Population PK Analysis Base Model Development

After completing all steps of the model development, the model that best fit the data was a 3-compartment model with linear elimination. Zero-order, first-order, and sigmoid-absorption models for oral and AOM were evaluated. Doses administered orally were best described by sigmoid absorption (infusion to depot compartment followed by first-order absorption), which delays the time to measurable concentrations, and doses administered by injection to the arm, thigh, or gluteal muscle were best described by standard first-order absorption.

The evaluation of the effect of CYP2D6 metabolizer status on the CL/F of aripiprazole showed it to be highly statistically significant (P < .000015) with the CL/F for CYP2D6 PM subjects estimated to be approximately half the CL/F of CYP2D6 EM subjects. The effect of the coadministration of CYP2D6 and CYP3A4 inhibitors on CL/F, oral Ka, and relative bioavailability was evaluated and the presence of each inhibitor was found to significantly reduce the CL/F of aripiprazole.

With the addition of the sparse PK data from the phase 3 study (predose samples and single samples on days 7, 14, and 28 after dosing), the estimation of the relative bioavailability of the AOM dose, as compared to the oral, was assessed and the ability to estimate all of the model parameters was evaluated. Following the investigations, the final base structural model remained unchanged except for the addition of relative bioavailability and only relative bioavailability, AOM Ka, CL/F, Vc/F, and related IIV terms could be estimated. All other parameters were fixed to the values from the model before adding the phase 3 data. It should be noted that before the addition of the sparse PK data, all model parameters (fixed and random effects) were well estimated (%RSE: 6%-46%), as shown in Table S4.

Covariate Analysis

A multivariable stepwise forward selection process was then performed. The effect of BMI as a power function and sex as a proportional function on AOM Ka and the effect of WTKG as a linear function on CL/F were found to be statistically significant (all individual covariate P values < .0037). Following the inclusion of covariates, it was determined that off-diagonal elements of the covariance matrix (describing the covariance of IIV terms) could not be successfully estimated. Proceeding with backward elimination, the effect of WTKG on CL/F was not statistically significant (P > .001) and was removed from the model.

Final PopPK Model

The final oral and AOM combined popPK model was a 3-compartment model with sigmoid absorption for oral dosing (allowing a small lag time before absorption) and first-order absorption for AOM dosing and included an estimated bioavailability of the AOM formulation, as compared to oral dosing. As mentioned for the base model, parameters including relative bioavailability for AOM, AOM Ka, CL/F, Vc/F, related IIV parameters, and RV terms were estimated in the final model, while all other parameters were fixed to values from the base model before the inclusion of the phase 3 study. The parameter estimates and associated equations of the final model are shown in Table 1, and the goodness-of-fit plots are shown in Figure 2.

Table 1. Final Model - Phase 1 and Phase 3 Oral + AOM Data Final Parameter Estimate Magnitude of Interindividual Variability (%CV) Parameter Population Mean %RSE Final Estimate %RSE Ka: oral first-order absorption rate (1/h) 0.540 Fixed 65.88 Fixed CL/F: clearance for EM (L/h) 3.71 4.0 38.34 6.9 CL/F: clearance for PM (L/h) 1.88 6.9 CL/F: proportional change in CL/F for CYP2D6 inhibitor –0.511 Fixed CL/F: proportional change in CL/F for CYP3A4 inhibitor –0.237 Fixed Vc/F: central volume (L) 93.4 8.8 124.50 15.2 Q1/F: intercompartmental CL/F (L/h) 0.591 Fixed NE NA Vp1/F: peripheral volume (L) 118 Fixed NE NA Q2/F: second intercompartmental CL/F (L/h) 28.8 Fixed NE NA Vp2/F: second peripheral volume (L) 134 Fixed NE NA R1: infusion rate of oral dose into depot compartment (mg/h) 9.33 Fixed NE NA IM Ka: AOM first-order absorption rate (1/h) 0.000904 5.3 55.59 8.2 F2: relative bioavailability for AOM 1.48 4.9 NE NA IM Ka: power for (BMI/28) -0.975 11.5 NE NA IM Ka: proportional shift for men 0.346 28.9 NE NA Phase 1 RV (%CV) 24.23 8.4 NA NA Phase 3 RV (%CV) 28.11 4.7 NA NA Minimum value of the objective function  =  48892.907 AOM, aripiprazole once monthly; BMI, body mass index; %CV, percent coefficient of variation; CYP, cytochrome P450; EM, extensive metabolizer; IM, intramuscular; NA, not applicable; NE, not estimated; PM, poor metabolizer; %RSE, relative standard error expressed as a percent; RV, residual variability. Note: Sigmoid absorption was described by R1, the infusion rate of the oral dose into the depot compartment, and Ka, the oral first-order absorption rate constant. The shrinkage of CL, Vc, oral Ka, and IM Ka was estimated as 7.3%, 52.2%, 8.2% (oral only), and 21.2% (IM only). The estimate of the clearance for extensive metabolizers was correlated with the estimate of the relative bioavailability for AOM (r  =  0.901). Related equations:

Goodness-of-fit plots for final model of phase 1 and phase 3 oral plus AOM data. The observed concentrations >500 ng/mL represent <1% of the data. Panels in the right column display a line of identity (solid black). All panels have loess smooth lines of the data for the extensive metabolizers (dashed blue) and for the poor metabolizers (dashed red). AOM, aripiprazole once monthly; CYP, cytochrome P450; Conc, concentration.

The bioavailability of AOM was estimated ≈48% higher, as compared to oral administration. The typical value of the AOM absorption half-life (0.693/AOM Ka) was estimated to increase with increasing values of BMI, with the AOM absorption half-life estimated to be longer for women. For a typical subject with a BMI of 28 mg/kg2, the estimated AOM absorption half-life was ≈32 days for women and 24 days for men. A graph showing the full relationship between AOM absorption half-life and BMI for men and women is included in Figure S1. The CL/F for CYP2D6 PM subjects and CL/F in the presence of strong CYP2D6 inhibitors was approximately half that of CYP2D6 EM subjects and the CL/F in the presence of strong CYP3A4 inhibitors was ≈24% lower than that of CYP2D6 EM subjects.

The goodness-of-fit plots (Figure 2, right panels) exhibit some underprediction for observed concentrations > 500 ng/mL (representing <1% of the data). Given that concentrations >500 ng/mL were observed only in the phase 3 study and occurred very infrequently, this underprediction bias could be the result of inaccurate dosing records (time of previous oral dose misrecorded, an additional oral dose taken before the clinic visit and not reported, or continued oral dosing after the 14-day lead-in that was not reported). Thus, this bias was not considered clinically meaningful and, overall, the model described the data well. This was further supported by the uniform spread of the weighted residuals about 0 over the full duration of sampling (≈9 months) and time since previous dose up to 2100 hours (≈88 days) after dosing (Figure 2, left panels).

In addition, as shown in Table 1, all parameters were estimated with reasonable precision (RSE <30%). The magnitude of the unexplained IIV in CL/F was small (38 %CV, coefficient of variation expressed as a percent), the unexplained IIV in oral Ka and AOM Ka was moderate at 66 %CV and 56 %CV, respectively, and the unexplained IIV in Vc/F was large (125 %CV). The rather large unexplained IIV in Vc/F was probably related to the absorption rate-limited PK of AOM.

Model Evaluation

The VPC of the final popPK model stratified by route of administration for the model development data set is displayed in Figure 3. The VPC shows a close correspondence of the observed and model-simulated 5th, median, and 95th percentiles across the full range of time since previous dose with the exception of an underprediction of the 5th percentile for oral dosing (represents ≈3 subjects). Overall, the VPC indicates that the model had no significant biases, represented an adequate fit to the data, and was appropriate for use in the simulations.

Visual predictive check of the final model, stratified by administration route. Top panel, oral. Bottom panel, AOM. AOM, aripiprazole once monthly; CI, confidence interval.

The summary statistics of the %PPE and |%PPE| for the external validation data set indicated that the final popPK model adequately described the 400-/300-mg dose group with a median %PPE of –6.8% and a median |%PPE| of 29.2%. However, the 50-/25-mg dose group did not fully meet the acceptance criteria with a median %PPE of –1.73% and a median |%PPE| of 41.3%. While the 50-mg AOM treatment arm median |%PPE| was close to the validation criteria and only slightly above the prespecified limit of 40%, the 75th percentiles of the |%PPE| (74.6%) provided further indication that the final popPK model did not adequately extrapolate to describe the 50-/25-mg dose. Because the 50-/25-mg dose group was included in study 31-07-247 only as a low-dose group for the noninferiority design and was not of clinical relevance, this treatment arm was excluded from the E-R analyses rather than rebuild the popPK model to adequately fit concentrations following this dose. As shown in Figure S2, a VPC of the model for the validation data set was also performed and confirms the information described above.

Model Simulations

For the 663 subjects included in the model development data set, individual model-predicted parameters and Cmin,ss, Cmax,ss, and AUC0-τ,ss (where τ is 24 hours for oral dosing and 672 hours for AOM dosing) were calculated using the Bayesian PK parameter estimates following virtual 10-mg oral aripiprazole administration, and following virtual 400-mg AOM administration. On average, the AOM absorption half-life was ≈24 days for men and 36 days for women. The average terminal elimination half-life was ≈7.5 days for men and women. The mean (standard deviation [SD]) CL/F for the 621 EM and 42 PM subjects was 3.90 (1.53) L/h and 2.02 (0.837) L/h, respectively. The mean (SD) CL/F for the 13 EM subjects taking CYP2D6 inhibitors and 25 EM subjects taking CYP3A4 inhibitors was 1.78 (0.665) L/h and 3.13 (1.26) L/h, respectively. For AOM dosing, the mean (SD) values of steady-state PK exposures were as follows: Cmin,ss  =  195.9 (102.3) ng/mL, Cmax,ss  =  321.5 (126.0) ng/mL, and AUC0-τ  = 178.5 (74.9) mg •  h/L.

For the 611 subjects in the model development data set who received aripiprazole AOM, there were no clinically significant changes in Cmin,ss, Cmax,ss, or AUC0-τ,ss across sex or quintiles of BMI (Figure S3). The figure further indicates that Cmin,ss was generally higher following 400 mg of AOM dosing, as compared to 10-mg oral aripiprazole dosing and that Cmax,ss was generally lower following 400 mg of AOM dosing, as compared to 30-mg oral aripiprazole dosing.

As shown in Figure 4, panel 1, differing dose initiation schemes showed that the median concentrations were within the therapeutic window by day 7 following a 400-mg AOM dose alone. It was also shown that with dosing of 10- to 20-mg oral aripiprazole before and for 14 days after the first AOM dose (as recommended)12 median concentrations remained within the therapeutic window for the full time course of the first dose. As shown in Figure 4, panel 2, for subjects with a known poor CYP2D6 metabolizer status, median steady-state concentrations after dosing of 300-mg AOM (as recommended)12 remained centered within the therapeutic window, while concentrations following dosing of 400-mg AOM approached the upper limit of the therapeutic window. As shown in Figure 4, panel 3, a dose reduction to 300-mg aripiprazole AOM for chronic coadministration of CYP2D6 or CYP3A4 inhibitors12 and a dose reduction to 200-mg aripiprazole AOM for chronic coadministration of both inhibitors12 (recommended dose adjustments based on simulations) is expected to result in median steady-state concentrations remaining within the therapeutic window.

Simulated median concentration vs day. The dashed horizontal lines represent the therapeutic window. Unless specified otherwise, all groups were administered the specified amount of oral aripiprazole to steady state followed by 400-mg AOM with or without 14 days of concomitant administration of the specified amount of oral aripiprazole. Panel 1: First 2 doses, stratified by dosing initiation scheme. Panel 2: Following steady-state administration of specified AOM dose, concentration versus days since previous active dose for CYP2D6 poor and extensive metabolizers. Panel 3: Simulated median steady-state concentration vs days since previous active dose. All groups were administered the specified dose of AOM to steady state with or without the presence of chronic concomitant administration of CYP2D6 or CYP3A4 inhibitors. Panels 4 and 5: Second or third dose delayed by 7 or 8 days, stratified by reinitiation of dosing without and with supplemental oral therapy, respectively. Panels 6 and 7: Fourth or 10th dose delayed by 14 or 15 days, stratified by reinitiation of dosing without and with supplemental oral therapy, respectively. AOM, aripiprazole once monthly; CYP, cytochrome P450; EM, extensive metabolizers, PM, poor metabolizers, SS, steady state.

To further investigate the repercussions of delayed dosing, simulations delaying the second, third, fourth, and 10th aripiprazole AOM doses by differing lengths of time were conducted; the effect of reinitiating AOM dosing with or without concomitant oral therapy was also assessed. The median aripiprazole plasma concentration–time profiles for these simulations are displayed in Figure 4, panels 4 through 7. When the second and third doses of aripiprazole AOM were delayed by more than 1 week, the median aripiprazole concentrations for the AOM dose administered with 14 days of concomitant oral therapy reached levels similar to the doses administered on schedule by approximately the third day after dosing. After the third day, the concentrations declined and returned to a concentration pattern similar to that of reinitiating dosing following a 1-week delay without oral therapy. Similar patterns were observed when the fourth and 10th doses were delayed by >2 weeks followed by reinitiation with oral concomitant therapy, as compared to a 2-week delay followed by AOM dosing alone.

Exposure-Response Analysis of Time to Relapse

The analysis data set included 85 impending relapse events (48 events or 56.5% for placebo and 37 events or 43.5% for the 400-/300-mg AOM dose group). The analysis data set included 530 censored subjects (72 subjects or 13.6% for placebo and 458 subjects or 86.4% for the 400-/300-mg AOM dose group). As a result of subjects receiving aripiprazole before randomization to placebo, the mean (SD) predicted aripiprazole Cmin was 47.8 (65.3) ng/mL for subjects assigned to placebo and 180.9 (83.1) ng/mL for subjects assigned to 400-mg AOM. Furthermore, the mean (SD) model-predicted aripiprazole Cmin for all dose groups (placebo, 300-mg AOM, and 400-mg AOM) was 101.7 (90.0) ng/mL in impending relapse subjects and 161.5 (93.6) ng/mL in censored subjects.

The results from the dose-response analysis showed that the time to impending relapse was significantly shorter for subjects in the placebo group as compared with subjects in the aripiprazole AOM 400-/300-mg group (hazard ratio, 8.009; P < .0001; log rank test).

The Kaplan-Meier plot of time to impending relapse, stratified by quartiles of the model-predicted aripiprazole Cmin proximate to the time of relapse or censoring, is shown in Figure 5. For Cmin > 95 ng/mL (the highest 3 quartiles), there was little difference in the survival distribution function regardless of concentration.

Kaplan-Meier plot of survival (no relapse) vs time for placebo and 400-/300-mg aripiprazole AOM treatment groups, grouped by quartiles of predicted aripiprazole Cmin. Quartile 1 is Cmin ≤95 ng/mL; Quartile 2 is 95 < Cmin ≤146 ng/mL; Quartile 3 is 146 <Cmin ≤200 ng/mL; and Quartile 4 is 200 <Cmin. Note: The minimum model-predicted Cmin was not 0 for the placebo treatment arm because of incomplete washout of prior oral dosing. The minimum model-predicted Cmin was 0.000329 ng/mL. AOM, aripiprazole once monthly; Cmin, minimum predicted drug concentration.

Initial modeling indicated that the proportional hazard assumption was not met. Thus, parametric functional forms of the survival model were assessed. The exponential distribution resulted in the best fit to the data. However, there was bias in the model predictions for Cmin concentrations >95 ng/mL (the highest 3 quartiles). The model predicted a decreasing E-R relationship between Cmin and time to relapse in the 3 highest quartiles, whereas the observed data showed a similar time to relapse in the 3 highest concentration quartiles. The model misfit at the highest predicted concentrations may be the result of unknown influences, or it could be indicative of a concentration-threshold relationship of efficacy instead of a continuous relationship.

To explore the potential of a concentration-threshold relationship for efficacy, 2 groups of predicted Cmin were evaluated (<95 ng/mL vs ≥95 ng/mL). A statistically significant relationship between time to impending relapse and grouped aripiprazole Cmin was detected (Table 2). The hazard ratio for aripiprazole Cmin ≥95 ng/mL to that for aripiprazole Cmin <95 ng/mL was equal to 4.41 with a 95% confidence interval ranging from 2.89 to 6.75. Thus, a subject with a diagnosis of schizophrenia and a predicted aripiprazole Cmin ≥95 ng/mL is 4.41 times less likely to relapse, as compared to a subject with a predicted Cmin <95 ng/mL. As illustrated in Figure 6, there was good agreement between the observed and model-predicted estimates of the survival distribution function for both groups of model-predicted Cmin, illustrating a threshold concentration effect whereby predicted concentrations ≥95 ng/mL are associated with greater efficacy over time.

Table 2. Parameter Estimates for Exponential Survival Model of Impending Relapse as a Threshold Function of Model-Predicted Aripiprazole Cmin (<95 ng/mL and ≥95 ng/mL) Parameter Parameter Estimate Standard Error 95% Confidence Interval P Value Intercept 6.256 0.1474 5.97 6.55 <.0001 Predicted aripiprazole (Cmin ≥ 95 ng/mL) proximate to the event 1.484 0.2177 1.06 1.91 <.0001 Calculated hazard ratio of expected survival time for Cmin ≥95 ng/mL:Cmin <95 ng/mL 4.41 NA 2.89 6.75 NA Cmin, model-predicted minimum aripiprazole concentration; NA, not applicable. Note: Calculated ratio of expected survival time was calculated as eparameter estimate.

Observed (red line) and model-predicted (blue dashed line) probability of survival vs time for groups of predicted aripiprazole 0 < Cmin ≤95 ng/mL and 95 < Cmin ≤580 ng/mL. The shaded regions show the 90% prediction interval of the model-predicted probability of survival vs time. Cmin, minimum predicted drug concentration; PI, prediction interval.