Introduction
 Top of page
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Conflict of interest
 References
Omalizumab is a recombinant DNAderived humanized monoclonal antibody that selectively binds human immunoglobulin E (IgE). The antibody is an immunoglobulin (Ig) G_{1}κ with a human framework and complementarity determining regions (CDRs) from a humanized antiIgE murine antibody [1]. The causal role of IgE in allergic disease is well established [1–3]. Theallergic cascade is initiated when IgE bound to highaffinity FcεRI receptors on the surface of basophils and mast cells is crosslinked by allergen, resulting in the degranulation of these effector cells and the release of inflammatory mediators such as histamine and leukotrienes. Omalizumab interrupts the allergic cascade by (i) forming complexes with IgE and preventing the arming of effector cells, (ii) aiding offloading of mast cells and basophils by trapping IgE as it dissociates from the receptor, and (iii) downmodulating FcεRI as a direct consequence of the reduction in free IgE concentrations [4–12].
Administration of omalizumab significantly decreases serum free IgE concentrations, resulting in improved control of atopic asthma and, most probably, other atopic conditions. As a result of omalizumab binding to IgE, lowering its free concentration, total serum IgE concentrations rise. Such an increase could occur by two mechanisms: (i) omalizumab–IgE complexes could be eliminated more slowly than free IgE due to the ability of the IgG portion of complexes to access the Brambell receptor, sparing them from lysosomal degradation [13], and (ii) the complexes, being of higher molecular mass (at least 340 kDa for the dimer but up to 1000 kDa for the hexamer [14]), filter less effectively through the vascular endothelium and are therefore retained within the smaller plasma volume of distribution [15–18].
However, these mechanisms have yet to be confirmed, although a mechanismbased PK/PD model of the pharmacokinetics of omalizumab and its binding to IgE has been published for a limited number of subjects [19]. The concentration–time profiles of omalizumab, free and total IgE exhibited many of the same properties as other therapeutic antibodies. In addition, the model allowed the estimation of both drugspecific kinetic parameters and those that are related to endogenous IgE production and elimination.
We now present an alternative model, based on the concentration–time profiles of omalizumab, free and total IgE in Japanese subjects. As in the previous model, it incorporates three entities, namely free omalizumab, free IgE and the omalizumab–IgE complex, but each with their own clearance and volume of distribution. The relationship between these entities is defined by the law of mass reaction, assuming, unlike in previous work [19], that they are always at equilibrium. This simplification enabled the successful analysis of large quantities of sparse data using NONMEM with a binding model, which was impossible with the previous model. Given the timescale (weeks) of clinical studies with monoclonal antibodies, and the short equilibration time (hours) for the antibody–IgE complexation reaction, such an assumption is considered valid. The concentration–time profiles of the three compounds can then be explored simultaneously by a population model, which enables the prediction of statistical distributions of individual profiles using covariate values (body weight and baseline IgE) to decrease unexplained interindividual variability.
Therapeutically, a table based on the pretreatment IgE concentration and body weight has been constructed to estimate the omalizumab dose required to decrease trough free IgE concentrations (based on samples drawn immediately prior to drug treatment in a multiple dose regimen) to between 12 and 21 ng ml^{−1}, the range associated with clinical efficacy [20]. The frequency distribution of the IgE response is such that >90% of patients achieve suppression at concentrations <50 ng ml^{−1}. The present model mimics this frequency distribution of free IgE. Furthermore, although the model parameters were estimated using data from Japanese patients only, simulated distributions of free IgE overlay well the steadystate data from independent studies in White patients treated according to the dosing table. This finding indicates that the model is predictive and that there are effectively no differences in the pharmacokinetics of omalizumab between Japanese and Whites.
Results
 Top of page
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Conflict of interest
 References
In the studies used in the model building (1101 and 1305), 202 healthy subjects and patients were administered omalizumab. A total of 3192 samples (1037 omalizumab, 1191 total IgE and 964 free IgE) were used for model building. Two hundred and seventyfive free IgE concentrations that were above the upper limit of quantification (150 ng ml^{−1}) were excluded. Seven hundred and seven patients were administered omalizumab in studies 007, 008 and 009; 531 patients who had evaluable trough concentrations in these studies were used for the external validation of the model. Demographic data are summarized in Table 1.
The estimated PK/PD parameter values are shown in Table 3. The covariate–parameter effects (body weight for omalizumab clearance and distribution volume and baseline IgE for free IgE clearance and rate of IgE production) were included and confirmed as statistically significant (P < 0.01). Interindividual variability for the random effects associated with the PK/PD parameters ranged from 13% (V_{X}) to 40% (k_{a}). Intraindividual variability from the observation equations ranged from 17% to 22%. The standard error (SE) for the estimated fixedeffects parameters (θ) ranged from 2% to 20% of θ. With the exception of free IgE, the individual weighted residuals, IWRES, showed a symmetric distribution around zero through the whole range of predicted values (Figure 2). Free IgE showed asymmetry for higher predicted values, as samples containing concentrations >150 ng ml^{−1} were not quantifiable.
Table 3. Population estimated model parameters and related information PK/PD parameter  Population mean [θ (SE for θ)]  Interindividual variance (ω,% CV) 

CL_{x}/f (ml h^{−1})*  7.32 (0.153)  20.3 
CL_{X}/f exponent for body weight  0.911 (0.135)  
ΔCL_{C}/f (ml h^{−1})  5.86 (0.920)  34.9 
CL_{E}/f (ml h^{−1})†  71.0 (4.68)  25.3 
CL_{E}/f exponent for baseline IgE  −0.281 (0.0312)  
P_{E}/f (µg h^{−1})†  30.3 (2.04)  23.1 
P_{E}/f exponent for baseline IgE  0.657 (0.0301)  
Correlation between η(CL_{E}/f) and η(P_{E}/f)  0.968  
V_{X}/f (ml)*‡  5900 (107)  13.0 
V_{X}/f exponent for body weight  0.658 (0.100)  
V_{C}/f (ml)  3630 (223)  25.0 
k_{a} (h^{−1})  0.0200 (0.00114)  39.9 
K_{d0} (nm)  1.07 (0.118)  
α  0.157 (0.0306)  
 Intraindividual variance (σ,% CV) 


Omalizumab  16.7 
Total IgE  21.1 
Free IgE  21.8 
To confirm the necessity for the expression allowing affinity to vary with the ratio of omalizumab to IgE, the loglikelihood NONMEM objective functions were compared for models with and without variation in K_{d}. With concentration dependence allowed (α ≠ 0), the NONMEM objective function decreased significantly by 107.
In building the basic model, the influence of the broad range of baseline IgE (IgE_{0}) was not negligible and the optimization process did not converge without the inclusion of covariates. Therefore, the basic model included the covariate of IgE_{0} on P_{E}/f.
In the preliminary analysis, the influences of body weight, baseline IgE, age and sex on the PK/PD parameters were evaluated visually using the scatter plot between POSTHOC estimations of each PK/PD parameter and each demographic factor. As a result, the following combinations of covariates and PK/PD parameters were examined:
(1) IgE_{0} on CL_{E}/f; (2) BW on CL_{X}/f; (3) BW on V_{X}/f; (4) BW on V_{C}/f; (5) AGE on k_{a}; (6) AGE on V_{X}/f; (7) SEX on V_{X}/f.
In the first examination step, the combinations of (1) to (4) were included in the model, and the significance was confirmed by backward elimination. During this process (1) to (3) showed a significant change in the objective function value (−2LL > 12.12, P < 0.001), and (4) did not show a significant change. Baseline IgE was chosen as the covariate on P_{E}/f and CL_{E}/f, and the correlation between η(P_{E}/f) and η(CL_{E}/f) included the use of a block statement in order to stabilize the model. The inclusion of correlations, between these η's gave significant drops in the objective function value.
In a second examination step, combinations of (5) to (7) were in corporated one by one into the model built in the above step. No significant change in the objective function value was observed for (5) to (7).
As the result, the final model was developed to include the covariates shown in Table 3. The apparent clearance of omalizumab (CL_{X}/f) and free IgE (CL_{E}/f), the apparent rate of IgE production (P_{E}/f) and apparent distribution volume of omalizumab (V_{X}/f) depend onbaseline IgE and body weight according to the following equations:
Thus, doubling body weight increases the apparent clearance and volume of distribution of omalizumab by (2^{0.911} − 1) · 100% = 88% and (2^{0.658} − 1) · 100% = 58%, respectively. Doubling baseline IgE decreases the apparent clearance of free IgE by 18% and increases the apparent rate of IgE production by 58%.
The results of internal validation of the model are shown in Figure 3 for the singledose study 1101 and in Figure 4 (upper panel) for the multipledose study 1305. Free IgE is predicted to decrease as the dose of omalizumab increases from 75 to 375 mg. Individual observed values were mostly within the 80% prediction intervals and the extent of interindividual variability specified in the model was similar to that observed. Some random deviations occur in the free IgE concentrations for the 150 mg dose group. However, the number of points within the 80% prediction intervals of free IgE for all dose groups was 390 of 491, or 79.4%. Even though the observed values of five of 12 subjects in the 150mg group were not within the 80% prediction intervals, a binominal test Pvalue of 0.073 showed that this deviation was not significant. The observed median values of free IgE concentration in this group were mostly captured within the 95% prediction intervals for the medians (data not shown). Figure 4 (upper panel, study 1305) shows that the observed median values after multiple dosing were mostly captured within the 95% prediction intervals.
The results of the external validation are shown in Figure 4 (lower panel) for the multipledose study 007, and in Figure 5 for the distributions of predicted and observed predose trough samples at steady state (studies 008 and 009). The observed median values following multiple doses of omalizumab are close to the 95% prediction intervals of the median (Figure 4).
The shapes of the predicted and observed distributions were similar (Figure 5), and the 95% prediction intervals included the observed median in most cases. Although one may initially conclude that the model is not predictive, as >5% of the observed medians were outside the 95% prediction intervals, this is most likely due to the posterior predictive simulation not accounting for uncertainty in the NONMEM estimated values. To overcome this, an additional simulation was performed with uncertainty added to each parameter. The resultant uncertain 95% prediction intervals for the medians are shown in Figure 5 as horizontal bars. The intervals did not broaden to any great extent, but now there were no significant deviations of observed medians outside the prediction intervals for total IgE and, most relevent to clinical efficacy, free IgE (binomial test P = 0.2262).
Discussion
 Top of page
 Abstract
 Introduction
 Methods
 Results
 Discussion
 Conflict of interest
 References
Consistent with other therapeutic monoclonal antibodies [26] and with previously reported results [19], an increase in total IgE was observed during treatment with omalizumab. This increase is caused by both a redistribution of ligand from extravascular sites, and a decrease in its rate of elimination due to slower clearance of the omalizumab–IgE complex compared with that of the free ligand [15–17]. The present mechanismbased directligand binding model includes both of these mechanisms, giving rise to model parameters that are physiologically and physicochemically relevant.
Values of the apparent clearances obtained for free omalizumab and free IgE were 7.32 and 71.0 ml h^{−1} for a typical 61.1kg patient with 482.4 ng ml^{−1} baseline IgE. The typical apparent distribution volumes of both compounds were 5900 ml. Therefore, the halflives of omalizumab and IgE were 23 and 2.4 days, very close to previously reported values of 23 and 2.5–2.7 days for human IgG [24, 25] and IgE [24, 25, 27]. The mean halflife of total omalizumab calculated noncompartmentally in study 1101 was 18.2 days. This difference of 5 days compared with the value for free omalizumab is probably due to the fact that noncompartmental analysis calculates the clearance of the sum of free and complexed omalizumab and, therefore, the value is a mixture of the more slowly cleared free together with the more rapidly cleared complex. The clearance of the omalizumab–IgE complex was estimated to be 5.86 ml h^{−1} higher than that of free omalizumab. It is likely that the presence of IgE bound to omalizumab IgG interferes with the ability of the Brambell FcRn receptor [13] to rescue the IgG from lysosomal degradation. However, the fact that clearance of the complex is not as rapid as that of free IgE suggests that some level of rescue does occur, leading to an accumulation of total IgE compared with that observed at baseline.
When corrected for the 62% subcutaneous bioavailability of omalizumab [28], the absolute distribution volumes for a typical 61.1kg subject are 3660 ml for free omalizumab, 2250 ml for the complex (Table 3). The latter is very close to the volume of plasma (2130 ml) for a subject of that body weight [29]. The volumes for omalizumab and IgE are somewhat larger, probably reflecting distribution to the tissue interstitium [30–32]. It is known that the concentration of immunoglobulin in interstitial fluid is lower than in blood [30–32], due to restricted vascular endothelial permeation and continual lymphatic drainage. Therefore, as expected, the IgG–IgE complex, with its higher molecular weight (340–1000 kDa) and hence lower tightjunctional permeability than free IgG (150 kDa) or free IgE (190 kDa), will appear to have a smaller distribution volume. Further, even if the complex were to permeate, due to the low concentration, any molecules of the complex should dissociate. Therefore, it is concluded that the observed increase in total serum IgE is caused not only by differences in clearance between IgE and complex, but also by a more restricted distribution volume.
Following internal and external validation, the model described the pharmacokinetic and pharmacodynamic responses over a broad range of conditions with respect to different subpopulations, doses and dose intervals. In particular, the response at steady state was determined by only three clearance parameters and the rate of IgE production. K_{d} was assumed to be identical in all patients, but was dependent upon the molar ratio of total omalizumab to total IgE.
Clearance of free IgE and the rate of production of IgE were shown to be accurately predicted by baseline IgE concentration; clearance and volume of distribution of free omalizumab by body weight. Therefore, the pharmacodynamic response is mainly a function of body weight, baseline IgE and dosage. The results of the simulations were obtained using only population PK/PD parameters from the model building, body weight and baseline IgE concentration in the validation dataset. The simulations, based on the two Japanese studies, were predictive of the distribution of the free IgE biomarker response in an independent nonJapanese population.
In conclusion, a mechanismbased population PK/PD model was established for omalizumab binding to IgE and its predictability was confirmed for the clinically important variable, free IgE. There was no significant deviation of predicted from observed median total and free IgE trough concentrations at steady state. The model, even though its parameters were estimated from small clinical pharmacological studies, mimicked the extent of free IgE variability in larger longterm Phase III studies, the predicted medians consistently being within 25% of observed values and the tails of the predicted distributions being close to those of the observed data across a fivefold range of dose. Furthermore, since the model was developed using Japanese patient data, and the posterior predictive evaluation was against data from Whites, there are unlikely to be notable differences in omalizumab pharmacokinetics and IgE pharmacodynamics between the populations.
Finally, the general model, specifying a monoclonal antibody, or other agent, binding to a target ligand in an equilibrium reaction with a fixed stoichiometry, is of general applicability given the increasing number of biotechnologically derived molecules being discovered and developed as therapeutic agents. The model described allows for the determination not only of drug characteristics, but also of those of an endogenous ligand, including halflife and rate of production, without direct administration of the natural ligand. This approach should be a powerful tool in the understanding of the role of many potential target ligands in the pathophysiology of diseases.