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¤ Current address: Clinical Research Division, Bassett Healthcare Research Institute, Bassett Healthcare, Cooperstown, New York, United States of America

Conceived and designed the experiments: AE-T PG EA JM GA CK. Performed the experiments: AE-T PG. Analyzed the data: AE-T PG EA JM GA CK. Contributed reagents/materials/analysis tools: AE-T PG. Wrote the paper: AE-T PG EA JM GA CK.

GWA is a consultant for Pliva and has done antimicrobial research for Pfizer, Abbott, Aventis, Bayer, GlaxoSmithKline, and Bristol-Myers Squibb. All other authors are employees of Pfizer, Inc., who sponsored this analysis.

A recent drug interaction study reported that when azithromycin was administered with the combination of ivermectin and albendazole, there were modest increases in ivermectin pharmacokinetic parameters. Data from this study were reanalyzed to further explore this observation. A compartmental model was developed and 1,000 interaction studies were simulated to explore extreme high ivermectin values that might occur.

A two-compartment pharmacokinetic model with first-order elimination and absorption was developed. The chosen final model had 7 fixed-effect parameters and 8 random-effect parameters. Because some of the modeling parameters and their variances were not distributed normally, a second mixture model was developed to further explore these data. The mixture model had two additional fixed parameters and identified two populations, A (55% of subjects), where there was no change in bioavailability, and B (45% of subjects), where ivermectin bioavailability was increased 37%. Simulations of the data using both models were similar, and showed that the highest ivermectin concentrations fell in the range of 115–201 ng/mL.

This is the first pharmacokinetic model of ivermectin. It demonstrates the utility of two modeling approaches to explore drug interactions, especially where there may be population heterogeneity. The mechanism for the interaction was identified (an increase in bioavailability in one subpopulation). Simulations show that the maximum ivermectin exposures that might be observed during co-administration with azithromycin are below those previously shown to be safe and well tolerated. These analyses support further study of co-administration of azithromycin with the widely used agents ivermectin and albendazole, under field conditions in disease control programs.

This paper describes the use of a modeling and simulation approach to explore a reported pharmacokinetic interaction between two drugs (ivermectin and azithromycin), which along with albendazole, are being developed for combination use in neglected tropical diseases. This approach is complementary to more traditional pharmacokinetic and safety studies that need to be conducted to support combined use of different health interventions. A mathematical model of ivermectin pharmacokinetics was created and used to simulate multiple trials, and the probability of certain outcomes (very high peak blood ivermectin levels when given in combination) was determined. All simulated peak blood levels were within ranges known to be safe and well tolerated. Additional field studies are needed to confirm these findings.

The operational efficiency of disease elimination programs in developing countries could be improved by integrating delivery of several interventions at local (village and district) levels

A recent pharmacokinetic study evaluated co-administration of azithromycin, ivermectin and albendazole

The purpose of this analysis was to model the ivermectin pharmacokinetic data from the recently reported interaction study

Data from a historical Phase I study with intensive sampling in healthy subjects was used to develop a population pharmacokinetic model for ivermectin

Blood samples were collected predose and at 0.5, 1, 1.5, 2, 3, 4, 6, 8, 10, 12, 24, 36, 48, 72, 96, 120, 144, and 168 hours after drug administration during each of the study phases. Samples were collected into heparinized Vacutainers. Blood samples were centrifuged at 3000 rpm for 15 minutes and the plasma samples were collected in plain plastic tubes without anticoagulant and then stored at −80°C. Samples were shipped frozen overnight on dry ice to BAS Analytics (West Lafayette, IN) for sample analyses. Ivermectin is detected in the body as two metabolites (22,23-dihydroavermectin-B1a (H2B1a) and 22,23-dihydroavermectin-B1b (H2B1b), and these were assayed using a validated high performance liquid chromatography system with liquid chromatography/mass spectrographic detection. The assays were linear over the ranges of 2.5–1000.0 ng/mL and 2.5–20.0 ng/mL, respectively. The precision values for both assays were <10%. In terms of accuracy, while the bias was not exceeded (±15%) for H2B1b for either the high or low quality control (QC) samples, they were for H2B1a during long-term stability testing (−21.8% at the low QC and −17.3% for the high QC) (see

Eighteen healthy Caucasian volunteers were enrolled in and completed this study (9 males and 9 females, mean [±SD] age, 39.4±10.5 years, weight 78.2±12.4 kg, ivermectin dose 15.5±2.6 mg).

All the data from both arms of the cross-over study were fitted simultaneously. The data set contained pooled pharmacokinetic, demographic/covariate, and dosing information. Data were analyzed using nonlinear mixed-effects modeling with the NONMEM software system, Version V, Level 1.1 (GloboMax LLC, Ellicott City, MD) with the PREDPP model library and NMTRAN subroutines. Computer resources included personal computers with Intel Pentium 4 processors, Windows XP Professional operating system, the GNU Fortran Compiler, GCC-2.95 (Win-32 version also known as G77; GNU Project,

The first-order conditional estimation method with η-ε interaction (FOCEI) was employed for all model runs. Individual estimates of pharmacokinetic parameters were obtained using POSTHOC (an empirical Bayesian estimation method). The random effect models sufficiently described the error distributions. For this analysis all interindividual errors were described by exponential error models on selected parameters (Equation 1)._{i}^{Pi}^{2}

The data could not support a full covariance block for the OMEGA matrix. Modeling began with the assumption of no covariance between interindividual random effects (diagonal ω matrix). Later, the covariance between clearance (CL) and volume of distribution in the central compartment (Vc) was estimated. For pharmacokinetic observations in this analysis, the residual error model was described by a combined additive and proportional error model (Equation 2)._{ij}_{pij}_{aij}^{2})).

After the structural pharmacokinetic model was established, known physiologic relationships were incorporated into the covariate-parameter models. For example, the change in physiologic parameters as a function of body size was both theoretically and empirically described by an allometric model (Equation 3) _{i}_{ref}_{TVP}_{allo}

Assessment of model adequacy and decisions about increasing model complexity were driven by the data and guided by goodness-of-fit criteria, including: (i) visual inspection of diagnostic scatter plots (observed vs. predicted concentration, residual/weighted residual vs. predicted concentration or time, and histograms of individual random effects; (ii) successful convergence of the minimization routine with at least 2 significant digits in parameter estimates; (iii) plausibility of parameter estimates; (iv) precision of parameter estimates; (v) correlation between model parameter estimation errors <0.95, and (vi) the Akaike Information Criterion (AIC), given the minimum objective function (OBJ) value and number of estimated parameters

Final model parameter estimates were reported with a measure of estimation uncertainty including the asymptotic standard errors (obtained from the NONMEM $COVARIANCE step). A limited covariate modeling approach emphasizing parameter estimation given the available data, rather than stepwise hypothesis testing, was implemented for this population pharmacokinetic analysis. The study population contained equal numbers of males and females. As such, age, weight and gender were explored as potential covariates. First, pre-defined covariate-parameter relationships were identified based on exploratory graphics, mechanistic plausibility of prior knowledge, and then a full model was constructed, with a fixed allometric relationship of body weight on clearance and volume parameters. Interindividual variability could not be incorporated on all fixed-effects parameters to get successful FOCE runs. For residual variance, a separate residual error was assigned for each of the treatment arms. A combined additive and proportional error model was used with 4 parameters to be estimated for the residual error. Various population models were evaluated, but only two models that best described the data (as determined by the log likelihood criterion and visual inspection) are presented. The first modeling approach was a population model that included all subjects. Because some of the modeling parameters and their variances were clearly not normally distributed, and showed asymmetric distribution, a mixture model was developed.

A second modeling approach was a population mixture model as it met our criteria for model adequacy and provided supporting evidence of the dichotomy of the observed individual data. Each subpopulation would have an associated submodel with different fixed or random effects. This model was adopted to accommodate the fact that only some of the individuals exhibited a pronounced increase in ivermectin bioavailability during the interaction arm of the study. It was preferred over a population model with and without outlier individuals, as it gave a better fit to the data as measured by change in OBJ, and met our criteria for a successful run in terms of a complete successful convergence with reasonable estimate for precision for both fixed and random effects.

Model development was guided by various goodness-of-fit criteria, including diagnostic scatter plots. Checking of the individual fits was also employed as part of judging the model performance for each patient. The final model and parameter estimates were then investigated with the predictive check method. This method was similar to the previously described posterior predictive check, but assumes that parameter uncertainty is negligible, relative to interindividual and residual variance

One thousand Monte Carlo simulation replicates of the original data set were generated using the final non-mixture and mixture population pharmacokinetic models. Distributions of Cmax across all data simulations were compared with Cmax distribution in the observed data set. The simulated data from each of the 1000 virtual trials (18000 subjects for each treatment period) were assembled, and the similarity between the actual observed data and simulated data was examined by comparing the 95% predictions intervals of the simulated data with the original observed data.

Assessment of the relationship between azithromycin and ivermectin by noncompartmental analysis showed that mean ivermectin AUC and Cmax was increased by 31% and 27%, respectively (see ^{2} (0.03).

Solid line serves as a reference point of no change of ivermectin bioavailability; dotted line is Loess fit (local regression fit) to indicate lack of linear relationship. Circles are the observed individual values.

Ivermectin concentration-time data were best described by a two-compartment pharmacokinetic model with first-order elimination and absorption (

The best fit was obtained by models for two subpopulation (A and B), characterized by different F values, relative to the baseline model that included all subjects. Parameters: central and peripheral compartment volumes, total body clearance (CL), inter-compartmental clearance (Q), rate of absorption, and relative bioavailability (F). Note that albendazole was administered in both baseline and interaction phases.

The final non-mixture model had 7 fixed-effect parameters and 8 random-effect parameters as shown in ^{2}). With each model developed, we checked the distribution of

Observed versus predicted and individual predicted plasma ivermectin levels. The solid line represents the line of identity (top panels). Residual versus predicted plasma ivermectin levels and weighted residual versus time, (bottom panels).

Parameter (unit) | Point Estimate | SEE | %RSE | %IIV |

Fixed Effect Parameters | ||||

θ_{CL (L/h)} | 11.8 | 3.87 | 32.79 | |

θ_{Vc (L)} | 195 | 123 | 63.07 | |

θ_{Ka(1/h)} | 0.24 | 0.11 | 45.83 | |

θ_{Q (L/h)} | 18.9 | 8.99 | 47.56 | |

θ_{Vp (L)} | 882 | 415 | 47.05 | |

θ _{trt effect on Ka} | 1.42 | 0.295 | 20.77 | |

θ _{trt effect on F} | 1.14 | 0.034 | 2.98 | |

Inter-individual Variability | ||||

ω_{CL} | 0.023 | 0.109 | 473.913 | 15.165 |

Cov _{CL, Vc} | −0.011 | 0.055 | −500 | 10.488 |

ω_{Vc} | 0.063 | 0.093 | 147.619 | 25.099 |

ω_{F1} | 0.061 | 0.061 | 100 | 24.698 |

Residual Variability | ||||

σ^{2} _{Baseline prop} | 0.099 | 0.025 | 25.25 | |

σ^{2} _{Baseline add} | 0.00 | |||

σ^{2} _{co-admin prop} | 0.081 | 0.033 | 40.74 | |

σ^{2} _{co-admin add} | 0.00 |

Parameter (unit) | Point Estimate | SEE | %RSE | %IIV |

Fixed Effect Parameters | ||||

θ_{CL (L/h)} | 12.30 | 5.24 | 42.60 | |

θ_{Vc (L)} | 190 | 164 | 86.32 | |

θ_{Ka(1/h)} | 0.24 | 0.11 | 44.54 | |

θ_{Q (L/h)} | 19.0 | 8.61 | 45.32 | |

θ_{Vp (L)} | 841 | 412 | 48.99 | |

θ _{trt effect on Ka} | 1.38 | 0.16 | 11.67 | |

θ _{F1 Subpop A} | 0.99 | 0.24 | 23.84 | |

θ _{F1 Subpop B} | 1.37 | 0.16 | 11.90 | |

θ_{mix proportions} | 0.55 | 0.47 | 86.47 | |

Inter-individual Variability | ||||

ω_{CL} | 0.04 | 0.19 | 497.31 | 19.29 |

Cov _{CL, Vc} | 0.01 | 0.08 | 1605.11 | 27.80 |

ω_{Vc} | 0.08 | 0.12 | 158.91 | 7.13 |

ω_{F1} | 0.07 | 0.09 | 127.76 | 26.57 |

Residual Variability | ||||

σ^{2} _{Baseline prop} | 0.09 | 0.02 | 25.28 | |

σ^{2} _{Baseline add} | 0.00 | |||

σ^{2} _{co-admin prop} | 0.08 | 0.02 | 29.40 | |

σ^{2} _{co-admin add} | 0.00 |

Both the population and individual predictions adequately described the AUC profiles for each subject (

The solid line represents the fit predicted by the typical pharmacokinetic mixture model parameters. The dashed line shows the fit of the post hoc estimates of the population model. Circles represent the observed concentrations.

The solid center lines represent the median values of the 1000 simulated data sets, whereas the upper and lower lines represent the 97.5th and 2.5th quantiles of the simulated data, respectively.

Simulated maximum concentrations for each individual's Cmax values were summarized across 1000 simulation replicates of the original population pharmacokinetic database and plotted as box plots (

Lower panel: Maximum concentration data from 1000 simulation replicates using the non-mixture model in all subjects (open boxes) and from the mixture model in subpopulations A and B (shaded and hatched boxes). The line in the interior of the box denotes the median, the bottom and top edges denote the first and third quartiles, respectively. The lines from the top and bottom edges extend to 1.5 times the interquartile range. Values exceeding the interquartile range are plotted as individual points.

There are a number of interesting findings from this analysis of data from an interaction study of ivermectin and azithromycin. This is the first published population model of ivermectin pharmacokinetics. It demonstrates the utility of population mixture modeling as an approach to explore drug interactions, especially where there may be population heterogeneity. The mechanism for the interaction was identified (an increase in bioavailability in one subpopulation). The model was used to simulate multiple clinical trials, to identify the maximum exposures that might be observed during co-administration, which permits comparison with previously published safety and pharmacokinetic data.

Ivermectin has been approved for use in humans for 2 decades, yet relatively limited pharmacokinetic data have been published. Recent studies using modern assay methods have characterized its pharmacokinetics using noncompartmental methods in the context of drug combination studies for treatment of onchocerciasis and lymphatic filariasis _{50} 0.18–0.4 µM;

The variability of the magnitude of change in ivermectin pharmacokinetics observed in the interaction phase

The final mixture model provided a good description of ivermectin data from both treatment periods. Goodness-of-fit criteria revealed that the final model was consistent with the observed data and that no systematic bias remained. The data points (

Typically, a mixture modeling approach would not be considered at the outset of a population pharmacokinetic analysis. Because of the unexplained remaining variability (see above), in the present analysis, the following decision rules were used in the evaluation of the mixture model: (i) The Estimation step and Covariance step terminated successfully; (ii) 95% CI for Mixture partition did not include 0 nor 1; and (iii) the change in the OBJ between mixture and non-mixture models was >5.99 (χ^{2}; p<0.05, 2df). In the present analysis, the difference was 19.8.

The mixture model identified the interaction between azithromycin and ivermectin to be due to changes in bioavailability in Subpopulation B. Their mean estimate of bioavailability (F) was 1.37 relative to baseline, whereas F was unchanged for Subpopulation A (0.97). Inspection of noncompartmental data for Subpopulation B were consistent, showing higher Cmax and earlier Tmax values (Cmax A: 54.3 ng.h/mL; B: 67.8 ng.h/mL; Tmax A: 4.1 h; B: 3.4 h). There were no differences in apparent clearance or volume of distribution. However the mechanism for the increase in bioavailability is unclear. Azithromycin, like ivermectin, is a substrate for Pgp, however it has minimal inhibitory effects on this transporter in vitro

The model was used to simulate the range of peak ivermectin concentrations that might be encountered if azithromycin and ivermectin were co-administered. These simulated data were then compared with the Cmax data reported in the high-dose ivermectin safety study

Interestingly, simulations from both the mixture model and the non-mixture model had generally similar predictions of ivermectin exposures (average estimates and variability). Both models confirmed that the maximum concentration achieved in the interaction phase would not exceed 201 ng/mL (

There are several important caveats to this analysis. The data collected from the drug interaction study was not intended for population analysis, and a larger data set would have been desirable. The use of a mixture model could be criticized on the basis that random variations in the data could be ascribed

In conclusion, this analysis demonstrates the utility of a population model approach to analyze drug interaction data. The mechanism for the interaction was identified (an increase in bioavailability in one subpopulation). The model was also used to simulate multiple clinical trials, to identify the maximum exposures that might be observed during co-administration, and provides confidence that the peak ivermectin exposures would never exceed mean exposures that have previously been shown to be safe and well tolerated.