Establishing the Exposure‐QT Relationship During Bedaquiline Treatment Using a Time‐Varying Tuberculosis‐Specific Correction Factor (QTcTBT)

ABSTRACT

Evaluating QT prolongation induced by anti‐tuberculosis (TB) drugs in patients with active TB, who often experience tachycardia, is challenging due to the limitations of Fridericia's correction factor (QTcF) in decorrelating QTc from heart rate (HR). Previous exposure‐QTcF analyses in patients with active TB were able to alleviate the limitation of QTcF but required advanced model‐based methodologies, incorporating a non‐drug‐related, “secular” trend in the model to dissociate drug and non‐drug‐related effects on QT. Recently, we developed and validated a time‐varying QT correction method (QTcTBT) that more accurately accounts for the HR changes during TB treatment. In the present work, using data from 429 patients with multidrug‐resistant TB across two Phase IIb trials, we re‐evaluated the exposure‐QTc relationship for bedaquiline by applying QTcTBT instead of QTcF. Our analysis showed that when HR changes were accounted for using QTcTBT, a typical maximum M2 (bedaquiline metabolite) concentration (326 ng/mL, mean maximal concentration (Cmax) at the end of 2‐week loading phase) was associated with a 7 ms QTc interval prolongation (90% CI: 5.9–8.2). This estimate closely aligns with the previously reported M2 effect of 7.9 ms (90% CI: 6.8–9.3), derived from the exposure‐QTcF model. The consistency between the two methodologies further supports the use of QTcTBT for estimating the QTc prolongation effects of anti‐TB drugs.

Summary.

• What is the current knowledge of the topic?

  • ○
    M2, the main metabolite of bedaquiline, prolongs the QT interval associated with bedaquiline treatment. Previous analyses generally applied the Fridericia correction method to correct QT for heart rate (HR), resulting in an overestimation of the change in QTc from baseline QTcF (ΔQTcF). This overestimation may have resulted in unnecessary interruptions in effective treatment. Various model‐based approaches have addressed this HR‐driven bias in ΔQTcF. These analyses indicate consistently that the worst‐case mean QTc increase associated with M2 does not exceed 10 ms.
• What question did this study address?

  • ○
    Can the recently developed QT correction method (QTcTBT) enable a more straightforward concentration–QT analysis by accounting for the gradual changes in HR throughout treatment, even in the absence of placebo data?
• What does this study add to our knowledge?

  • ○
    This study demonstrates that QTcTBT can simplify exposure‐QTc analysis in patients with TB and confirms QT prolongation < 10 ms at therapeutic bedaquiline/M2 levels.
• How might this change drug discovery, development, and/or therapeutics?

  • ○
    The time‐varying QTcTBT method allows for a more reliable establishment of the drug exposure‐QTc relationship in patients with active TB by accurately accounting for HR changes. This method will benefit future exposure‐QTc analyses in the TB field and clinical applications, as it does not require placebo data or complex modeling techniques to separate HR effects from drug‐related QTc changes from baseline.

1. Introduction

Tuberculosis (TB) remains a significant global burden, causing an estimated 1.25 million deaths worldwide in 2023. Among these cases, multidrug‐resistant (MDR) or rifampicin‐resistant (RR) TB was estimated to affect 400,000 individuals [1]. Treatment of MDR‐TB always involves a combination of drugs [2], some of which can cause QT prolongation. QT prolongation occurs when the duration of the ventricular action potential extends due to abnormalities in potassium ion channels, increasing the risk for sudden life‐threatening cardiac arrhythmias, such as torsade de pointes [3].

Bedaquiline is currently recommended in the first‐line treatment regimens of MDR‐TB [2]. While bedaquiline is widely used with success [4], its main metabolite, M2, is associated with QT prolongation [5]. Bedaquiline may also be used in combination with other QT‐prolonging drugs, for example, clofazimine, moxifloxacin, levofloxacin, delamanid, and pretomanid. The combination of these drugs could increase the risk of QT interval prolongation. Therefore, the need to monitor the QT interval accurately is important [2, 6, 7, 8, 9, 10, 11, 12]. However, such monitoring can be challenging and burden treatment programs.

Assessing a drug's QT liability in patients with active TB, who commonly have tachycardia, is challenging as the standard Fridericia correction often underestimates the QTc interval at elevated heart rate (HR) [13, 14]. This was shown to result in an artificially short QTcF at baseline [15]. Effective treatment generally leads to HR normalization, such that QTcF provides accurate HR correction at the end of successful treatment. Consequently, the correlation between HR and QT changes with time throughout treatment [16]. This results in a bias in QTcF change from baseline (ΔQTcF), which earlier model‐based analyses addressed by estimating a time‐dependent QT effect [14, 15, 17].

We previously developed a time‐varying correction factor for QT (QTcTBT) to adjust for HR changes in TB patients during treatment accurately [16]. QTcTBT is a time‐varying correction method, changing from 0.4081 (Olliaro's correction factor, QTcO, developed for TB patients prior to treatment) to 0.33 (QTcF) at a rate characterized by a half‐life of 7.74 weeks [13, 16, 18]. In this work, we established the M2 concentration‐QT relationship using QTcTBT instead of QTcF to evaluate the QTcTBT method's robustness further.

2. Methods

2.1. Data

The data used in this analysis was the same as in the previous exposure‐QT analysis based on QTcF [17], including newly diagnosed MDR‐TB patients from study TMC207‐C208 (2 stages, randomized, double‐blinded, placebo‐controlled trial) [19, 20] and newly diagnosed or treatment‐experienced MDR‐TB patients from the TMC207‐C209 study (a single‐arm open‐label trial) [12]. Participants received bedaquiline (400 mg once daily for 2 weeks, then 200 mg three times a week) or a placebo for 24 weeks (8 weeks in the C208 stage 1 study) together with background anti‐TB regimens which largely excluded other QT‐prolonging drugs. The trials adhered to Good Clinical Practice standards and were approved by the local ethics committees. Written informed consent was obtained from all patients or their representatives. The trials are registered on ClinicalTrials.gov under NCT00449644 for the C208 study and NCT00910871 for the C209 study. Single and triplicate electrocardiograms (ECG) were obtained from all patients. Single ECGs were measured up to an hour before taking the drug (8 AM), and triplicate ECGs were measured just before drug intake (8 AM) and 5 h afterwards. In the C208 study, at Week 8 (stage 1) and Week 24 (stage 2), additional triplicate ECGs were performed 36‐ and 48‐h post‐dose. QT interval was corrected using two formulas: QTcF = QT_uncorrected/RR^0.33 or QTcTBT = QT_uncorrected/RR^CF(t), where CF(t) = 0.4081–0.0781 × (1‐e ^{(−ln(2) × t/7.74)}) [16, 18]. Individual bedaquiline and M2 concentrations were predicted for all time‐matched ECG records based on individual pharmacokinetic (PK) data available from the studies and a published PK model developed on the same dataset to ensure all ECGs were accurately time‐matched with PK data [21].

2.2. QTc Model

2.2.1. Structural Model

The QTc model used to analyze QTcF and QTcTBT was adapted from Tanneau et al.'s exposure‐QTcF model [17]. The model structure includes a time‐on‐treatment effect that represents a non‐drug‐related asymptotic change in QT over time, also referred to as a secular trend (Equation 1), 24‐ and 12‐h circadian rhythm cycles (Equation 2), the effect of M2 (Equation 3), and patient covariates influencing the QT baseline (Equation 4), including the effects of other QT‐prolonging drugs, if present. The full QTc model (Equation 5) was used to analyze QTcF and QTcTBT. The QTcTBT model code is available in Supporting Information S1.

$$\mathrm{TE}\left(t\right)=\text{QTcmax}\times \left(1-e^{\frac{-\mathit{ln}\left(2\right)\times t}{t_{1/2}}}\right)$$ (1)

$$\begin{array}{c}\text{CIRC}\left(\text{CTIME}\right)=A_{24}\times \cos \left(\frac{2\pi \left(\text{CTIME}-{\phi }_{24}\right)}{24}\right)+\hfill \\ A_{12}\times \cos \left(\frac{2\pi \left(\text{CTIME}-{\phi }_{12}\right)}{12}\right)\hfill \end{array}$$ (2)

$$\mathrm{M}2\mathrm{EF}\left({\text{Conc}}_{\mathrm{M}2}\right)=\frac{{\text{Emax}}_{\mathrm{M}2}\times {\text{Conc}}_{\mathrm{M}2}}{\mathrm{EC}{50}_{\mathrm{M}2}+{\text{Conc}}_{\mathrm{M}2}}$$ (3)

$$\begin{array}{c}{\mathrm{QTc}}_{\text{baseline},\mathrm{i}}={\mathrm{QTc}}_{\text{baseline}}+{\mathrm{\theta }}_{\text{Clofazimine}}\times {\text{Comed}}_{\text{Clofazimine},\mathrm{i}}+{\mathrm{\theta }}_{\text{Moxifloxacin}}\hfill \\ \times {\text{Comed}}_{\text{Moxifloxacin},\mathrm{i}}+{\mathrm{\theta }}_{\text{Calcium}}\times \left({\mathrm{Ca}}_{\mathrm{i}}-{\mathrm{Ca}}_{\text{median}}\right)\hfill \\ +{\mathrm{\theta }}_{\text{Potassium}}\times \left({\mathrm{K}}_{\mathrm{i}}-{\mathrm{K}}_{\text{median}}\right)+{\mathrm{\theta }}_{\text{Female}}\times {\mathrm{Sex}}_{\text{female},\mathrm{i}}\hfill \\ +{\mathrm{\theta }}_{\text{black}}\times {\text{Race}}_{\text{black},\mathrm{i}}+{\mathrm{\theta }}_{\mathrm{Age}}\times \left({\mathrm{Age}}_{\mathrm{i}}-{\mathrm{Age}}_{\text{median}}\right)\hfill \end{array}$$ (4)

$$\mathrm{QTc}{\left(\mathrm{t}\right)}_{\mathrm{i}}={\mathrm{QTc}}_{\text{baseline},\mathrm{i}}+\mathrm{TE}\left(\mathrm{t}\right)+\text{CIRC}\left(\text{CTIME}\right)+\mathrm{M}2\mathrm{EF}\left({\text{Conc}}_{\mathrm{M}2}\right)$$ (5)

where, TE(t) represents the time‐on‐treatment effect (non‐drug associated QTc changes), QTmax is the maximum QT change at the steady state of the asymptotic (non‐drug associated) function, t_1/2 is the half‐time required to achieve QTmax, CIRC denoted the circadian variation of QT throughout the day, with A representing the amplitude of the 24‐ or 12‐h oscillator and φ indicating the acrophase of the 24‐ or 12‐h oscillator, CTIME refers to the clock time, M2EF is the effect of M2, Emax is the maximal effect of M2 on QTc, EC50 is the concentration achieving 50% of the effect of Emax effect, Conc_M2 is the concentration of M2, Comed is the time‐varying comedication used at ECG measurement time points.

2.2.2. Statistical Model

Residual unexplained variability (RUV) was modeled using a two‐level additive structure: one accounting for variability among triplicate measurements taken on a single occasion and another accounting for variability between samples. Log‐normally distributed inter‐individual variability (IIV) was included for QTc_baseline, EC50_M2, RUV, and RUV_triplicates. The IIV of QTmax was modified from a proportional to an additive model to capture variability better when the typical change in QTc was zero or close to 0, as expected if QTcTBT eliminates the need for a significant secular trend in the QTc model. Correlations between IIV from Tanneau's QTcF model were removed due to model instabilities observed when applied to the QTcTBT model while evaluating time‐effect models. Covariate parameterisations were kept as in the original model, with time‐varying clofazimine and moxifloxacin, baseline serum calcium, serum potassium, sex (female), race (being black), and patients' age included as additive factors on QT_baseline.

2.3. Evaluation of Time‐on‐Treatment Effect

QTcTBT was developed to indirectly adjust for the suboptimal correction QT, enabling the model to distinguish between drug and non‐drug‐related effects on QTc [16]. In this study, we aimed to determine whether utilizing QTcTBT would enable the removal of non‐drug‐related effect components from the QTc model, thereby simplifying the exposure‐QTc analysis and its interpretation.

2.4. Evaluation of the M2 Effect

To investigate this, we tested three different assumptions for time‐on‐treatment effect models. A systematic shift represents a constant shift in QT that occurs for all patients. Based on this definition, we tested (1) a model with a systematic shift in QTc over time for all patients, with differences between individuals according to IIV (as in the original QTcF‐based model), (2) no systematic shift in QTc over time, but with IIV allowing for individual changes in QTc (capturing the natural, random variation in QT interval) and (3) neither a systematic nor individual shifts in QTc over time.

To evaluate the effect of M2, the linear (Equation 6), Emax (Equation 3), and power (Equation 7) drug effect models were compared. The model that best described the data was selected to analyze the effect of M2 on QT.

$$\mathrm{M}2\mathrm{EF}={\text{Slope}}_{\mathrm{M}2}\times {\text{Conc}}_{\mathrm{M}2}$$ (6)

$$\mathrm{M}2\mathrm{EF}={\mathrm{S}}_{\mathrm{M}2}{\times \text{Conc}}_{\mathrm{M}2}^{\mathrm{\gamma }}$$ (7)

where, M2EF represents the effect of M2 on QT, SlopeM2 is the slope of the linear M2 effect, allowing interpretation of the M2 effect in ms per 100 ng/mL, S _M2 is the scaling factor of the power function, and γ is the power exponent of the M2 effect.

2.5. Model Evaluation and Cross‐Validation

Model evaluation was based on the objective function value (OFV), likelihood ratio tests, parameter estimates' values and precision, visual predictive checks (VPCs), and predictive performance assessed through cross‐validation. Parameter uncertainty was obtained through sampling important resampling (SIR) [22]. There was no comparison of performance between QTcF and QTcTBT models using likelihood ratio tests, as they are considered different datasets.

Cross‐validation is the preferred approach for evaluating predictive performance and was used to compare the predictive performance of different models. It provides insight into how well a model fits the data and assesses its ability to predict data not used for model fitting, ensuring model generalizability when applied to an independent dataset [23, 24, 25, 26]. In this study, we used repeated 10‐fold cross‐validation to assess the effects of time‐on‐treatment and M2 on the model's predictive performance. The dataset was divided into 10 subsets (folds), and in each fold, nine subsets served as the training set, while one subset served as the test set. This process was repeated for all 10‐fold. Parameters estimated from the training set were used to predict the test set to obtain the OFV. The sum of the OFVs of all test sets across all folds provided the model's performance. The entire 10‐fold cross‐validation was repeated 10 times with different random partitions, thereby increasing robustness and reducing the variability in performance estimation due to random splits. Model performance was compared using the mean OFVs from 10 repetitions, and the 95% confidence interval (CI) was calculated as the mean $\pm 1.96\frac{\sigma }{\sqrt{10}}$, while σ is the standard deviation (SD). The model demonstrating the lowest mean OFV was considered superior if the difference was statistically significant, as determined by a paired t‐test. This criterion ensured that both performance and parsimony were considered when selecting the final model [23, 27].

In a scientific white paper, Garnett et al. suggested that the analysis for model‐derived ΔΔQTc (the placebo‐corrected change from baseline QTc) should ensure that the upper bound of the two‐sided 90% CI does not exceed 10 ms at the highest clinically relevant exposure [28]. The final model was applied to derive the two‐sided 90% CI of ΔΔQTc at the highest clinically relevant exposure. Across Phase 2 studies, median M2 concentrations varied from 142 to 250 ng/mL depending on the dosing regimen and study population [14, 15, 17, 29]. Based on findings from the pivotal Phase 3 STREAM Stage 2 trial, a concentration of 326 ng/mL was selected as the highest clinically relevant exposure. This value represents the mean maximum concentration (Cmax) at the end of the loading regimen [5].

2.6. Software

The analysis was conducted using NONMEM version 7.5, supported by Perl‐speaks‐NONMEM (PsN, version 5.3.0) [30], on a Linux operating system hosted on the Uppsala Multidisciplinary Center for Advanced Computational Science (UPPMAX) cluster. Additionally, statistical software R, version 4.2.2, and R packages such as Xpose4, ggplot2, and tidyverse were used for data management, exploratory analyses, diagnostic graphics, and post‐processing of the data and NONMEM outputs.

3. Results

Data from 429 individuals, including 18,306 QT measurement records, were analyzed. ECG observations from Day 1 (the day before treatment initiation) through the end of treatment (Week 8 visit for C208 stage 1, Week 24 visit for C208 stage 2 and C209) were included. Baseline participant characteristics are summarized in Table 1. The exposure‐QTc models utilized either calculated QTcF or QTcTBT as observations. Based on individual M2 concentrations predicted by the published population PK model [21], the approved dosing regimen resulted in a median concentration (SD) of 322.2 (142.6) ng/mL, with the highest individual concentration of 826.8 ng/mL at the Week 2 visit. Additionally, the median (SD) through concentration from pre‐dose samples with matching ECGs was 204.3 (155.6) ng/mL across visits.

TABLE 1.

Participants' baseline characteristics.

	C208 study		C209	Total
	Placebo	Bedaquiline	Bedaquiline
N	105	98	226	429
Sex, female, N	39 (37)	31 (32)	80 (35)	150 (35)
Age, years	34 (18–61)	31 (18–63)	32 (18–68)	33 (18–68)
Weight, kg	53 (35–83)	53 (37–81)	57 (30–113)	55 (30–113)
Race/ethnicity, N
Caucasian or White	13 (12)	8 (8)	56 (25)	77 (18)
Black	40 (38)	40 (41)	73 (32)	153 (36)
Hispanic	15 (14)	13 (13)	0 (0)	28 (7)
Asian	6 (6)	9 (9)	89 (39)	104 (24)
Other	31 (30)	28 (29)	8 (4)	67 (16)
TB drug susceptible status, N
Drug‐sensitive TB	4 (4)	3 (3)	3 (1)	10 (2)
MDR‐TB	63 (60)	70 (71)	89 (39)	222 (52)
Pre‐MDRTB	16 (15)	17 (17)	43 (19)	76 (18)
XDRTB	5 (5)	3 (3)	37 (16)	45 (10)
Missing	17 (16)	5 (5)	54 (24)	76 (18)
Comedication uses, N
Clofazimine	0 (0)	0 (0)	24 (11)	24 (6)
Moxifloxacin	4 (4)	3 (3)	2 (1)	9 (2)
Serum calcium at baseline, IU/L	2.53 (2.28–2.84)	2.53 (2.3–2.81)	2.43 (2.15–2.86)	2.48 (2.15–2.86)
Serum potassium at baseline, IU/L	4.3 (3.4–5.8)	4.4 (3.6–5.8)	4.1 (2.7–5.4)	4.3 (2.7–5.8)

Note: N = number of subjects; continuous variables were presented as median (range), and categorical variables were presented as number of subjects (%). Comedication use was counted for participants who used it at any time point during treatment.

Abbreviations: MDR, multidrug‐resistant; TB, tuberculosis; XDR, extensively drug‐resistant (definition as before the year 2021).

3.1. Model Selection and Evaluation Based on Predictive Performance

The predictive performance of the QTcTBT models from 10 repetitions of 10‐fold cross‐validation is shown in Figure 1. The QTcTBT model with a time‐on‐treatment effect but no systematic shift performed comparably to the model with a time‐on‐treatment effect and a systematic shift, with mean OFVs of 106,513 (95% CI 106,507—106,519) and 106,508 (95% CI 106,501—106,514), respectively. In contrast, the mean OFV for the QTcTBT model without a time‐on‐treatment effect was substantially worse. Considering both model performance and the principle of parsimony, the QTcTBT with time‐on‐treatment effect but no systematic shift model was selected, and the M2 effect was subsequently evaluated. Among the three‐drug effect models (Emax, linear, and power), the Emax M2 model yielded the best performance, whereas the linear and power models performed comparably.

FIGURE 1.

Model performance of the QTcTBT from 10 repetitions of 10‐fold cross‐validation. (A) The mean objective function value (OFV) and 95% confidence intervals (CIs) of the QTcTBT model with the Emax M2 effect were evaluated under different model structures describing QT changes. (B) Mean OFV and 95% CIs for the QTcTBT model incorporating a time‐on‐treatment effect without a systematic shift and an M2 effect described by linear, Emax, and power drug effect models.

Parameter estimates from the Emax M2 effect model are presented in Table 2, while those for the linear and power M2 effect models can be found in Supporting Information S2. As shown in Figure 2, VPCs showed that the QTcTBT models adequately capture the data under all three assumptions of time‐on‐treatment effects. In contrast, for QTcF, the model incorporating time‐on‐treatment effects and a systematic shift performed best among the three assumptions of time‐on‐treatment effects (see VPCs in Supporting Information S3).

TABLE 2.

Parameter estimates of the QTcF and QTcTBT models with Emax drug effect model.

Parameters estimates (%RSE)	No time‐on treatment effect		Time‐on treatment effect without systematic shift		Time‐on treatment effect with systematic shift		Published exposure‐QTcF model [17]
	QTcF	QTcTBT	QTcF	QTcTBT	QTcF	QTcTBT	QTcF
QT baseline (ms)	402 (0.3)	408 (0.3)	401 (0.3)	408 (0.3)	401 (0.3)	409 (0.3)	400 (0.3)
Drug effect
Emax M2 (ms)	21.4 (7.0)	19.5 (14.1)	23.8 (13.2)	23.9 (16.9)	27.6 (15.2)	22.9 (16.0)	28.6 (13.8)
EC50 M2 (ng/mL)	278 (19.0)	597 (27.0)	451 (27.3)	789 (28.1)	799 (26.8)	679 (28.4)	851 (24.9)
Time‐on treatment effect
QTmax (ms)			0 FIX	0 FIX	6.65 (11.6)	−3.17 (47.3)	6.50 (11.8)
Half‐life QTmax (weeks)			10.7 (29.5)	18 (48.1)	7.35 (20.1)	18.5 (48.5)	6.44 (17.9)
Circadian rhythm
A 24 (ms)	2.19 (59.8)	1.75 (53.3)	2.61 (46.4)	1.73 (55.3)	2.78 (42.8)	1.64 (60.6)	2.76 (45.3)
φ 24 (h)	4.24 (30.4)	5.94 (43.6)	4.8 (27.3)	5.68 (41.9)	4.88 (25.6)	5.68 (45.6)	4.91 (27.5)
A 12 (ms)	0.978 (44.3)	1.32 (33.7)	1.27 (29.8)	1.18 (36.9)	1.45 (26.8)	1.1 (39.4)	1.46 (26.7)
φ 12 (h)	5.35 (28.2)	4.13 (26.9)	4.71 (25.7)	4.1 (28.5)	4.49 (23.2)	4.18 (31.6)	4.5 (23.4)
Covariates
Clofazimine comedication use (time‐varying) (ms)	11.4 (15.0)	10.2 (16.1)	11.6 (16.4)	10.2 (18.1)	10.8 (17.1)	10.5 (17.5)	11.8 (15.6)
Moxifloxacin comedication use (time‐varying) (ms)	5.64 (36.2)	1.36 (146.3)	4.36 (56.9)	2.06 (118.0)	3.06 (79.4)	2.42 (100.4)	2.47 (98.4)
Serum calcium (ms/IU/L)	−19.7 (10.5)	−2.29 (91.7)	−13.9 (17.5)	−4.79 (49.7)	−9.37 (25.9)	−6.31 (38.7)	−8.74 (28.3)
Serum potassium (ms/IU/L)	−1.6 (27.5)	−1.71 (25.8)	−1.32 (36.6)	−1.46 (32.6)	−1.27 (37.6)	−1.47 (32.3)	−1.25 (38.5)
Sex (female vs. male) (ms)	7.1 (21.1)	8.93 (16.6)	6.63 (23.2)	8.52 (17.7)	6.81 (22.6)	8.48 (17.8)	7.75 (19.1)
Race (black vs. non‐black) (ms)	−6.05 (24.5)	−6.93 (21.2)	−6.64 (22.9)	−6.51 (22.9)	−7.25 (21.1)	−6.32 (23.6)	−6.86 (21.3)
Age (ms/year)	0.341 (17.7)	0.355 (16.8)	0.333 (18.7)	0.346 (17.6)	0.335 (18.6)	0.347 (17.6)	0.349 (17.0)
Inter individual variability (IIV)
QT baseline (%CV)	3.5 (3.7)	3.4 (3.7)	3.6 (3.8)	3.4 (3.7)	3.6 (3.7)	3.4 (3.7)	3.7 (3.8)
QTmax			13 a (14.2)	16.28 a (30.6)	9.92 a (8.9)	16.22 a (31.2)	167 b (12.8)
EC50 M2 (%CV)	329 (26.3)	434.6 (45.4)	210.2 (25.3)	203.8 (27.0)	190.2 (23.2)	210.2 (27.5)	277 (28.8)
RUV (%CV)	24.7 (9.7)	23.5 (11.0)	22.1 (11.3)	21.1 (12.1)	21.7 (11.3)	21.3 (12.1)	21.5 (11.2)
RUV triplicates (%CV)	24.3 (5.7)	23.9 (5.7)	24.3 (5.7)	23.9 (5.7)	24.3 (5.7)	23.9 (5.7)	24.3 (5.57)
Residual unexplained variability (RUV)
RUV additive (ms)	8.73 (1.9)	8.53 (1.9)	8.25 (1.8)	8.02 (1.9)	8.25 (1.8)	8.01 (1.9)	8.19 (1.8)
Box‐Cox transformation of IIV RUV	2.89 (24.2)	2.96 (26.8)	3.87 (24.1)	4.1 (25.4)	3.98 (24.0)	4 (25.5)	4.11 (24.0)
RUV triplicates additive (ms)	6.87 (1.5)	7.38 (1.5)	6.87 (1.5)	7.38 (1.5)	6.87 (1.5)	7.38 (1.5)	6.87 (1.5)
Box‐Cox transformation of IIV RUV replicates	0.786 (42)	0.747 (45.5)	0.821 (40.7)	0.789 (43.3)	0.824 (40.5)	0.788 (43.4)	0.825 (41.1)

Note: The %RSE, percent relative standard error, %CV is calculated as $100\times \sqrt{e^{{\omega }^2}-1}$ for exponential inter individual variability (IIV), including QT baseline, EC50, RUV, and RUV_triplicates.

^a IIV for QTmax was calculated as the standard deviation (SD) for the additive IIV model.

^b IIV for QTmax was calculated as %CV for the proportional IIV model.

FIGURE 2.

Visual predictive checks (VPCs) of QTcTBT versus time after the first bedaquiline dose (top panels) and M2 concentrations (bottom panels) for each time‐on‐treatment effect model. (A, D) QTcTBT model without a time‐on‐treatment effect, shown as QTcTBT versus time (A) and QTcTBT versus M2 concentrations (D). (B, E) QTcTBT model with a time‐on‐treatment effect but no systematic shift. (C, F) QTcTBT model with a time‐on‐treatment effect and a systematic shift. Black dots represent QTcTBT observation data. The solid lines represent the 50th percentile of the observed data, while the dashed lines represent the 2.5th and 97.5th percentiles. The blue and red shaded areas show the simulation‐based 95% confidence intervals of the 2.5th, 50th, and 97.5th percentiles.

3.2. Time‐on‐Treatment and and M2 Effects on QTc

The baseline of QTc was estimated to be lower in the QTcF models compared to the QTcTBT models, with values ranging from 401 to 402 ms for QTcF and 408 to 409 ms for QTcTBT. Regarding the QTcTBT time‐on‐treatment effect, the estimated time to reach half of QTmax was 18 weeks for the model without a systematic shift and 18.5 weeks for the model with a systematic shift. However, the estimated time to reach QTmax was beyond the observation range, as the longest observation included in the analysis was at Week 24. The QTmax estimate for the QTcTBT model was a decrease of 3.17 ms, while the QTcF was an increase of 6.65 ms.

The impact of M2 on QTcTBT was assessed using simulation based on typical Emax and EC50 values. At an M2 concentration of 326 ng/mL, the estimated QTc prolongation varied across models: 6.88 ms for the model without a time‐on‐treatment effect, 7.01 (90% CI 5.95–8.16) for the model with a time‐on‐treatment effect but no systematic shift, and 7.39 (90% CI 6.43–8.57) for the model incorporating both a time‐on‐treatment effect and a systematic shift. In all scenarios, the upper bounds of the two‐sided 90% CI for the M2 effect remained below the 10‐ms threshold. The M2 effect simulation for the model with a time‐on‐treatment effect but no systematic shift is illustrated in Figure 3, while simulations for the other models are presented in Supporting Information S4.

FIGURE 3.

Simulation of the M2 effect (Emax model) on QTcTBT using sampling importance resampling (SIR) from two models: The QTcF model, which incorporates a time‐on‐treatment effect with a systematic shift based on the published exposure‐QTcF model [17] (left) and the QTcTBT model includes a time‐on‐treatment effect but no systematic shift (right). The solid black line represents the median M2 effect, and the green shaded area shows the two‐sided 90% confidence intervals (CIs) of the typical M2 effect. The blue shaded area indicates the range of observed M2 concentrations. The vertical red line marks the clinically relevant M2 concentration (326 ng/mL), and the horizontal red line represents the 10 ms threshold for ΔΔQTcTBT. The horizontal black dashed line shows the typical Emax (maximum M2 effect on QTc), while the vertical black dashed line represents the typical EC50 (the concentration required to reach 50% of Emax).

A similar analysis was conducted for the QTcF models, revealing higher QTc prolongation estimates at 326 ng/mL M2. The QTc increases were 11.6 (90% CI: 10.6–12.7) for the model without time‐on‐treatment effects, 9.97 (90% CI: 8.77–11.20) for the model with time‐on‐treatment effects but no systematic shift, and 8.00 (90% CI: 6.95–9.33) for the model incorporating both time‐on‐treatment effects and a systematic shift. Additionally, the QTcF model re‐estimated from the previously published exposure‐QTcF model [17] (equivalent to the current model with time‐on‐treatment effects including a systematic shift but using a proportional rather than an additive IIV on QTmax) showed a QTc increase of 7.93 ms (90% CI: 6.84–9.26), as illustrated in Figure 3.

This result suggests that QTcTBT provided better consistency across different assumptions regarding the time‐on‐treatment effect in M2 effect estimation compared to QTcF, with an M2 effect deviation of 0.51 ms for QTcTBT versus 3.6 ms for QTcF. Although the M2 effect estimates from the linear and power drug effect models performed worse than the Emax model, both models remained consistent when using QTcTBT, with QT‐prolonging ranging from 6.3 to 6.7 ms for the linear model and 6.8–7.6 ms for the power model.

4. Discussion

In this exposure‐QTc analysis, we used QTcTBT as the dependent variable instead of QTcF to better account for the HR changes during TB treatment. Our results show that QTcTBT was estimated to be reduced by 1.88 ms at Week 24 (95% CI: −6.11 to −0.14), compared to 6.01 ms (95% CI: 4.62–7.40) in the QTcF model. This suggests that QTcTBT effectively mitigates the previously described non‐drug‐related secular trend, reducing the need for a complex time‐on‐treatment effect model when estimating drug‐induced QT prolongation. This simplification is particularly valuable in MDR‐TB treatment regimens, which often include several QT‐prolonging agents.

The exposure‐QTc model was adapted from a previously published exposure‐QTcF model [17]. In this adaptation, the IIV on QTmax was modified from a proportional to an additive structure to capture the small QT changes more accurately, especially when QTmax is close to zero. Cross‐validation confirmed that QTcTBT models incorporating a time‐on‐treatment effect without a systematic shift performed comparably to those with a systematic shift, supporting the model's robustness while maintaining simplicity. Importantly, QTcTBT also enabled reliable individual‐level predictions by accounting for natural, random QTc changes over time, thus enhancing the model's clinical applicability. However, the individual time‐on‐treatment effect was included in the model primarily to improve.

The Emax drug effect model best described the M2 effects. However, the power and linear models also provided M2 effect estimates at clinically relevant concentrations that aligned with those of the Emax model. The consistency with the linear model may be explained by the high estimated EC50 from the Emax model (789 ng/mL), indicating that the drug effect remains within a near‐linear portion of the exposure–QTc curve with the currently approved dosing regimen. The power model supports this interpretation by indicating a sub‐linear relationship between M2 concentration and QT prolongation, where increases in M2 concentration led to a smaller increase in the QT effect.

When accounting for HR changes during TB treatment using the time‐varying QTcTBT correction method, M2 did not prolong the QT interval substantially by more than 10 ms at clinically relevant concentrations, regardless of the time‐on‐treatment effects assumption. The upper bound of the 90% CI consistently remained ≤ 8.57 ms. This result is consistent with the previously published QTcF model, in which the non‐drug associated effect was captured via the secular trend in the exposure‐QTc model [17]. In that model, the estimated effect of M2 at 326 ng/mL M2 was 7.93 ms (90% CI: 6.84–9.26). The consistency in the estimated M2 effect size across different time‐on‐treatment effect assumptions supports the robustness of using QTcTBT for estimating the M2 effect. It suggests that a time‐on‐treatment effect may not be necessary when using QTcTBT. When QTcTBT can be calculated, we recommend starting with a base model that includes an individual random time‐on‐treatment effect without a systematic shift. If QTcTBT cannot be used and a constant correction factor, such as QTcF, is applied, incorporating a systematic shift with a time‐on‐treatment effect is important to help distinguish drug‐related changes from those due to changes in heart rate over time.

Although the typical effect of M2 and its 90% CI are not in excess of the 10 ms threshold, the IIV in the EC50 of M2 was estimated to be very high across all scenarios, indicating that M2‐induced QT prolongation can vary substantially among individuals. In particular, in MDR TB regimens where BDQ is combined with other QT‐liable drugs, regular QTc interval monitoring is recommended. Furthermore, these results highlight that failing to account for the time‐on‐treatment effects by ignoring or specifying them incorrectly can lead to bias in drug effect assessment, especially when using QTcF, a time‐independent QT correction method. For instance, in the QTcF models, the drug effect was estimated to be 11.6 ms (90% CI: 10.6–12.7) at 326 ng/mL when the time‐on‐treatment effect was not considered, leading to an overestimation compared to properly accounting for HR changes during TB treatment. Such overestimation could potentially lead to overly cautious safety assessments, affecting benefit–risk evaluations and possibly resulting in the unnecessary discontinuation of effective treatment. The QTcTBT method helps mitigate this bias by incorporating time‐on‐treatment effects directly into the correction factor, providing a more accurate and robust framework for assessing QT liability in TB patients. In clinical settings where QTcTBT is not available, ECG monitoring of QTcF at baseline and at Weeks 2, 4, 8, and 12 during 6‐month bedaquiline treatment is recommended by van Beek et al. [15]. This monitoring schedule helps balance the risk of missing QTcF prolongation above 500 ms with the risk of unnecessary treatment interruption.

Overall, this study demonstrates both the simplicity and effectiveness of using QTcTBT in model‐based exposure‐QTc analysis, compared to QTcF for evaluating the drug‐induced QT prolongation specifically, as well as its applicability to traditional non‐model‐based QTc analysis. It also demonstrates how this correction method can simplify the analysis process and produce reliable results in research settings. However, further studies in real‐world settings, such as prospective evaluation of QTcTBT's performance in decorrelating QTc and HR compared to QTc, are needed. In addition, the relationship between QT interval and arrhythmia needs to be better investigated.

Author Contributions

T.V. wrote the manuscript. M.O.K. and E.M.S. designed the research. T.V. performed the research. All authors analyzed the data.

Conflicts of Interest

A.G.D. and B.R. are employed by Janssen. All other authors declared no competing interests for this work.

Supporting information

Data S1: