Evaluation of QT Liability for PF-05251749 in the Presence of Potential Circadian Rhythm Modification.

PF-05251749 is a dual inhibitor of casein kinase 1 δ/ε, key regulators of circadian rhythm. As a result of its mechanism of action, PF-05251749 may also change the heart rate corrected QT (QTc) circadian rhythm, which may confound detection of drug-induced QTc prolongation. In this analysis, a nonlinear mixed effect model including a multioscillator function was developed in addition to fitting the prespecified linear mixed effect concentration-QTc model, to identify QTc liability of PF-05251749 in the presence of potential circadian rhythm change. The modeling results suggested lack of clinically meaningful QTc prolongation (upper bound of 90% confidence interval for ∆∆QTc < 10 milliseconds) and that the drug-induced QTc circadian rhythm change was not present. However, simulation results indicated that inference of drug-induced QTc prolongation could be misleading if the drug effect on QTc circadian rhythm is not properly addressed. The modeling and simulation results suggest that prespecification of the concentration-QTc model should be reconsidered for drugs with circadian rhythm modulation potential.

WHAT IS THE CURRENT KNOWLEDGE ON THE TOPIC?

☑ As a result of the ability for prespecification, the linear mixed effect (LME) model has been widely used for concentration‐heart rate corrected QT (CQTc) analysis. A recently published white paper also supported using a prespecified LME model for CQTc analysis. However, LME model does not have a flexibility to incorporate circadian rhythm variability for drugs with circadian rhythm modulation potential.

WHAT QUESTION DID THIS STUDY ADDRESS?

☑ The objective of this analysis was to evaluate QTc liability of PF‐05251749 in the presence of potential QTc circadian rhythm change. Model‐derived simulation followed to investigate if significant drug‐induced QTc circadian rhythm change would affect the inference of the CQTc slope estimate.

WHAT DOES THIS STUDY ADD TO OUR KNOWLEDGE?

☑ Drug‐induced QTc circadian rhythm change and drug‐induced clinically meaningful QTc prolongation for PF‐05251749 was not detected. The modeling and simulation results demonstrated that if the drug effect on QTc circadian rhythm was not properly addressed in CQTc model, inference of drug‐induced QTc prolongation could be misleading.

HOW MIGHT THIS CHANGE CLINICAL PHARMACOLOGY OR TRANSLATIONAL SCIENCE?

☑ Prespecification of the CQTc model should be reconsidered if circadian rhythm change is expected based on the pharmacology of the drug. Developing a more biologically based nonlinear mixed effect model in addition to fitting the prespecified LME model enables simultaneous evaluation of drug effect on QTc prolongation as well as physiological rhythm change for drugs with circadian rhythm modulation potential.

Circadian rhythm represents a biological process exhibiting 24‐hour cycles, which plays a critical role for the optimal functioning of organisms. Disruption of the circadian rhythm is observed in patients with Alzheimer's disease (AD) and various types of mood disorders as evidenced by sleep‐cycle alterations.1, 2, 3, 4 Therefore, entrainment of misaligned circadian behavior is a promising target for the treatment of AD or major depressive disorder.5, 6

The circadian system of the body is regulated by an endogenous biological clock located in the suprachiasmatic nucleus of the anterior hypothalamus. The suprachiasmatic nucleus ensures rhythmic expression of the clock genes period (PER1, PER2, and PER3) and cryptochrome (CRY1 and CRY2), which are ultimately translated into physiological circadian rhythm.7 Casein kinases 1 (CK1) δ/ε were shown to phosphorylate CRY and PER proteins, leading to proteasome‐mediated degradation and inhibition of circadian locomotor output cycles kaput (CLOCK)/brain, muscle Arnt‐like 1(BMAL1) transcriptional activity, acting as a negative feedback for clock genes.8 A mutation in the human CK1 δ gene has been linked to familial advanced sleep phase syndrome characterized by early sleep and early morning awakening.9 Also, CK1‐inhibiting compounds showed a remarkable period‐lengthening effect in clock cell lines.10 These findings suggest that pharmacologic manipulation of CK1 can significantly alter the circadian rhythm.

PF‐05251749 is a novel, brain‐penetrable, highly selective, dual inhibitor of CK1 δ/ε developed to treat multiple diseases related to the disrupted circadian rhythm. The inhibition of CK1 disrupts CLOCK/BMAL1 transcriptional activity, and the disruption of the BMAL1 gene was reported to induce a time‐of‐day prolongation in heart rate corrected QT (QTc) intervals during the light phase.11 As a result of this mechanism of action, PF‐05251749 may also change the QTc circadian rhythm, which may confound the detection of drug‐induced QTc prolongation. Therefore, the primary objective of this modeling analysis was to evaluate the QT prolongation risk of PF‐05251749 in the presence of potential circadian rhythm change based on recently conducted single‐ascending dose and multiple‐ascending dose phase I clinical studies of PF‐05251749.

Because the purpose of a concentration‐QTc (CQTc) analysis is to provide a valid inference of the QTc prolongation potential of a drug, prespecification of the model is preferred.12 The ability to estimate biologically relevant parameters in a model with oscillatory time functions is likely to be dependent on the study design. Therefore, a more simple linear mixed effect (LME) model with nominal time as factor variables has been used as a prespecified CQTc model. However, because the diurnal variation is described as a fixed factor effect, the LME model may not be flexible enough to account for any changes in circadian rhythms. To address the potential QTc circadian rhythm change by PF‐05251749, a nonlinear mixed effect (NLME) model with oscillatory time functions was considered in this analysis. Subsequently, the developed NLME model was used for model‐based clinical trial simulations, and the performances of LME and NLME models were compared in evaluating QTc prolongation risk of a drug with QTc circadian rhythm modulation potential.

Methods

Study design

The CQTc analysis was conducted using pooled data from studies B8001001 and B8001002. Briefly, study B8001001 was a phase I study with single escalating oral doses of PF‐05251749 and study B8001002 was a phase I study with multiple escalating doses of PF‐05251749. A summary of the study designs and pharmacokinetic‐electrocardiogram (ECG) matched time points are provided in Table  .

Both studies were placebo‐controlled studies conducted under fasted conditions (except one fed group in B8001001), and concomitant medications were not allowed. Electrocardiogram measurement procedures were the same between those studies in that triplicate 12‐lead ECGs were collected in a supine position both at baseline and during treatment (except a single ECG was measured in part B of study B8001001). The PF‐05251749 concentrations of both study data were analyzed at the same lab, Pfizer Inc (Groton, CT). Therefore, there were no specific concerns on pooling data from studies B8001001 and B8001002 to be used in the concentration‐QTc analysis. The different study conditions such as fed and single ECG measurement were evaluated as potential covariates in the covariate analysis.

Both 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.

LME model development

The following LME model was used to describe the concentration‐QTc relationship:where i indexes the ith individual, j indexes the jth measurement time, m indexes the nominal time since first dose, and QTcF is the arithmetic mean of Fridericia corrected QT (QTcF) triplicates (or single QTcF for part B of study B8001001). The intercept parameter QTcF0 represents the mean QTcF response in the absence of drug (conc = 0) at day 1 predose (baseline; time = 0); NMTM represents the mean QTc difference for other nominal times relative to nominal time 0; COV is important covariates identified in the covariate analysis; slope represents the population mean slope; conc is the observed PF‐05251749 plasma concentration around the time of the ECG collection; and (etas) represent subject‐specific random effects, which are assumed to be normally distributed with mean 0 and variance‐covariance matrix ω2 (omega); and (epsilon) represents the residual random variable with mean 0 and variance σ2 (sigma). An unstructured matrix was used for the random effects covariance matrix.

Covariate analysis was performed for sex, fed condition, study, PM dosing, and cerebrospinal fluid sampling cohort (part B of study B8001001) effect on baseline. A stepwise covariate model‐building procedure approach was employed involving both forward addition (based on a significance level of P < 0.05) and backward elimination (based on a significance level of P < 0.001).

The LME model recommended in the scientific white paper on concentration‐QTc modeling (white paper model) was also tested for the placebo‐corrected QTcF change from baseline (∆∆QTcF) estimation.12 The mathematical expression is as follows:

where is the change from baseline in QTcF, TRT is a treatment specific intercept, BASE is a fixed effect of baseline , and is overall mean of .

NLME model development

Because the LME model addresses time effect as a fixed factor, it will not be able to capture a potential drug effect on QTc circadian rhythm. Therefore, a NLME model with cosine functions was fitted to the data to describe a 24‐hour circadian variation. The following NLME model was used to describe the 24‐hour circadian variation as well as concentration‐QTc relationship: where circ is a circadian rhythm function consisting of two amplitudes ( and ) and two phases ( and ), t is a 24‐hour clock time, and COV is the selected covariates from LME model development.

The drug effect on QTc circadian rhythm was evaluated in terms of either phase delay or period lengthening with additional parameters on cosine functions. The following equations were used to describe drug‐induced QTc circadian rhythm change:

where E is a phase delay parameter and E is a period‐lengthening parameter. Bracketed expressions are indicator functions that = 1 if the condition in bracket is true and = 0 otherwise.

Simulation

To investigate the effect of drug‐induced QT circadian rhythm change on the inference of concentration‐QT slope estimate as well as QT liability, a simulation study was performed based on the selected final NLME model (model 1 in Table 2). The design of the simulated trials was identical to the CQTc analysis data set for PF‐05251749, including pharmacokinetic concentrations. QTcF data were simulated under the following four different scenarios: (i) clinically meaningful QT prolongation (slope = 0.00242 milliseconds/ng/mL, such that the predicted mean ∆∆QTc at steady‐state maximum concentration (Cmax) of supratherapeutic dose ≥ 10 milliseconds) in the presence of concentration‐dependent phase delay (no delay and maximum 1, 2, 3, 4, and 5 hours of delay) in a QT circadian rhythm, (ii) clinically meaningful QT prolongation in the presence of concentration‐dependent period lengthening (no lengthening and maximum 1.1‐fold, 1.2‐fold, 1.3‐fold, 1.4‐fold, and 1.5‐fold lengthening) in a QT circadian rhythm, (iii) no QT prolongation (slope = 0) in the presence of a phase delay in a QT circadian rhythm, and (iv) no QT prolongation in the presence of period lengthening in a QT circadian rhythm. For concentration‐dependent circadian rhythm change, the maximum effect (Emax)‐half maximal effective concentration (EC50) function was used with EC50 of 50 ng/mL such that the maximum QTc rhythm change is achieved at a very low concentration within the observed range. A total of 1,000 data sets were simulated for each scenario, and then both the LME (Eq. 1) and NLME models (true model) were fitted to investigate the performance of each model for detecting QTc prolongation in the presence of QTc circadian rhythm change.

Table 2

Parameter estimate of the developed nonlinear mixed effect models

Parameter	Model 1 (RSEa, %)	Model 2 (RSEa, %)	Model 3 (RSEa, %)	Model 4 (RSEa, %)	Model 5 (RSEa, %)
QTcF0, millisecond	410 (0.686)	410 (0.688)	410 (0.689)	410 (0.687)	411 (0.687)
SEXF, millisecond	16.5 (26.8)	16.6 (26.6)	16.5 (26.7)	16.6 (26.7)	16.5 (26.8)
A1	0.00732 (17.5)	0.00573 (23.8)	0.00625 (27.5)	0.00706 (16.1)	0.00749 (18.3)
ϕ1, hour	25.1 (1.96)	23.9 (4.21)	24.9 (2.46)	26.1 (2.07)	25.1 (1.93)
A2	0.00899 (7.48)	0.00874 (7.10)	0.00885 (7.40)	0.00906 (7.07)	0.00901 (7.55)
ϕ2, hour	12.9 (1.66)	11.7 (6.31)	12.6 (3.08)	13.7 (2.34)	12.9 (2.15)
σ, millisecond	6.79 (1.52)	6.78 (1.52)	−6.78 (1.52)	6.77 (1.52)	6.79 (1.52)
P1002, millisecond	−17.7 (18.5)	−17.9 (18.3)	−17.7 (18.4)	−17.7 (18.5)	−17.7 (18.5)
Slope, millisecond/ng/mL	0.00121 (28.4)	0.00117 (29.5)	0.00126 (27.2)	0.00114 (30.2)	0.00119 (29.6)
ED1, hour	—	1.09 (66.3)	—	—	—
ED2, hour/ng/mL	—	—	0.000188 (101)	—	—
EL1	—	—	—	−0.0724 (31.6)	—
EL2	—	—	—	—	−0.00000406 (300)
ωint	0.0382 (13.2)	0.0382 (13.2)	0.0381 (13.2)	0.0383 (13.1)	0.0382 (13.2)
ωslope, millisecond	0.00178 (35.7)	0.00180 (35.6)	0.00180 (35.8)	0.00178 (35.3)	0.00177 (35.7)
OFV	11,964.43	11,963.83	11,963.41	11,956.59	11,964.33

A1 and A2, amplitude 1 and 2 in the circadian rhythm function; ED, a phase delay parameter; EL, a period lengthening parameter; OFV, objective function value; P1002, mean baseline QTcF difference for Study B8001002 relative to Study B8001001; QTcF0, mean QTcF response in the absence of drug and covariate effects at Day 1 predose (baseline; time=0); RSE, relative standard error; SEXF, mean baseline QTcF difference for females relative to males; ϕ1 and ϕ2, phase 1 and 2 in the circadian rhythm function; σ, residual random variability; ωint, intersubject variability for baseline QTcF; ωslope, intersubject variability for slope.

RSE values for intersubject variability terms (ωint and ωslope) were calculated based on the variance.

For the drug‐induced QT prolongation case, bias in slope estimate and the false‐negative rate in detecting QTc liability were used to evaluate model performance. The bias in slope estimate was calculated with an estimation error as follows:

The false‐negative rate in detecting QT liability was calculated based on the upper bound of the 90% confidence interval (CI) of the ∆∆QTcF estimate:

where I is an indicator function that = 1 if the condition in bracket is true and = 0 otherwise.

For no QT prolongation case, model performance was evaluated with a false‐positive slope rate (lower bound of 95% CI for slope > 0) and a false‐positive study rate for QTc liability (upper bound of 90% CI for ∆∆QTcF at supratherapeutic dose ≥ 10 milliseconds).

Results

LME model results

Key assumptions about the relationship between concentration and QTc interval were graphically evaluated first as recommended in the scientific white paper on concentration‐QTc modeling.12 The exploratory plots are provided in Figure  . The exploratory plots suggested that (i) drug effect on heart rate is not significant, (ii) QTcF is independent of heart rate, (iii) lack of hysteresis between drug concentrations and ∆QTcF, and (iv) a linear concentration‐QTcF relationship is a reasonable assumption. Therefore, QTcF was selected as a sufficient correction method, and the LME model was used for CQTc model development.

Parameter estimates and visual predictive check of the final LME model are summarized in Table 1 and Figure  , respectively. Covariate analysis identified gender and study as important covariates on intercept, so those effects were included in the final model. Females tend to have 16.5 milliseconds higher baseline than males as expected,13 and study B8001002 subjects tended to have 19.9 milliseconds lower baseline than study B8001001 subjects. The slope estimate was positive and statistically significant, but the magnitude was small, indicating a 1.36‐millisecond increase in QTcF per 1,000 ng/mL increase in PF‐05251749 concentration.

Table 1

Parameter estimate of the final linear mixed effect model

Parameter	Estimate	RSE, %a
QTcF0 (millisecond)	410	0.671
Slope (millisecond/ng/mL)	0.00136	26.0
NMTM0.5 (millisecond)	−2.60	29.7
NMTM1.5 (millisecond)	−0.601	129
NMTM2.5 (millisecond)	−1.73	56.4
NMTM3 (millisecond)	2.91	32.3
NMTM4 (millisecond)	1.05	91.6
NMTM5 (millisecond)	7.16	13.0
NMTM8 (millisecond)	−3.53	26.8
NMTM12 (millisecond)	−1.68	57.7
NMTM24 (millisecond)	−0.643	115
NMTM48 (millisecond)	−6.28	17.7
NMTM73.5 (millisecond)	0.263	379
NMTM144 (millisecond)	−0.497	192
NMTM144.5 (millisecond)	−2.24	44.0
NMTM145.5 (millisecond)	1.41	70.6
NMTM147 (millisecond)	4.32	22.6
NMTM149 (millisecond)	5.30	18.2
NMTM168 (millisecond)	−0.581	165
NMTM217.5 (millisecond)	3.14	31.8
NMTM312 (millisecond)	−1.37	70.5
NMTM312.5 (millisecond)	−1.44	69.4
NMTM313.5 (millisecond)	1.39	72.7
NMTM315 (millisecond)	4.10	24.2
NMTM317 (millisecond)	5.44	17.9
NMTM336 (millisecond)	−0.877	110
NMTM369 (millisecond)	−0.149	648
P1002 (millisecond)	−19.9	16.2
SEXF (millisecond)	16.5	26.1
σ (millisecond)	6.61	1.53
ωint (millisecond)	15.0	13.1
ωslope (millisecond)	0.00169	35.5

NMTMm, mean QTcF difference for other nominal times relative to nominal time 0; P1002, mean baseline QTcF difference for Study B8001002 relative to Study B8001001; QTcF0, mean QTcF response in the absence of drug and covariate effects at Day 1 predose (baseline; time=0); RSE, relative standard error; SEXF, mean baseline QTcF difference for females relative to males; σ, residual random variability; ωint, intersubject variability for baseline QTcF; ωslope, intersubject variability for slope.

RSE values for intersubject variability terms (ωint and ωslope) were calculated based on the variance.

NLME model results

Parameter estimates of the NLME models and the final model visual predictive check are summarized in Table 2 and Figure  , respectively. One and two cosine functions were tried for placebo data, and two cosine functions described the data better, with an objective function value (OFV) drop of 28.77 points (degrees of freedom = 2). Therefore, two cosine functions were used to describe the circadian rhythm for THE NLME models. All parameters were precisely estimated with small relative standard error, except the circadian rhythm change parameters (E D or E L). Circadian rhythm change parameters from models 2–5 were not statistically significant, nor did they induce a significant OFV reduction (at a significance level of P < 0.001) when compared with model 1, indicating that the presence of drug‐induced QT circadian rhythm change was not supported in the current study data. Therefore, the selected final NLME model was model 1. Estimates of the baseline‐related parameters (QTcF0, mean baseline QTcF difference for females relative to males (SEXF), and mean baseline QTcF difference for Study B8001002 relative to Study B8001001 (P1002) in Table 2) were similar to the estimates from the LME model (Table 1). The statistically significant positive slope from the NLME model was also similar to the LME model slope estimate. The parameter estimate indicated an 1.21‐millisecond increase in QTcF per 1,000 ng/mL increase in PF‐05251749 concentration.

∆∆QTcF prediction

The developed LME and NLME models as well as the prespecified white paper model were used to produce predictions of ∆∆QTcF. As summarized in Figure 1, the ∆∆QTcF prediction results were similar across the three different models. All of the models indicated that the upper bound of 90% CI for ∆∆QTcF was less than 10 milliseconds at steady‐state Cmax of both the therapeutic and supratherapeutic doses. Therefore, the QT prolongation of a regulatory threshold is unlikely at the expected PF‐05251749 therapeutic exposure.

Figure 1

Model‐derived ∆∆QTcF vs. PF‐05251749 concentration plot across different types of models. Blue line and shaded regions represent mean prediction and 90% confidence intervals (CIs), red arrow is upper bound of 90% CI at mean steady‐state maximum concentration (Cmax) for lowest therapeutic dose (50 mg), purple dashed arrow is for highest therapeutic dose (400 mg), and green dotted arrow is for supratherapeutic dose (750 mg). LME, linear mixed effect; NLME, nonlinear mixed effect; QTcF, Fridericia corrected QT interval; ∆∆QTcF, placebo‐corrected QTcF change from baseline.

Model‐derived clinical trial simulation

Detectable drug‐induced QTc circadian rhythm change was not observed in the analysis data set. However, the following key question remains: If there were detectable drug‐induced QTc circadian rhythm changes, would they affect the inference of CQTc slope estimate? To investigate this question, a simulation study was performed using the final NLME model. Figure 2 shows the fitted QTc circadian rhythm (red line) as well as the QTc rhythm change scenarios for phase delay and period lengthening.

Figure 2

Two scenarios of drug‐induced QTcF circadian rhythm change. hr, hour; QTcF, Fridericia corrected QT interval.

QTc prolongation case in the presence of QTc circadian rhythm change

Estimation errors of the CQTc slope for phase delay scenarios are summarized in Figure 3. For the LME model that incorporates the nominal time effect as a fixed factor, bias in the slope estimate was dependent on the differing degrees of phase delay. The slope estimates were negatively biased in the presence of a maximum 1–3 hours delay (−11.5 to −6.13% difference compared with true slope), whereas they were positively biased in the presence of a maximum 5 hours delay (17.6% difference). When the drug effect on the QTc circadian rhythm was properly captured using the NLME model, the bias in the slope estimate was not significant with <1% difference across different degrees of phase delay. Precision of the slope estimate (standard error) was similar between the LME and NLME models (data not shown).

Figure 3

Box and whisker plots of the estimation errors for slope parameters in both LME and NLME models across different phase‐ delay scenarios. Boxes denote the 25th and 75th percentiles, and the closed circles denote the median. Whiskers represent the 5th and 95th percentiles. hr, hour; LME, linear mixed effect; NLME, nonlinear mixed effect.

Figure 4 summarizes the estimation errors for the period‐lengthening scenario. The overall interpretation of the results was similar to the phase‐delay scenario; bias in the slope estimate was dependent on the degrees of period lengthening for the LME model, whereas it was consistently small with a <2.71% difference for the NLME model across different degrees of period lengthening. Bias of the LME model was worse than the phase‐delay case, with −38.1 to −27.2% difference in the presence of a maximum 1.1‐fold to 1.3‐fold period lengthening. The negative bias was reduced in the presence of a maximum 1.5‐fold period lengthening (−5.68% difference). Precision of the slope estimate (standard error) was similar between the LME and NLME models (data not shown).

Figure 4

Box and whisker plots of the estimation errors for slope parameters in both LME and NLME models across different period lengthening scenarios. Boxes denote the 25th and 75th percentiles and the closed circles denote the median. Whiskers represent the 5th and 95th percentiles. LME, linear mixed effect; NLME, nonlinear mixed effect.

Model performance for the LME and NLME models was further evaluated by assessing the false‐negative rate in detecting QTc liability when the underlying true signal was positive. The results for both phase delay and period lengthening are summarized in Figure 5. As expected from the bias observed in the slope investigation, the false‐negative rate for the LME model was dependent on the degrees of phase delay and period lengthening: as high as 13.3% for the phase‐delay scenario and as high as 70.0% for the period‐lengthening scenario. On the other hand, the false‐negative rate for the NLME model was consistently small across different scenarios of circadian rhythm change, with < 2.71% for phase delay and < 6.33% for period lengthening.

Figure 5

False‐negative study rate for clinically meaningful QT prolongation case (upper bound of 90% confidence interval for ∆∆QTcF ≥ 10 milliseconds) in both LME and NLME models across different scenarios of QTcF circadian rhythm change. hr, hour; LME, linear mixed effect; NLME, nonlinear mixed effect; QTcF, Fridericia corrected QT interval; ∆∆QTcF, placebo‐corrected QTcF change from baseline.

No QTc prolongation case in the presence of QTc circadian rhythm change

When the underlying truth was no QTc prolongation (true slope = 0), model performance was summarized assessing false‐positive slope rates as shown in Figure 6. Consistent with the generally negative bias in slope estimates seen in Figures 3 and 4, the false‐positive slope rate for the LME model was generally small for most of the QTc circadian rhythm change scenarios except that the rate was relatively high in the presence of a 5‐hour phase delay (11.7%). For the NLME model, the false‐positive slope rate was consistently small, with 2.90–3.81% for the phase‐delay scenario and 2.77–4.63% for the period‐lengthening scenario. Even with the false‐positive slope, the magnitude of the slope was small such that the false‐positive rate for QTc liability was zero across all of the circadian rhythm change scenarios.

Figure 6

False‐positive slope rate for no QT prolongation case in both LME and NLME models across different scenarios of QTcF circadian rhythm change. hr, hour; LME, linear mixed effect; NLME, nonlinear mixed effect; QTcF, Fridericia corrected QT interval.

Discussion

Circadian variations in QT intervals have been previously characterized by a cosine14, 15 or a multioscillator function including ≥2 cosine functions.16, 17 In the present study, a potential PF‐05251749 effect on QTc circadian rhythm change was evaluated simultaneously with QTc prolongation using the NLME model based on a multioscillator function. Two cosine functions best described the placebo data in this analysis, and the circadian parameter estimates (Table 2) were similar to the previously reported QTc circadian parameters based on two cosine functions.16 Also, the fitted shape of the placebo QTc circadian rhythm (red line in Figure 2) was similar to the previously reported QTc circadian pattern, with a large drop from midnight to 9 am, a large increase from 4 pm to midnight, and relatively flat between 9 am and 4 pm.18 When evaluated with the proposed NLME model, the QTc rhythm change parameters were not supported in the data set. Both LME and NLME model results indicated that a 10‐millisecond placebo‐adjusted change from baseline, which is a regulatory threshold, can be excluded. The upper bound of the two‐sided 90% CI for ∆∆QTcF at the steady‐state mean Cmax of the supratherapeutic dose was 8.28 milliseconds for the LME model and 7.64 milliseconds for the NLME model.

The hypothesized drug‐induced QTc circadian rhythm change for PF‐05251749 was not detected in the current study data set. The PF‐05251749 effect on a physiological circadian rhythm was previously evaluated using clock gene data from a phase I multiple‐ascending dose study. When daily leukocyte messenger RNA levels of multiple periodic genes were investigated, the genes showed dose‐dependent phase delays by day 7, with the largest drug effect on the PER3 gene of a mean 9.2 hours (am dosing) and 19.9 hours (pm dosing) delay at the top dose.19 The gold standard circadian rhythm biomarker, dim light melatonin onset (DLMO), also showed a maximum phase delay of 2.1 hours (am dosing) and 2.3 hours (pm dosing) by day 15.20 The discrepancy between DLMO and the PER3 gene phase shift is the result of the censoring of the DLMO end point limited by the study design. Based on these findings, the drug‐induced phase delays on the QTc circadian rhythm were tested only at the steady state (day ≥ 7) for NLME models 2 and 3, but a circadian rhythm change parameter was still not supported, with a very large relative standard error and insignificant OFV drop. Undetectable QTc circadian rhythm change may be attributed to limited information coming from sparse steady‐state ECG sampling times in this study (0, 0.5, 1.5, 3, 5, and 24 hours on days 7 and 14). As a result, within the current study setting, acute QTc circadian rhythm change was not detected.

The CQTc modeling methodology has been extensively studied in recent decades, and the International Conference on Harmonization (ICH) “E14 Questions & Answers (R3)” document was revised to accept CQTc modeling as a primary analysis to evaluate the QT prolongation risk of new drugs.21 A recently published white paper proposed a prespecified LME model for CQTc analysis, such that if basic assumptions are met in the exploratory graphical checks, the proposed LME model can be used.12 In the present analysis, an LME model based on QTcF was used, which is different from the white paper model using ∆QTcF as a dependent variable. By using an LME model based on QTcF, the slope parameter can be comparable with the NLME model slope, and ∆∆QTcF estimates can be easily calculated from the slope estimate. Because the model used nonbaseline corrected value (QTcF) as a dependent variable, more covariates than in the white paper model were included in the intercept to describe the baseline characteristics. Other than that, the basic model structure was analogous to the white paper model. The performance of the white paper model was also investigated, and as expected from the similar model structure, the ∆∆QTcF estimates for PF‐05251749 were similar to the QTcF‐based LME model (Figure 1). The simulation results for bias in the slope estimate under the circadian rhythm modification scenarios were almost identical to the QTcF‐based LME model (results not shown).

However, fitting the prespecified LME model without taking the drug pharmacology into account could lead to a misinterpretation of the QT liability as seen in the simulation results, especially for a drug with circadian rhythm modification potential. The LME model is commonly used to quantify the concentration‐QTc relationship of a drug, but it handles circadian rhythm with a fixed factor effect of nominal time and may not capture the effects of variation within the rhythmicity. When the LME model was fitted to the CQTc data set including circadian rhythm changes, the estimated CQTc slope was either positively or negatively biased depending on the degree of circadian rhythm change. This bias in slope could induce significantly high type I or type II errors. These potential errors were highlighted in the drug‐induced QTc circadian rhythm change scenarios (1–5 hours of phase delay or 1.1–1.5 fold of period lengthening), and the false‐negative QT liability rate was as high as 70% for period lengthening case. An interaction term between nominal time and dose was also tested within the LME model to investigate if it could account for the drug‐induced circadian rhythm change. However, those LME model runs were terminated because of a singularity error, most likely a result of the large number of parameters to be estimated (number of time points × number of doses). On the other hand, the proposed NLME model was able to simultaneously address both circadian rhythm change and QTc prolongation with one or two additional parameters and assuming a functional form of the circadian rhythm.

Normal QTc circadian rhythm can be disrupted via drug‐associated changes22 or disease status.19 Delaying the circadian rhythm by temporarily lengthening the period has been reported for an inhibitor of CK1 enzymes.23, 24 In the current simulation analysis, one‐directional circadian rhythm change scenarios, either drug‐induced phase delay or drug‐induced period lengthening, were tested to simplify the simulation scheme (Figure 2). The phase‐delay scenario was fitted with an additive effect to the phase parameter (ϕ), and ≥ 98.7% convergence rate was achieved with the first‐order conditional estimation with interaction method. The period‐lengthening scenario was able to be described by a multiplicative effect on both phase and period parameters, but the first‐order conditional estimation with interaction method had numerical difficulties, and therefore the stochastic approximation expectation maximization method was used. With the stochastic approximation expectation maximization run, the convergence rates were still low (64.3–99.9%) compared with phase‐delay scenarios. Because a robust inference was the main interest and prespecification of the model is desired for CQTc analysis, modifying the NLME model for a higher convergence rate was not considered. However, it should be noted that when significant period lengthening is expected, standardization of the NLME model could be even more challenging, and a data‐driven model development approach would need to be considered.

The are several limitations of this modeling and simulation. First, day −1 baseline ECGs are not available, which could limit detection of circadian rhythm change in the QTc intervals. However, day −1 baseline is not typically acquired in early phase I studies, and placebo data can be used for QTc circadian rhythm detection.12, 25 In addition, the simulation study showed that the NLME model produced acceptable results in the absence of day −1 baseline (Figures 3 and 4). Second, direct drug effects on both circadian rhythm and QTc prolongation were assumed, but the time delay between drug exposure and QTc circadian rhythm change may also happen. Third, sensitivities of the simulation results to different parameter sets such as EC50 have not been fully evaluated. Fourth, the simulation comparison was one‐sided, i.e., simulation was performed based on the NLME model, and the performance of the prespecified LME model was compared with the true model. Fifth, only two different, one‐directional ways of QTc circadian rhythm change were assessed, either phase delay or period lengthening. However, changes in circadian rhythm could be multidirectional, such as phase delay along with amplitude increase.26 The current study suggested two simple mathematical ways to describe the possible QTc circadian rhythm change, but as more data are gathered with drugs that have the potential to modulate circadian rhythm, the appropriate functional form of rhythmical changes in the QTc interval should be reevaluated.

In conclusion, prespecification of the CQTc model should be reconsidered if circadian rhythm change is expected based on the pharmacology of the drug. Misspecification of the rhythmic change could induce significant type I and type II errors in detecting QT prolongation risk. Developing a more biologically based NLME model in addition to fitting the prespecified LME model enables simultaneous evaluation of drug effect on QTc prolongation as well as circadian rhythm modulation.

Funding

Pfizer Inc. provided funding support for this research.

Conflicts of Interest

Y.H., D.C., S.R., C.C., and T.N. are employees and shareholders of Pfizer Inc.

Author Contributions

Y.H., D.C., S.R., C.C., and T.N. wrote the manuscript. Y.H. and T.N. designed the research. Y.H. performed the research. Y.H. analyzed the data.

Table S1.

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Figure S1A.

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Figure S1B.

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Figure S1C.

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Figure S1D.

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Figure S2.

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Figure S3.

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Model code 1.

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Model code 2.

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Data set 1.

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Data set 2.

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Data 1. Simulation for phase delay.

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Data 2. Simulation for period lengthening.

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