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PHARMACOKINETICS AND PHARMACODYNAMICS |
From the Department of Pharmacokinetic and Pharmacodynamic Sciences (Dr Sun, Dr Lu, Dr Joshi, Dr Bruno), Department of Specialty Biotherapeutics (Dr Kwon), and Biostatistics (Mr Compton), Genentech, Inc, South San Francisco, California.
Address for reprints: Amita Joshi, PhD, Late Stage BioTherapeutics, Department of Pharmacokinetic and Pharmacodynamic Sciences, MS 70, Genentech, Inc, 1 DNA Way, South San Francisco, CA 94080.
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Key Words: Efalizumab • psoriasis • population pharmacokinetics • nonlinear mixed effect modeling • NONMEM analysis • Psoriasis Area and Severity Index (PASI) score
Efalizumab has recently been approved for the treatment of moderate to severe plaque psoriasis for adult patients who are candidates for systemic or photo therapy. Psoriasis is an inflammatory disease characterized by hyperproliferation of keratinocytes and accumulation of activated T cells in the epidermis and dermis of psoriatic lesions. In early studies, intravenous (IV) administration of single and multiple doses of efalizumab to psoriatic patients down-modulated CD11a expression on the T cell surface and induced significant disease improvement (as measured by the Psoriasis Area and Severity Index [PASI] score)3,4 in a dose-dependent manner at doses of 0.3 mg/kg or higher.5,6 The clinical efficacy of efalizumab monotherapy was further confirmed and its safety profile established in 4 randomized, double-blind, placebo-controlled trials in subjects with moderate to severe plaque psoriasis at 0.3 mg/kg/wk intravenously7 and at 1 and 2 mg/kg/wk subcutaneously.8-10
The pharmacokinetics and pharmacodynamics of efalizumab have been well characterized following single-dose IV administration to psoriatic patients over a wide range of doses (0.03-10 mg/kg).5,11 Efalizumab clearance is concentration dependent, with a fast receptor-mediated clearance at a low plasma concentration and a slower clearance closer to that of other IgG1 immunoglobulins at a high concentration (3 mg/L or greater) after saturation of the receptor involved.11 Binding to cell surface CD11a followed by internalization is one likely clearance mechanism for this anti-CD11a antibody.12
This article describes analysis based on data obtained following long-term multiple subcutaneous (SC) weekly doses of 1 and 2 mg/kg for up to 12 weeks in 1 phase I and 3 large phase III or IIIb studies. The data were analyzed using a population approach with the following objectives: (1) to find a structural pharmacokinetic model that can describe the data from patients administered a 1-mg/kg dose, (2) to estimate the magnitude of interpatient variability in pharmacokinetic parameters, and (3) to assess the potential influence of demographic and pathophysiological covariates on efalizumab clearance.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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10% body surface area affected, had clinically stable disease for 3 months prior to screening, had a history of prior use of systemic antipsoriasis therapy or were candidates for systemic therapy, and had a Psoriasis Area and Severity Index (PASI) score of 12 or greater at screening. Subjects were required to discontinue the use of most therapeutics during a 12-week study period. Subjects were required to specifically discontinue topical psoriasis treatments (except bland emollients and tar or salicylic acid preparations for scalp psoriasis) from day -14 before dosing, systemic treatments for psoriasis or psoralen and UVA therapy (PUVA) from day -28, immunosuppressive medications for any other indication than psoriasis from day -28, and concomitant experimental agents and other non-lymphocyte-depleting monoclonal antibodies or immunoadhesion molecules from day -28 or 5 half-lives prior to first dosing, whichever was longer. Subjects could withdraw or be withdrawn from the study at any time. The protocol and consent form were reviewed and approved by the institutional review boards for each of the study sites (see acknowledgments), and subjects provided signed consent before commencing the study. The 4 clinical trials of weekly SC efalizumab for plaque psoriasis included 1 phase I open-label study to evaluate safety, efficacy, and pharmacokinetics; 2 randomized, double-blind, placebo-controlled phase III studies; and 1 open-label phase IIIb study to evaluate the safety and efficacy of efalizumab. In each study, the treatment period was 12 weeks. Subjects received an initial conditioning dose of 0.7 mg/kg followed by 11 weekly SC doses of 1 mg/kg or 2 mg/kg of efalizumab monotherapy. In the phase I study, efalizumab in serum was measured prior to dosing (trough) on day 7 and then every 4 weeks (days 28, 56, 77). In addition, following the last dose on day 77, serum efalizumab was measured at days 78, 79, 80, 84, 91, 98, and 105. In the 2 phase III studies, only 1 trough sample was obtained at the end of 12 weeks of treatment (day 84). In the phase IIIb study, 2 trough samples were obtained at mid-treatment (day 42) and after the last dose (day 84). The specific times of efalizumab administration and blood sampling were documented in the clinical database, except for 2 phase III studies in which only the dates were recorded. Therefore, for the 2 phase III studies, the dosing and sampling times were calculated as the differences of the actual dates between the first SC dose and each event (dosing or sampling event). With the long half-life of efalizumab of 5 to 8 days, this imputation is not likely to bias the estimation of population pharmacokinetic (PK) parameters.
Assay
Serum efalizumab concentrations were determined by an enzyme-linked immunosorbent assay (ELISA) method using full-length LFA-1 (mLFA-1) as the capture reagent and horseradish peroxidase conjugated goat antihuman IgG antibody as the reporter. The limit of quantification (LOQ) for the assay was 0.039 µg/mL in neat serum. Intra-assay precision ranged from 2.1% to 7.1%, and interassay precision ranged from 5.5% to 11.5% across the low (0.71 ng/mL), medium (2 ng/mL), and high (8 ng/mL) concentration range of the assay (data on file, Genentech, Inc, San Francisco). Serum efalizumab concentrations below the LOQ of the assay were excluded from the analysis. Samples were shipped frozen, and analyses were conducted at Genentech, Inc.
Data Analysis
The analyses were performed with the NONMEM program (Version V, GloboMax, Hanover, Md) using the first-order method.13 The structural model was built using the rich data obtained in the phase I study. The covariate effects were then assessed on the full database after merging the phase III data. One-compartment models with first-order input and either first-order (linear) or Michaelis-Menten (nonlinear) elimination were fit to efalizumab concentration-time data. Interpatient variability in the pharmacokinetic parameters was modeled according to an exponential model (ie, assuming lognormal distribution):
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A multiplicative covariate regression model was implemented as follows:
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where 
jP denotes the proportional difference between the "true" parameter (Pj) of individual patient j and the typical value (
j) in the population, adjusted for values of covariates equal to those of this individual patient. The s are random effects with mean zero and variance 
2. The 
s are the regression coefficients to be estimated for continuous (eg, WT) or dichotomous (eg, obesity) covariates. Continuous covariates were centered around their median (med(WT)) values, thus allowing 1 to represent the clearance estimate for the typical patient with median covariates. Dichotomous covariates were coded 0 or 1 (eg, OBS = 0 for nonobese, OBS = 1 for obese). Dose was also considered as a covariate and was coded DOSE = 0 when patients received 1 mg/kg and DOSE = 1 when patients received 2 mg/kg.
Residual error was modeled as a combination of proportional and additive components.
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where Cpij and 
pij are the ith measured and model-predicted (true) concentrations, respectively, for patient j, and 
ij, prop ij, add denote the proportional and additive residual intraindividual random errors, distributed with zero means and variances 
and 
. Residual variability was also provided as (
) for proportional residual error or as (
) for additive residual error.
Individual estimates of random effects () and individual PK parameter values were obtained using post hoc empirical Bayesian estimation based on the population parameters (as prior information) and the patient's observed concentrations. A number of goodness-of-fit plots and graphical representations useful for model diagnoses were produced from NONMEM-generated tables using SigmaPlot 2000 (SSPS Inc, Chicago) and S-PLUS (Version 2000, MathSoft Inc, Cambridge, Mass). Plots were made of individual random effects versus covariates (base and final models) to judge the appropriateness of the covariate model.
Comparison of alternative structural models and construction of the regression model for efalizumab were based on the objective function values (OFV) and likelihood ratio test. Differences (
) in OFV of greater than 7.9 for 1 degree of freedom, corresponding to a significance level of P < .005, were used for discrimination between hierarchical models. A nominal P value of .005 was chosen because the P values computed by the first-order method are known to be anticonservative.14,15 The OFV of nonhierarchical models (eg, Michaelis-Menten and linear-compartment models) were compared using the following information criteria: Akaike information criterion (AIC) = OFV + 2p and Bayesian information criterion (BIC) = OFV + p • log(n), where p is the number of parameters in the model, and n is the number of data points.16,17 A permutation test was performed to estimate the actual significance level of selected covariates.14 The individual covariate vector was randomly permuted in the data set, breaking any existing parameter-covariate relationships while maintaining a relevant structure of the PK and covariate data. The final model was then fitted to the data with randomly permuted covariate values, and the value for the fit of the reduced model (removal of this covariate) was determined. This was done repeatedly (500 iterations) to obtain an empirical reference distribution for the values under the null hypothesis. The values in the reference distribution were ranked, and the values corresponding to the fifth percentile represent the cutoff values to use for actual significance of 5%. Similarly, an estimate of the corresponding true significance level can be obtained by determining the fraction of values in the empirical distribution greater than the observed value.14
A bootstrap resampling technique18 was used to evaluate the stability of the final model and estimate confidence intervals (CIs) of parameters. This model evaluation consists of repeatedly fitting the model to 500 bootstrap replicates of the data set. The data sets are replicated by randomly sampling the patient data (including concentration-time data, dosing history, and covariates), with replacement up to the total number of patients in the original data set. The median of the 500 parameter estimates was compared with the point estimates obtained with the original database. The 95% CI of parameter estimates was taken as the 2.5 to 97.5 percentile range of bootstrapped parameter estimates.
Steady-state exposure was simulated in 500 patients using the final population pharmacokinetic model and covariates obtained by randomly sampling the subject's data from the data set with replacement.
Finally, empirical Bayes estimates of individual parameters and of drug exposure (day 84 trough) in the pivotal phase III studies were generated. Predicted day 84 trough was summarized by patient weight quartiles. For investigating exposure-response relationship, the day 84 trough (approximately steady-state) concentration was predicted from the final model, and its relationships with responses were examined.
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RESULTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Pharmacokinetic data were available from 1130 efalizumab-treated subjects (93% of 1212 efalizumab-treated subjects in these studies). Subjects positive for antiefalizumab antibodies (human antihuman antibodies (HAHA), n = 42, 3.7%) were not included for the analysis because it is known that antiefalizumab antibodies interfere with the efalizumab ELISA assay, and therefore efalizumab concentration data in the presence of HAHA are unreliable. It is not known whether these antibodies are neutralizing. Therefore, the analyses were conducted on 1088 subjects (1869 data points). Among the subjects, 66 from the phase I study contributed a median of 10 data points per subject, 320 from the phase IIIb study contributed 2 samples per subject, and 702 from the phase III study contributed 1 data point per subject. The baseline covariates assessed in the analysis were age, weight (WT), height (HT), body mass index (BMI), gender, obesity, race, PASI score, and lymphocyte count. Body mass index was calculated as BMI = WT in kg/(HT in cm/100)2. Patients were classified as obese when their BMI was 30. Median age of patients was 44 years (range, 18-74 years), median weight was 91 kg (range, 43-192 kg), 720/1088 patients were men, 557/1088 patients were obese based on the above criteria, median PASI score was 17.1 (range, 5.6-70.8), median lymphocyte count was 1.8 K/cm2 (range, 0.5-5.2 K/cm2), and 367/1088 patients received the 1-mg/kg dose level.
Base Model
The 1-compartment linear model with a mixed error provided the best fit to the data. However, goodness-of-fit plots indicated that this model tended to overpredict the first trough level and last data point (35 days after the last dose) with concentrations below 3 µg/mL, as illustrated by the fit of a representative patient treated at the 1-mg/kg dose given in Figure 1. A very similar fit was observed for patients who received 2 mg/kg. The nonlinear Michaelis-Menten elimination model (1 more parameter) only provided marginal improvement of the fit ( = 6.4, which was better by the AIC but not by the BIC). The goodness-of-fit plot was similar for the lower concentrations. The Michaelis-Menten constant (km) was very poorly estimated and very high (145 µg/mL), compared to the observed concentrations, indicating that the model was essentially operating in the linear domain. Two different models with first-order elimination or Michaelis-Menten elimination were tested during the model development stage and found to be similar in terms of fitting the data. A model with the combination of first-order elimination and Michaelis-Menten elimination was tried and gave almost the same results as the model with only Michaelis-Menten elimination (data on file). The Michaelis-Menten model only provided a very limited improvement of the fit, and the parameters were poorly estimated with a very high Km, indicating that the data did not support the Michaelis-Menten model. The 1-compartment linear model was therefore retained as the base model. Estimated parameters are given in Table I. Notably, the additive part of the error model of 1.36 µg/mL is large compared to the concentrations measured 35 days after the last dose (typically <0.50 µg/mL). The large residual variance for these concentrations is consistent with the lack of fit previously discussed. Removing the additive part in the residual error model (add) did not improve the fit for these low concentrations and resulted in an increase in the objective function ( = 88).
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Covariate Effects
Covariate effects were only assessed for efalizumab apparent clearance (ie, CL/F, where F is the absolute bioavailability of SC efalizumab). Because the drug is administered by body weight, during the analysis, body weight was used as the body size measurement for easy clinical interpretation. Weight ( = -367), obesity ( = -253), PASI score ( = -62), lymphocyte count ( = -38), and age ( = -22) were found to independently influence CL/F ( for the univariate comparison of the model with the covariate vs the base model). In addition, after adjustment for the previous covariates, patients treated in the 2-mg/kg dose group were found to have a decreased CL/F ( = -64 when added to the model with other covariates) compared to the 1-mg/kg dose group. The final model for efalizumab apparent clearance was therefore as follows:
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All parameters were stable following bootstrapping. That is, the median parameters from the 500 bootstrapped databases were within 5% of the corresponding point estimates from the original database (data not shown). Parameter estimates for the final model and their 95% bootstrapped CIs are given in Table I. Population mean CL/F and V/F estimates using the final model applied to the full database were similar to those obtained with the base model and the phase I database (not shown). The goodness-of-fit plot for the final model did not show any systematic deviations except the trend to overpredict low concentrations already discussed.
The covariate with the largest influence on CL/F variability was body size, with similar magnitude of effects for WT and BMI. WT was retained in the final model. The dependency of the CL/F random effect (jCL/F) on body weight seen with the base model is accounted for in the final model, as shown in Figure 2. The changes from the population mean CL/F value for patients with weight varying from the 2.5th percentile (57.2 kg) to the 97.5th percentile (139 kg) were -29.5% to +37.6%, respectively. The model-predicted steady-state trough levels for low (57.2 kg) and high (139 kg) body weight patients after 1 mg/kg are similar (8.32 and 9.60 µg/mL, respectively). Baseline PASI score showed less effect than WT; the changes from the population mean CL/F value for patients with low PASI scores (2.5th percentile of 12.0) or high PASI scores (97.5th percentile of 41.6) were -7.5% and 21.6%, with a predicted steady-state trough level of 9.88 and 7.25 µg/mL, respectively (1 mg/kg dose). Although obesity was a strong covariate in univariate analysis, after adjustment to weight, obese patients had only a 10% increase (CI: 1.5%-21%) in CL/F. The other pathophysiological covariates in the final model (LYM and AGE) had only modest effects. Patients in the 2.0-mg/kg/wk dose group had a 24.0% lower CL/F than the population mean CL/F value. This is consistent with the nonlinear PK profile of efalizumab shown in other studies over a wider range of dose.5,9 Efalizumab CL/F was not affected by gender or race.
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The P values obtained by the randomization test for 3 least significant covariates—OBS, LYM, and AGE—were P = .012, P < .005, and P < .005, respectively. Based on the randomization test, the change in should be greater than 5 to have actual significance at P < .05. This is consistent with the statement from a previous report14 that a higher cutoff should be used as a protective measure against introducing nonsignificant covariates in the model. As previously mentioned, these results show that the threshold level in each case was higher than the one given by the chi-square table (greater than 5 compared to 3.8 for P = .05). The randomization test established that these covariates have significant effect on CL/F, which is consistent with the NONMEM analysis results from the final model.
Simulation of the Model
Population simulations for efalizumab concentration versus time profiles for the 1.0-mg/kg/wk dosing group are shown in Figure 3. The simulations show that the trough concentrations would reach steady state after about 4 weekly administrations to achieve a mean plasma level of 9.0 µg/mL (day 84). The model-predicted concentrations are consistent with the observed values. Day 84 trough concentration weight quartiles show that patients received similar exposure across weight (Figure 5).
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Exposure-Response Relationships
To examine the relationship between the estimates of day 84 efalizumab trough concentration obtained from the model and response to treatment, the percent PASI improvement at day 84 relative to baseline was plotted versus the day 84 trough concentration (Figure 4). There was a small exposure-response relationship (r = 0.029).
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DISCUSSION |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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The pharmacokinetics of IgG1 after intravenous administration generally obeys a 2-compartment model.19 Following SC administration, efalizumab is absorbed with a 0.191-day-1 Ka (3.63-day absorption half-life), which masks the initial distribution phase of concentration decline observed following IV administration.11 Efalizumab pharmacokinetics is then consistent with a 1-compartment model with population mean estimates of apparent V and CL (actually V/F and CL/F) of 9.13 L and 1.29 L/d (for a 1-mg/kg dose), respectively. These estimates result in a half-life of 4.9 days. Assuming an absolute bioavailability of 50% (Genentech data on file), V would approximate plasma volume (4.5 L), as typically observed with IgG1, and CL (0.645 L/d) would be somewhat faster than that observed for other IgG1 antibodies when no significant receptor-mediated clearance is involved. This is consistent with the shorter half-life of efalizumab compared with the typical half-life of IgG1 of about 20 days.20
As most of the data were obtained at steady state, covariate effects were only assessed for efalizumab apparent clearance, the main parameter determining steady-state exposure. Baseline subject weight was the most important covariate in explaining clearance variability. Despite the change in CL/F with weight, efalizumab exposure is consistent across subject weight, which supports the body weight-based dosing strategy (mg/kg) for efalizumab given subcutaneously. Other statistically significant pathophysiological covariates only had modest effects on efalizumab clearance and steady-state exposure. None of these covariates (PASI, obesity, age, and lymphocyte count) warrants any change in dosing in subject subgroups. Efalizumab CL/F was not affected by gender or race. Finally, the population model was used to generate individual patient estimates of steady-state concentration in the pivotal phase III studies. The analysis examining the relationship between the predicted steady-state concentrations and response suggested no relationship between drug exposure and response (Figure 4). Similarly, no relationship was found between the safety and observed steady-state concentration (data not shown). So, safety or efficacy clinical endpoints were not found to be related to exposure estimates. Data from phase I studies with efalizumab5,6,11,21 indicate that as long as efalizumab serum or plasma concentrations are above 
3 µg/mL, pharmacodynamic effects on CD11a were maintained. Therefore, the steady-state exposure estimates obtained from these analyses are consistent with adequate dosing in these phase III studies.
In conclusion, the results from population PK analyses suggested that baseline body weight is the most important covariate for efalizumab CL/F value. This supports the current dosing strategy, in which efalizumab is administered based on a body weight-adjusted dose (mg/kg), ensuring a consistent exposure (day 84 trough) across a wide range of patient body weight as, illustrated in Figure 5.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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REFERENCES |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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