations with negative and positive a interaction parameters were analyzed separately (Fig. 5A,B). No statistically significant correlation was found between the negative a interaction parameters and the corresponding FIC indices (FICi-0: rs / /0.04, P / 0.85; FICi-1: rs / /0.09, P / 0.64; FICi-2: rs /0.21, P / 0.24) (Fig. 5A). For the positive a interaction parameters, statistically significant correlation was found with the FICi-0 (rs /0.81, P B/0.001) and FICi-2 (rs / 0.65, P / 0.004) but not with FICi-1 (rs /0.38, P / 0.12) (Fig. 5B). To further explore the relationship between a interaction parameters and FIC indices, the a interaction parameters were plotted against the corresponding FIC indices from low to high a values separately for interactions with negative (Fig. 5A) and positive (Fig. 5B) interaction parameters. Two patterns were detected. For negative interaction parameters, high a values (close to 0) tended to correspond to high FIC indices (Fig. 5A), whereas for positive interaction parameters, small a values (close to 0) tended to correspond to high FIC indices (close to 1) (Fig. 5B). This non-monotonic relationship between the interaction parameter a of the Greco model and the FIC index is depicted in Fig. 5C, where theoretical data are plotted. A monotonic FICi-2-a relationship was found when the Finney model was used (Fig. 5C). Given that replicates are required to obtain a summary parameter for BI-based models (as opposed to LA-based models, where each replicate resulted in a summary parameter) for the correlations between the BI- and LA-based models, the median summary parameter of LA-based models among the replicates were used. Thus, between the summary parameters of BI-based models, high correlation coefficients were obtained when the SSSI, rather than the MSSI, was used. Between the Greco and BI-based models, the interaction parameter, a, of the Greco model was highly correlated with the SSSI of both the semi-parametric (rs /0.782) and the non-parametric (rs /0.760) approaches. Between the FIC index and BIbased models, the strongest correlation was found between the SSSI of the non-parametric and the semi-parametric approaches and the FICi-0 (rs /0.98) and FICi-1 (rs /0.96), respectively. Statistically significant correlation was found between the BI-based models and the FIC index model even when combinations with positive and negative SSSI were analyzed separately. – 2005 ISHAM, Medical Mycology, 43, 133 /152

All correlations were significant at 0.01 level. For the correlation of the summary parameters obtained with LA-and those obtained with BI-based models the median parameter of the three replicates obtained with the LA-based models was used. b

Semiparametric BI

Greco Non-parametric BI


a

/0.888 /0.954 /0.823 0.757 0.885 0.816 0.980 1 /0.903 /0.956 /0.854 0.782 0.887 0.801 1 /0.981 /0.900 /0.871 0.760 1 FIC index

FICi-0 FICi-1 FICi-2 a SSSI MSSI SSSI MSSI

1

0.927 1

0.833 0.816 1

/0.745 /0.736 /0.624 1

/0.905 /0.808 /0.757 0.718 0.944 1

SSSI SSSI FIC-2 FIC-1 FIC-0

a

MSSI

Semi-parametric Non-parametric Greco FIC index

Bliss independence-based modelsb Models and Summary interaction parameters Loewe additivty-based models

Correlationa between different summary interaction parameters of parametric and non parametric approaches of Loewe additivity and Bliss independence Table 2


MSSI


143

Highly interactive drug concentrations For the FIC index model the larger the effect, the higher the Imax concentrations (and therefore the Imax concentrations) calculated based on FICi-0 (R : 0.008 /256 mg/l; GM: 3.76 mg/l) were higher than the corresponding values calculated based on FICi-1 (R : 0.004 /256 mg/l; GM: 1.92 mg/l) and FIC-2 (R : 0.004 /256 mg/l; GM: 0.75 mg/l) in most cases (data not shown). No statistically significant differences were found between the Imax concentrations of the Greco model (R : 0.03 /128 mg/l; GM: 1.32 mg/l) and the other models with the GM of the Imax concentrations determined with the Greco model (1.32 mg/l) to be between the Imax concentrations determined with the FICi-1 and the FICi-2. The BI-based models showed the strongest interactions at lower concentrations (R : 0.02 /128 mg/l, GM: 0.74 mg/l, for the nonparametric; R : 0.008 /64 mg/l, GM: 0.36 mg/l, for the semi-parametric) and were not statistically significantly different from those determined with the FICi-2, but not from those determined with FICi-0 and FIC-1. Statistically significant differences were also found between the Imax concentrations of the FIC-2 and FIC-0 (data not shown). Agreement between the models The levels of agreement between the models based on the interpretation of the results are summarized in Table 3, together with the results of the kappa test. Given that no additive interactions were found with the Greco model, for the comparisons with this model a unique cutoff was used for the determination of synergy and antagonism. For the comparisons between the BI- and LA-based models, the interpretation of median interaction parameter among the replicates was used for the Greco model while for the FIC index model synergy or antagonism was defined when all replicates resulted in FIC indices lower or higher than the chosen cutoff, respectively. In any other case, additivity/indifference was concluded. Between the Greco model and the FIC index model, the highest level of agreement for each type of FIC index was found when the cutoff 0.25 was used for the interpretation of the results, with FICi-0 and FICi-1 showing the highest levels of agreement (100%) followed by FICi-2 (78%). Among interactions classified as synergistic with the Greco model (a /0) all were classified as synergistic with FICi-0 and FICi-1 (5/0.25) and vice versa. Only 67% of Greco synergistic interactions were classified as synergistic with FICi-2 (5/0.25) with the remaining to

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Table 3 Agreement in % (kappa value) between the four models using different endpoints for the definition of synergy (SYN), additivity/ indifference (ADD), independence (IND) and antagonism (ANT)


Models and Interpretation endpoints

Agreement in % (kappa value) FIC index

FIC-0

Greco model SYN;a9/95%CI/0,ANT;a9/95%CIB/0 SYN;a9/95%CI/0,ANT;a9/95%CIB/0 SYN;a9/95%CI/0,ANT;a9/95%CIB/0 SYN;a9/95%CI/0,ANT;a9/95%CIB/0

SYN5/0.25, ANT/0.25 SYN5/0.5, ANT/0.5 SYN5/1, ANT/1 SYN5/4, ANT/4

100% 100% 96% 68%

Non parametric BI SYN; SSSI/100% IND; 100%B/SSSIB/ /100% ANT; SSSIB/ /100% SYN; MSSI9/95%CI/0 IND; MSSI9/95%CI incl. 0 ANT; MSSI9/95%CIB/0

SYN; range FICis B/1, ADD; range FICis incl. 1 ANT; range FICis/1 SYN; range FICis B/1, ADD; range FICis incl. 1 ANT; range FICis/1

Semi-parametric BI SYN; SSSI/150% IND; 150%B/SSSIB/ /150% ANT; SSSIB/ /150% SYN; MSSI9/95%CI/0 IND; MSSI9/95%CI incl. 0 ANT; MSSI9/95%CIB/0

SYN; range FICis B/1, ADD; range FICis incl. 1 ANT; range FICis/1 SYN; range FICis B/1, ADD; range FICis incl. 1 ANT; range FICis/1

Greco model SYN;a9/95%CI/0 ANT;a9/95%CIB/0 SYN;a9/95%CI/0 ANT;a9/95%CIB/0

Non parametric BI SYN; SSSI/100% ANT; SSSI 5/100% SYN; MSSI9/95%CI/0 ANT; MSSI9/95%CIB/ or incl. 0

94% (0.94)

Greco model SYN;a9/95%CI/0 ANT;a9/95%CIB/0 SYN;a9/95%CI/0 ANT;a9/95%CIB/0

Semi-parametric BI SYN; SSSI /150% ANT; SSSI5/150% SYN; MSSI9/95%CI/0 ANT; MSSI9/95%CIB/ or incl. 0

94% (0.94)

Semi-parametric BI SYN; SSSI/150% IND; 150%5/SSSIB/ /150% ANT; SSSI5/ /150% SYN; MSSI9/95%CI/0 IND; MSSI9/95%CI incl. 0 ANT; MSSI9/95%CIB/0

Non parametric BI SYN; SSSI/100% IND; 100%5/SSSIB/ /100% ANT; SSSI5/ /100% SYN; MSSI9/95%CI/0 IND; MSSI9/95%CI incl. 0 ANT; MSSI9/95%CIB/0

a b

FIC-1

(1.00) (1.00) (0.96) (0.70)

100% 96% 88% 64%

FIC-2

(1.00) (0.96) (0.88) (0.66)

78% 76% 72% 62%

(0.75) (0.74) (0.71) (0.64)

71% (0.65)

71% (0.64)

59% (0.46)a

65% (0.60)

65% (0.58)

53% (0.40)

71% (0.65)

76% (0.76)

65% (0.58)b

71% (0.65)

76% (0.76)

65% (0.58)

88% (0.88)

94% (0.94)

88% (0.95)

82% (0.92)

For FICi-2, higher agreement (65%, k/0.51) was found with 150% SSSI. For FICi-2, higher agreement (71%, k /0.59) was found with 200% SSSI.

be additive/indifferent (0.25 B/FICi 5/4). Among the interactions classified as synergistic with FIC-2 ( 5/0.25), 31% were antagonistic with the Greco model, consisting of the combinations of amphotericin Bitraconazole. In all cases half of the interactions classified as antagonistic with the Greco model were additive/indifferent with the FIC index model (0.25 B/ FICi 5/4). Between the FIC index and the non-parametric BI-based model the highest levels of agreement (71%) were found when the FICi-0 and FIC-1, and the levels of 100% and /100% SSSI, were used for the inter-

pretation of the results (Table 3). Between the FIC index and the semi-parametric BI-based model, the highest levels of agreement (76%) were found when the FICi-1, and the level of 150% and /150% SSSI, were used for the interpretation of the results. None of the interactions classified as synergistic with the FICi model were classified as antagonistic with the BI-based models, but not vice versa as half of the interactions classified as antagonistic with the FICi model were not antagonistic with BI-based models but mostly additive, and a few (B/12%) synergistic. Much higher levels of agreement (88 /100%) between the FIC index and the – 2005 ISHAM, Medical Mycology, 43, 133 /152


BI-based models were found when, for the interpretation of the FICi-0 or FICi-1, the cutoffs of 0.25, 0.5 or 4 were used. The highest agreement between the Greco model and the BI-based model was found using the same endpoints for SSSI (150% for semi-parametric and 100% for non-parametric) and MSSI. However, it must be noted that interactions were positive up to 150 or 100% SSSI, or with MSSI where the 95% CI included 0, had negative a values with the Greco model.


Discussion Different drug interaction models were used in this study to analyze the in vitro interaction of different antifungal drugs against various fungal species using the microdilution checkerboard technique. Interactions that varied in nature and degree, as assessed with the standard model in the field of medical microbiology, the FIC index model, were included, and head-to-head comparisons with three other models were made. The first and major problem in determination of the FIC index is the choice of the MIC endpoints for the two drugs alone and in combination [8]. Although complete inhibition of growth is the endpoint often used with antibiotics, this was not possible in the case of the S. prolificans strains tested against terbinafine and miconazole because complete inhibition of growth (MIC-0) was not observed for some data sets using any of the combinations of the two drugs. The interaction was synergistic, however, based on 75% (MIC-1) and 50% (MIC-2) inhibition of growth. Even when the MIC-0 was defined as in cases of C. albicans strains with 5-flucytosine and fluconazole, and A. fumigatus strains with amphotericin B and itraconazole, different FIC indices were obtained when the MIC-2 was used, reversing the interpretation of the results from synergistic and additive/indifferent to additive and synergistic, respectively. These discrepancies were due to trailing phenomena observed with C. albicans strains when the drugs were tested alone. Trailing was reduced when the two drugs were combined, thus confirming previous studies [16]. MIC-2 was less sensitive to trailing than were the other MIC endpoints. In the case of A. fumigatus strains, the fungicidal action of amphotericin B at high concentrations of amphotericin B may cover the fungistatic action of itraconazole and vice versa at sub-MIC concentrations of amphotericin B and high concentrations of itraconazole. The MIC-2 endpoint was less sensitive to this effect than were the other MIC. However, some of the discrepancies between FICi-0, -1 and -2 might be due to off-scale MIC – 2005 ISHAM, Medical Mycology, 43, 133 /152

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alone and in combination when the MIC-0 and MIC-1 were used, resulting in approximated FIC indices. Another drawback of the FIC index model is the summary parameter for each data set and the interpretation of this parameter [12]. According to the guidelines [13,19], among all SFIC indices calculated for all iso-effective combinations of a data set, the SFICmin is reported as the FICi unless SFICmax exceeds 4. Synergy is claimed when the FICi is lower than 0.5 and antagonism when FICi is higher than 4. These cutoffs were chosen in this study in order to diminish the effect of the intraexperimental error (9/1 dilution) of antifungal susceptibility testing because a twofold drug dilution scheme was followed [21,22]. The drawback of this approach is that the SFIC of a single well attempts to describe the whole checkerboard without taking into account the interactions occurring at other concentrations and levels of effect, and without including its uncertainty. Particularly for data sets in which the SFIC ranged from 0.5 to 4, it is not clear whether to report the SFICmin or the SFICmax. An alternative solution could be the calculation of the average SFIC and its 95% CI among all SFICi of a data set. Furthermore, combinations with small differences in growth (e.g. 10%) may change dramatically the FIC index (up to 3 log2). Outliers can affect the results, particularly when checkerboards were abnormal, and therefore subjective exclusion or inclusion of iso-effective wells was necessary. In order to constrain the inter-experimental error, replicates were performed resulting in FIC indices in most of the cases within 3 log2 (i.e. 0.25 /1 or 1 /4). For the interpretation of the results, different endpoints have been used in the literature. Based on reproducibility of the results, high reproducibility was found with FICi-1 and the FICi-0 (100%) when the cutoffs of 0.25 and 4 were used for the lower and the upper limit of additivity/indifference, respectively, in order to interpret each replicate individually. These cutoffs are 2 log2 below and above the additivity level 1 and can be obtained after taking into account one doubling dilution error (often observed with the NCCLS methodology) for both drugs, alone or in combination, within any direction of the checkerboard. Although, different cutoffs can be found in the literature [23 /26] the cutoffs recommended from the guidelines [7] and commonly used for the upper and lower limit of synergy and additivity/indifference are 0.5 and 4, respectively. These cutoffs, although arbitrary, are more stringent for defining antagonism than synergy because the cutoff of synergy (i.e. 0.5) is 1 log2 while the cutoff of antagonism (i.e. 4) is 2 log2 different than 1 (additivity). Therefore, the cutoffs 0.25 and 4 should be


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used for the lower and the upper limit of additivity/ indifference, respectively, which has also been suggested in previous studies [27,28]. By using stringent and arbitrary criteria to describe in vitro interactions, the inherent errors in laboratory tests might be less problematic but are not eliminated completely. Furthermore, given that most of the FIC indices lie between 0.5 and 1 [25,29 /31], large amounts of information about the drug interactions can be lost that might be important in vivo [32]. There are several approaches with which to overcome these problems without losing important information; these include smaller dilution steps, overlapping dilution series, continuous dilutions, more accurate techniques or replication [28,32,33]. When replicates were analyzed, high reproducibility was found in the present study, when synergy and antagonism was concluded if all replicates resulted in FIC indices lower or higher than 1, respectively, and additivity or indifference was concluded when the range of the FICi included 1. In addition, the departure of the FIC index from 1 can be evaluated statistically by checking whether the 95% CI overlapped 1, in which case no statistically significant interaction should be concluded. In order to overcome the above-mentioned drawbacks of the FIC index model, another model based on the Loewe additivity zero-interaction theory was used / the fully parametric model described by Greco et al . [1]. The model fitted well to the data derived from all drug-combination /strain pairs based on the R2 and sum of squares. However, when the residuals were analyzed statistically and graphically, the model deviated systematically from the data. This deviation was statistically significant in all fits, with negative interaction parameters (antagonistic interactions), and was located at high concentrations of either drug at which the experimental response surface was above the additive (antagonistic combinations). For this, the Greco model did not follow the curvature of the experimental response surface and it resulted in growth, although experimentally no growth was observed. For the fits with positive interaction parameters (synergistic interactions), statistically significant deviation was found for the C. albicans strains. This deviation was due to the trailing phenomena observed with fluconazole, which also resulted in bad fit of the Emax model when the latter was fitted to the concentration-effect curves of fluconazole for the C. albicans strains. In order to diminish the effect of trailing, the concentration-effect curves for trailers could be normalized by setting the growth observed in concentrations at which the trailing was apparent as 0%. For the S. prolificans strains tested with miconazole and

terbinafine, although a statistically significant deviation of the model was not found, residual plots and threedimensional graphs revealed the area where the model did not describe the experimental surface precisely. This area was located at relatively high concentrations, where the largest bowing of the response surface was observed (Fig. 2Ci). For this, the Greco model resulted in a flatter response surface (Fig. 2Cii). The Greco model assumes that the concentrationeffect curves of each drug at any level of the other drug follow the Emax model with variable parameters (IC50 and slopes), as is shown in Fig. 2Aii. However, in the case of antagonistic interactions, where the response surface concaves down and bell-shaped concentrationeffect curves are apparent (see the concentration effect curve of 5-flucytosine in the presence of 128 mg/l of fluconazole in Fig. 2Ai), the Emax model does not appear to hold true. These bell-shaped curves are also observed, although less clear, in synergistic interactions (Fig. 2Ci), where the response surface concaves up (concentration effect curve of terbinafine in presence of 8 mg/l miconazole). This deviation of the model is more pronounced, with strong interactions and declines, as the interaction parameter approaches 0. This deviation is not reported in previous studies in which the Greco model was used because low (close to 0) interaction parameters were found in these studies and data on goodness of fit (except the 95% CI) are not presented in most [8,15,34,35]. However, given the inaccuracy of the standard methodologies for in vitro antifungal susceptibility testing, this deviation should be explored further. Based on the results derived with the Greco model, no additivity was found using the MODLAB spreadsheet, which might indicate the sensitivity of the model in detecting even weak interactions. The results were very reproducible as all replicates were concordant. Although positive interaction parameters covered a broad range of values (from 1 to 10 000), the negative interaction parameters were bounded in a narrow range (from /0.04 to /0.51), possibly indicating the inability of the model to differentiate different degrees of antagonistic interactions, as was also discussed above in relation to the difficulty with the Greco model in describing the response surfaces. One of the assumptions of the Greco model is that antagonistic combinations cannot coexist with synergistic ones in the same data set, and if such a case is found it is due to artifacts or experimental errors [36]. However, Berenbaum summarized many types of interactions where both antagonism and synergy are present at different concentrations [3]. These types of interactions cannot be described with the Greco model. – 2005 ISHAM, Medical Mycology, 43, 133 /152



Concentration-dependent interactions were found for Candida albicans tested with the combination of fluconazole with fluphenazine, where antagonism was observed at low concentrations of fluconazole and synergy at higher concentrations [37]. These results are also supported by molecular studies on the mechanism of action. Similar phenomena were observed when itraconazole was combined with fluphenazine against itraconazole-resistant Aspergillus fumigatus strains (unpublished data). Because biphasic types of interactions might exist, two other models that can accommodate mosaics of interactions were used to analyze the interaction of antifungal drugs. These models are based on Bliss independence zero-interaction theory without any assumption about the shape of the concentration-effect curves of the single drugs (non-parametric approach) or that the latter followed the Emax model (semiparametric approach) [12]. With these models, the type of interaction was assessed for each combination of the tested drug concentrations. Both models resulted in a mix of statistically significant synergistic and antagonistic combinations for most of the data sets, with the relative proportion ranging from purely synergistic for the S. prolificans strains to purely antagonistic for C. glabrata strains. The levels of synergy or antagonism determined with the non-parametric and the semi-parametric model were comparable in most of the cases, except for some cases where more antagonistic interactions with S. prolificans strains and

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more synergistic interactions with C. albicans and A. fumigatus (Fig. 4) strains were found with the semiparametric approach. For the S. prolificans strains, the antagonistic interactions were found at the highest concentrations of the drugs. This might be due to precipitation at these high concentrations or evaporation phenomena, as these concentrations were in the outer wells of the microtiter plates. This affected the semi-parametric approach, because with this approach experimental errors are selectively eliminated with the fitting process only in the single-drug-containing wells and not in all directions of the checkerboard. For C. albicans and A. fumigatus strains, the bad fit of the Emax model to the concentration-effect curves of fluconazole and itraconazole, due to trailing effects and in vitro resistance, resulted in higher percent growth for each concentration of the drugs present alone. Consequently, the independent response surface determined with the semi-parametric approach was shifted at higher levels compared to that of the non-parametric approach, therefore resulting in higher levels of synergy, particularly at lower drug concentrations. Although the few antagonistic combinations found in particular with the semi-parametric approach for the S. prolificans strains could be due to experimental variation, the presence of both types of interactions at different concentrations might raise points for discussion about the mechanistic explanation of these observations. For instance, when itraconazole was

Fig. 4 Interaction surfaces obtained with the non-parametric (A) and the semi-parametric (B) approach of Bliss independence (BI) where the percent synergy (above the 0 plane) and antagonism (below the 0 plane) are shown. The combination of itraconazole and amphotericin B against Aspergillus fumigatus strain (AF1), resulted in 21% sum of statistically significant interactions (SSSI) and 1.29/11.6% mean SSI (MSSI) with the non-parametric approach of BI and 82% SSSI and 4.39/9.4% MSSI with the semi-parametric approach.



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combined with amphotericin B against itraconazoleresistant Aspergillus fumigatus, antagonistic interactions were found at concentrations around the MIC of amphotericin B (2 /0.5 mg/l) and synergistic ones at sub-MIC concentrations of amphotericin B (B/0.5 mg/l) (Fig. 4). Whether the antagonistic effects are related to the lack of ergosterol due to sterol biosynthesis inhibition by itraconazole, and the synergistic ones to the increased uptake of itraconazole inside the fungus due to damages of cell membrane caused by low concentrations of amphotericin B, suggested by previous studies [38,39], need to be confirmed with molecular studies. Then it would also be possible to evaluate mechanistically the validity of each of the zero-interaction theories used in the present study to assess the interaction of antifungal drugs. However, the same biphasic effect was also observed with the FIC index model, as synergy was found at 50% growth inhibition (which was observed in combinations with sub-MIC concentrations of amphotericin B) and additivity/indifference at 90% growth inhibition (which was observed in combinations with concentrations around the MIC of amphotericin B) (Fig. 1). In order to summarize the results obtained with the BI-based model for further comparisons, and with reserve as to their legitimacy from the mechanistic point of view, two approaches were followed. For each data set the sum and the mean together with its 95% CI of all statistically significant interactions were calculated. The approach developed by Prichard et al . [14] [where the volumes (% interaction /concentrations of the two drugs) above and below the 0 plane were calculated] was not followed because the final results are influenced unequally by small-degree interactions occurring at high concentrations. Therefore, based on the sum and the mean of statistically significant interactions, the latter was positive, without its 95% CI overlapping 0, when the sum was higher than 100% and negative when the sum was lower than /100% for the non-parametric approach. While the same is true for the semi-parametric approach based on 150% and /150% sum of statistically significant interactions, respectively, the level of 100% also could be used for the latter approach as only few data were found between these two levels. In addition, when the sum of all statistically significant interactions exceeded (for synergistic interactions) or was below (for antagonistic interactions) 200% and/200% respectively, the mean of all statistically significant interactions was statistically significant different from 0 at a higher significance level of P/ 0.01. Therefore, the cutoffs of 100 and 200% (in absolute values) for the sum of all statistically significant interactions may serve as cutoffs for weak

(0 /100%), moderate (100 /200%) and strong (/200%) interactions. Between the two approaches of BI, higher reproducibility among the replicates was found with the non-parametric approach, as the range of the sum of statistically significant interactions was within 150% for most of the strains. Despite the advantages and disadvantages of each model, the most important point is the nature of an interaction determined with each model and the discrepancy between them. Therefore, a head-to-head comparison was performed, including primary parameters (MIC, IC50, slope m ) used for the calculation of the summary interaction parameters (FICi, a, SSSI and MSSI) of each model, based on which of the combinations were classified to different interaction groups (synergy, zero-interaction or antagonism). Nonstatistically significant differences among the MIC-2, determined with the FIC index model, and the IC50, determined with the Greco and the semi-parametric BI models (within two doubling dilutions), as well as between the slopes of the concentration-effect curves determined by the two latter models, were found. This indicated that the Emax model could be used to determine the in vitro susceptibility of fungi and that fully parametric approaches do not affect the concentration-effect curves of the single drugs. When the summary parameters of each model were correlated, a statistically significant correlation was found for all models. A strong correlation was found between the FICi-0 and FICi-1, the interaction parameter a, the SSSI and the MSSI of both BIbased models. For the FIC index and the Greco model, no statistically significant correlation was found between the FICi and the a values, when the interactions with negative interaction parameters were analyzed separately. This might indicate the qualitative nature of the Greco model for combinations with negative interaction parameters, as discussed above, although when a large number of data sets were analyzed, positive statistically significant correlation was found between negative a interaction parameters and FIC-2 indices (unpublished data). However, because the FIC index model in itself is an approximation of the intensity of the interactions, such an assumption needs further exploration. Negative correlation was found between the FICi model and the other models as high FICi corresponded with low values of the other summary parameters. However, this monotonic relationship was not found for the a interaction parameters obtained with the Greco model as a biphasic correlation was found with experimental (Fig. 5A and 5B) as well as theoretical data (Fig. 5C). Thus although the – 2005 ISHAM, Medical Mycology, 43, 133 /152



magnitude of synergy and antagonism is related to the degree of departure of the FICi from 1 (i.e. the larger the degree of departure, the stronger the interactions) with the FIC index model, with the Greco model this seems to hold only for positive interaction parameters (i.e. the larger the degree of departure of a interaction parameter from 0, the stronger the synergy), as for negative interaction parameters the opposite was observed (i.e. the larger the degree of departure of a interaction parameter from 0, the weaker the antagonism). A monotonic FICi-a relationship was found using the Finney model, which was suggested by Greco et al . [2] in order to overcome the rise at high concentrations observed with the first model. This rise is more pronounced at a values lower than /0.5 and they were therefore not observed in the present study because most of the a values were higher than /0.5. Although this model shows a monotonic relationship with the FICi (Fig. 5C), preliminary studies show that it shares the same drawbacks, although to a lesser extent, as does the first model; inferring the same conclusions. The narrow range of negative a interaction parameters found in this study can be explained by the fact that there is a minimum at /1 and a maximum at 0 for the a values (Fig. 5C). The latter minimum is also confirmed by the fact that in none of the previous studies [8,15,18,34,40] in which combinations analyzed with the Greco model were found a values lower than /1. However, a values lower than /1 can theoretically be obtained (based on the above equation, which describes the FIC-2 /a relationship) when FICA "/ FICB, such as the interaction of flucytosine and

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fluconazole against C. glabrata , where isoeffective combinations were observed at concentrations 0.5and eightfold the MIC-2, respectively, in which case asymmetrical isobols (more bowed towards fluconazole axis) are obtained when normalized isobolograms are constructed. If this asymmetry is not due to experimental variation, and given that with the Greco model normalized isobols at 50% of the effect are always symmetrical (see fig. 6 in Greco et al . [2]), interactions with FICA "/FICB may not be described adequately with this model. Similar phenomena were also observed for synergistic interactions such as the interaction of itraconazole and amphotericin B against A. fumigatus, where isoeffective combinations were observed at concentrations of 0.25- and 0.06-fold the MIC-2, respectively, resulting in isobols more bowed towards itraconazole axis in the isobolograms. Fig. 5A depicts how the degree of antagonism is reversibly related with the magnitude of the a values for the experimental data, as increase in the FIC index is associated with increase in the interaction parameter a (closer to 0) for negative values, as opposed to the positive interaction parameters (Fig. 5B). The comparison of the models based on the interpretation of the results showed high levels of agreement between the Greco and the FIC index model when the cutoff of 0.25 was used to interpret the FICi-0, the FICi-1 and the FICi-2 of each replicate separately. Although one might expect the cutoff of 1 to show the highest agreement, as this is the theoretical level of additivity, this can be explained with the sensitivity of the FIC index model to experimental errors and random variation, and therefore its inability to detect

Fig. 5 Correlation between the FIC indices and the a interaction parameters obtained with the Greco model. (A, B) For all 51 data sets analyzed, the a values obtained with the Greco model were plotted against FICi-0 (fractional inhibitory concentration index 0) (closed squares), FICi-1 (closed triangle) and FICi-2 (closed reverse triangle) separately for interactions with negative (A) and positive (B) a interaction parameters, including the results of linear regression analysis for FICi-0 (solid line), FICi-1 (dotted line) and FICi-2 (dashed line). (C) Graphical representation of the theoretical relationship between the interaction parameter a and the FIC-2 index (assuming that FICA /FICB) defined by equation FICi-2/1/a /FICA /FICB (open reverse triangles), which is from the Greco model used in the present study, and equation FICi-2/1 /a (FICA /FICB)1/2 (open triangles), which is derived from an alternative model described first by Finney et al . [11]. Note the nonmonotonic behavior of the first equation (Greco) in contrast with the second equation (Finney). For negative interaction parameters, the first equation (Greco) has an asymptote at 0 whereas the second equation (Finney) at /2.



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small departures from additivity in combination with the ability of the Greco model to detect even small departures from additivity/indifference. Although in the present study all data sets classified additive/ indifferent with FICi model (0.25B/FICi5/4) were antagonistic with the Greco model (a B/0), this seems to be dependent on the data set analyzed, as found previously [18]. The highest level of agreement was found with FICi-0 and FICi-1, as an interaction at that level (i.e. 10 and 25% of growth, respectively) would result in a more bowed response surface with the Greco model and therefore in a larger departure from the additive response surface. From this point of view the results of the Greco model were dependent more on the type of interaction present at high levels of effect (i.e. 90% growth inhibition) than at lower levels (i.e. 50% growth inhibition). The highest levels of agreement between the BI-based models and the FICi model were found when the cutoffs of 0.25 and 4 were used to determine the upper limit of synergy and additivity/indifference, respectively, when only the median FICi among the three replicates, rather than the FICi of all replicates, was used for the comparisons (data not presented). However, when all three replicates were used to determine synergy (all FICi lower than 1) antagonism (FICi greater than 1) and additivity/indifference (in any other case), satisfactory levels of agreement were found [8]. For the BI models the corresponding levels of synergy and antagonism were 100% and /100% SSSI for the non-parametric approach and 150% and /150% SSSI for the semi-parametric approach, as discussed above. The latter resulted in higher levels of agreement with the other models using both the SSSI and MSSI for the interpretation of the results. The drug concentrations that showed the highest interactive effect (Imax), were not statistically significant different among the four models. The Imax determined with the Greco model were observed at concentrations showing growth between 25 and 50%. The Imax drug concentrations determined with the BI models were relatively lower and observed at concentrations showing 50% growth. These conclusions confirm previous observations [1,2], where the largest synergy was found at concentrations near but not exactly at the IC50 of the two drugs and that the isobols are more bowed (stronger synergy) at 90% pharmacological effect (i.e. 10% of growth). In conclusion, for the assessment of the interaction of antifungal drugs the FICi model is subjective and imprecise. Although when using the MIC-2 (50% of growth) for calculating the FICi, problems relating to trailing effects were eliminated, and even weak

interactions could be detected (such as with fungistatic /fungicidal combinations), lower levels of reproducibility and agreement with the other models were found than with other MIC endpoints. However, because interactions at different levels of effect (i.e. 50, 75 and 90% of growth inhibition) are important for describing the concentration-dependent nature of drug combinations, particularly when more than one type of interaction is present, the FICi using different MIC endpoints should be determined before inferring final conclusions for the drug combination. The cutoffs of 0.25 and 4 as the lower and upper limits of additivity/indifference, respectively, or the departure from 1 when replicates are performed, should be used for the interpretation of the results when analyzing single experiments. However, the drawbacks of this model, such as the monodimensional nature, lack of good summary, including statistical significance levels, and the sensitivity to experimental errors, remain. For the BI models, the sum of statistically significant interactions with any mechanistic reserve could be used to differentiate synergistic from antagonistic interactions, and 100% and 200% as cutoffs for weak and moderate interactions. Particular care to the choice of model should be given in semi-parametric approaches (especially with resistant and trailing strains) because the fitting process eliminates errors selectively in single drug concentrations but not in entire response surfaces. With the BI models, the multifactorial nature of drug interactions is emphasized and statistical significance levels are included. However, replicates are required, the results are dependent on the range of concentrations tested, variation within the replicates can affect the levels and nature of statistically significant interactions, and comparisons between different data sets are difficult. The Greco model was able to distinguish synergistic from non-synergistic interactions with a single concentration-independent non-unit interaction parameter, including statistically significant levels, without requiring replicates. It was reproducible, objective and less sensitive to experimental error. Given the inaccuracy of standard methodologies for in vitro antifungal susceptibility testing, statistically significant interactions may not be directly related to in vitro significant interactions. Fully parametric models can be applied in frugal experiments using the D-optimal design theory [41] and can be easily used in order to convert concentration /time triplets to time /effect relationships [42,43]. The Greco model did not describe precisely the response surface of antifungal combinations and deviation of the model from experimental data must therefore always be checked (i.e. the value of the sum of – 2005 ISHAM, Medical Mycology, 43, 133 /152



squares, residual plots, run test). The interaction parameters may be approximations, particularly when more than one type of interaction is present within a data set, and quantitative results might be difficult to obtain, particularly for antagonistic interactions. A monotonic relationship with the FICi model could be obtained using the Finney equation. As is pointed out by Greco et al . [2], the latter model is a model to assess drug interactions and efforts to develop a model that will describe precisely the response surface, should therefore be continued. Overall, when the LA-based models were compared with the BI-models, high levels of agreement and correlation were found by adjusting the endpoints for synergy and antagonism. Berenbaum showed that BI is a case of LA when the concentration-effect relationships are exponential [3]. Even when concentrationeffect relationships are following the Emax model, the shapes of the isobols for LA and BI at 50% effect level are similar when the slope of the Emax model is close to 1.2 as it is shown in the review by Greco et al. [2]. Slope parameters that are large in magnitude result in Loewe antagonism, whereas slope parameters that are small in magnitude result in Loewe synergy, when analyzed with BI theory [2]. In the present study, mean slopes (among replicates and strains) of each drug varied from 0.3 to 7.3. This might explain the fact that high levels of agreement were found when no interaction of BI encompassed interactions with SSSI from /150% (or /100%) to 150% (or 100%), as zero interactions with BI theory could be classified as antagonistic with LA theory for drugs with steep concentration-effect curves (slopes larger than 1) and synergistic for drugs with swallow concentration-effect curves (slopes smaller than 1). Thus when the slope of the Emax model for both drugs is close to 1.2, BI theory should provide similar results to LA theory. Finally, the models could be evaluated biologically if the mechanism of action was fully understood, although this might be complicated in growth assays where population factors and in vitro parameters could affect the interaction [3]. Therefore, drug interaction modeling should be focused on concentration-effect response surface approaches [12]. A comprehensive drug interaction model that describes the entire response surface and assesses the interaction with a single parameter is an attractive approach. However, even if the concentration-effect relationships of single drugs are well characterized and parameterized, the development of such a model that would be applicable to different interactions and tested against different microorganisms in various in vitro conditions is unlikely. Therefore, different models might be – 2005 ISHAM, Medical Mycology, 43, 133 /152

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required to assess the various combinations and possible interactions and to predict the clinical outcome of combination therapy.

Acknowledgements This work was supported by the Mycology Research Center of Nijmegen.

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