2.1 Study Design

This analysis was conducted on pooled data from three clinical studies (B7931005, B7981015, and B7981032). B7931005 was a phase 2a study to investigate ritlecitinib and brepocitinib in adults with AA with 50% or greater scalp hair loss (NCT02974868). The study consisted of three periods: a 24-week double-blind treatment period, an up to 48-week single-blind extension (SBE) period, and a 24-week extension period. Only the initial 24-week period and SBE period of ritlecitinib and placebo data were included in the analysis. In the first period, ritlecitinib 200 mg once daily (QD) for 4 weeks followed by ritlecitinib 50 mg QD for 20 weeks and matching placebo were administered. The SBE period started after a 4-week drug holiday. In the SBE period, responders with a ≥ 30% change from baseline (CFB) received placebo until they met the re-treatment criterion (% CFB at week 24 − % CFB post week 24 > 30%) and then were re-treated with ritlecitinib 200 mg QD for 4 weeks, followed by 50 mg QD. Non-responders received another course of ritlecitinib 200 mg QD for 4 weeks, followed by 50 mg QD for 20 weeks.

B7981015 was a phase 2b/3 study to investigate the efficacy and safety of ritlecitinib in adults and adolescents with AA (≥ 12 years) with 50% or greater scalp hair loss (NCT03732807). The treatment period comprised a 24-week placebo-controlled period followed by a 24-week extension phase. Eligible participants were randomized in a 2:2:2:2:1:1:1 manner to the following treatments: (1) ritlecitinib 200 mg QD for 4 weeks, followed by ritlecitinib 50 mg QD for 44 weeks; (2) ritlecitinib 200 mg QD for 4 weeks, followed by ritlecitinib 30 mg QD for 44 weeks; (3) ritlecitinib 50 mg QD for 48 weeks; (4) ritlecitinib 30 mg QD for 48 weeks; (5) ritlecitinib 10 mg QD for 48 weeks; (6) placebo for 24 weeks → ritlecitinib 200 mg QD for 4 weeks, followed by ritlecitinib 50 mg QD for 20 weeks; and (7) placebo for 24 weeks → ritlecitinib 50 mg QD for 24 weeks.

B7981032 was a phase 3 long-term study to evaluate the safety and efficacy of ritlecitinib in adults and adolescents with AA (≥ 12 years) with 25% or greater scalp hair loss (NCT04006457). All eligible participants enrolled in study B7981032 after participation in either B7931005 or B7981015 received ritlecitinib 50 mg QD. All de novo participants received ritlecitinib 200 mg QD for 4 weeks, followed by ritlecitinib 50 mg QD. Since the B7981032 study was not completed at the time of this analysis, the only available datacut at the time of modeling analysis was included in the analysis dataset.

All the studies were conducted in accordance with the Declaration of Helsinki and the principles of Good Clinical Practice. The final protocols were approved by the institutional review boards.

2.2 Study Assessment

Sparse pharmacokinetics (PK) samples were collected in all studies. The exposure metric was derived from empirical Bayes estimates (EBEs) of the final population PK model [7]. Average drug concentration (Cavg) during the time interval between previous SALT record and the current SALT record was calculated based on the patient’s dosing diary, to be used as the exposure metric for ER analysis.

SALT is a quantitative assessment of AA severity that captures percentage hair loss and was consistently collected as an efficacy endpoint in all studies [8]. The SALT score assessment schedule for each study is available in Supplementary Table S1 (see the electronic supplementary material). The score ranges from 0 to 100, where 100 represents complete hair loss and 0 represents no hair loss.

2.3 ER Analysis

The pharmacometric methodology of CBO analysis proposed by Hutmacher et al. was adapted and modified [9]. The non-boundary data were first scaled between 0 and 1, and a transformation family of Aranda-Ordaz functions was applied to help normalize the skewed distribution of CBO data as follows:

$$\begin z & = \frac \right) - 0}}, z \in \left( \right) \\ x & = h\left( \right) = \log \left[ \right)^ - 1}}} \right], \alpha \ne 0, \\ \end$$

(1)

where \(y\) is the observation in the SALT scale and \(x\) is the observation in the transformed scale. The transformation factor α was estimated during model fitting.

A general nonlinear mixed-effects model was then constructed based on the transformed response:

$$x\left| \right)} \right|\eta = \mu \left( \eta \right) + \sigma \cdot \varepsilon ,$$

(2)

where x|η represents x conditioning on a vector of subject-specific random effects η, μ(η) is a conditional mean, σ is the residual error magnitude, and ε is the residual random error, which is assumed to be normally distributed with mean 0 and variance 1. The conditional mean μ(η) was modeled as:

$$\mu \left( \eta \right) = f_ \left( \eta \right) - f_}}} \left( t \right) - f_}}} \left( t \right),$$

(3)

where \(_\) is the baseline as a function of fixed effects (BASE) and random effects (η) [BASE + η], \(_}}(t)\) is the placebo effect function, and \(_}}(t)\) is the drug effect function.

The placebo effect model was developed first, and then the drug effect model was added to the selected placebo effect model. For both placebo and drug effect functions, an indirect response model was considered using a latent variable approach to handle the delayed onset and offset of the response [10]:

$$\begin f_}}} \left( t \right) & = }\left( t \right) - \frac}1}} }}}1}} }}, f_}}} \left( t \right) = E\left( t \right) - \frac}2}} }}}2}} }} \\ \frac}\left( t \right)}}}t}} & = k_}1}} \cdot \left[ }}} \cdot P_}}} } \right] - k_}1}} \cdot }\left( t \right) \\ \frac}E\left( t \right)}}}t}} & = k_}2}} \cdot \left[ }}} \cdot C_}}} \left( t \right)}}}_ + C_}}} \left( t \right)}}} \right] - k_}2}} \cdot E\left( t \right) \\ }\left( \right) & = \frac}1}} }}}1}} }}, E\left( \right) = \frac}2}} }}}2}} }}, \\ \end$$

(4)

where \(}(t)\) and \(E\left(t\right)\) are latent variables, \(_}}\) is an indicator variable that equals 1 if treatment was given and equals 0 otherwise, \(_}}\) is the maximum placebo effect, \(_}}\) is the maximum effect, \(_}}\) and \(_}}\) are rate constants determining a delay between placebo or drug treatment and response, and \(}}_\) represents the Cavg yielding half of \(_}}\). \(_}}\) and \(_}}\) were parameterized as \(\frac}2}_}\), such that the rate constant of \(_}}\) and \(_}}\) can be viewed in the unit of time (\(_\) was estimated instead of \(_}}\) or \(_}}\)).

Data on the boundaries, 0 or 100, were treated as censored data when constructing the likelihood. The interpretation of censoring is similar to that in PK and pharmacodynamic (PD) assays in that if a more sensitive way of measurement were available, values of 0 or 100 would not have been observed. The likelihoods of 0 observations being less than the minimum observable non-zero value and 100 observations being greater than the maximum observable non-hundred value were estimated, such that the likelihood for all the data is maximized in the model development.

Inter-individual variability (IIV) was incorporated in BASE, \(_}}\), and \(_}2}\)/\(_}2}\) using a multiplicative exponential error model (\(_=_}}\bullet }(_)\) for ith individual) and \(_}}\) with an additive model (\(_=_}}+_\)) to allow both disease worsening and improving.

The covariates tested were effects of sex, weight, age, race, region, disease severity (alopecia totalis [AT]/alopecia universalis [AU] status), and prior treatment on BASE; sex, weight, age, race, region, disease severity, prior treatment, AA duration since first diagnosis (DURF), duration of current AA episode (DURC), and baseline SALT score on \(_}}\); and age, weight, region, disease severity, prior treatment, DURF, and DURC on \(_}2}\)/\(_}2}\). Stepwise covariate analysis was performed using both forward addition (p < 0.05) and backward elimination (p < 0.001).

Model adequacy was evaluated through changes in objective function value (OFV), visual inspection of diagnostic plots, precision of the parameter estimates, and decreases in IIV and residual variability. The final model was further evaluated for its predictive performance by visual predictive check (VPC).

ER analyses were performed using NONMEM version 7.5.0. Exploratory analyses, diagnostic plots, post-processing of NONMEM output, and simulations were performed with R version 4.0.3. Perl-speaks-NONMEM (PsN) version 5.2.6 was used for performing sampling importance resampling (SIR). The NONMEM analyses were conducted using the Laplace estimation method with interaction and ADVAN13 with TOL = 6. The stochastic approximation expectation maximization (SAEM) method with importance sampling (IMP) was used for the estimation algorithm.

2.4 Clinical Trial Simulation to Understand Full Dose-Response Based on Limited Dose Range Data

To better understand translation of the established ER relationship in the transformed scale into the original SALT scale, clinical trial simulation was performed for various QD doses. One thousand datasets of longitudinal SALT scores for 130 participants, an average sample of the single arms of the B7981015 study (n = 129–132), were simulated for placebo, 30-, 50-, 100-, 200-, 400-, and 600-mg ritlecitinib QD dosage regimens. The demography of the 130 participants was assumed to be identical to that of the 50-mg arm of study B7981015. For each trial simulation, PK profiles were simulated first using EBEs for the 50-mg arm from the PK model, and SALT profiles were then simulated using a parameter set randomly drawn from a multivariate normal distribution using the population estimates and corresponding variance–covariance matrix of the estimates from the final CBO model. The SALT scores were simulated based on the transformed scale first and then back-transformed into the original SALT scale. Both PK concentrations and SALT scores including residual variability were simulated every week up to week 48, and placebo-adjusted responder rates for SALT ≤ 20 at week 24 and week 48 were collected for each simulated trial. The median and 95% prediction interval (PI) of the placebo-adjusted responder rates from 1000 simulated trials were summarized for each dosage regimen.

2.5 Clinical Trial Simulation to Understand Loading Dose Effect

The purpose of this simulation was to delineate the loading dose effect on clinical onset of response as well as overall outcome. The simulation scheme was identical to that of the previous simulation except the explored dosing regimens. One thousand datasets of longitudinal SALT scores for 130 participants were simulated for placebo, 30 mg QD, 50 mg QD, and 200 mg QD for 4 weeks, followed by 30 mg QD and 200 mg QD for 4 weeks, followed by 50-mg QD dosage regimens. The SALT score was simulated for every week up to week 48 to correctly capture the onset of response. In study B7981015, the clinical onset was defined as the time when the responder rate for SALT ≤ 20 separated from placebo based on 95% confidence interval (CIs). Therefore, simulation results were summarized based on the placebo-adjusted SALT ≤ 20 responder rate, to evaluate when the lower bound of the 95% CI for placebo-adjusted responder rate became > 0. Since clinical onset based on this definition would be influenced by sample size, clinical trial simulation was conducted using the same sample size for the single arm of B7981015 (n = 130).

2.6 Clinical Trial Simulation to Evaluate Treatment Interruption Effect

Simulation was conducted to assess the impact of treatment interruption on loss of efficacy, SALT ≤ 20, after patients achieve a stable response. The study participants for the simulation were assumed to be identical to participants in study B7981015 (n = 715), and longitudinal SALT scores for each individual were simulated based on EBEs of final model parameters. In this simulation, all the participants were treated with 50 mg QD until week 96 to ensure the SALT response had reached a plateau, and SALT scores were simulated for every week up to week 144 (48 weeks after treatment withdrawal) to capture any changes of SALT score after treatment interruption. For responders, defined as participants achieving SALT ≤ 20 at week 96, time to lose SALT ≤ 20 response was collected and the proportions of responders losing SALT ≤ 20 response at various treatment interruptions with durations of 4, 6, 8, 10, 12, 14, 16, 24, 36, and 48 weeks were summarized.