Transcript poster - go

ROLE OF MODELING AND SIMULATION IN EVALUATING THE QTc PROLONGATION POTENTIAL OF DRUGS
Shashank Rohatagi, S. Song, N. Sarapa, Daiichi Sankyo Pharma Development, Edison, NJ;
T. Khariton, T. Carrothers, J. Kuwabara-Wagg, H. Kastrissios, Pharsight Corporation, Mountain View, CA.
Today, the Fridericia method is thought to be superior to the Bazett.[1] However, their common flaw is
assuming the same correction for all individuals, which ignores the inter-patient variability in the HR-QT
relationship. Under the “individual-correction” method, the exponent is estimated on an individual basis,

QT  QTc  RR
given an adequate number and quality of measurements.
Following HR correction, the steps taken in modeling corrected QT interval values (QTc) were as follows:
(Note: Data analysis was based on non-linear mixed-effects modeling and typically conducted in NONMEM 5
™ for PK and S-PLUS 6.2 ™ for PD):
1. Build population PK model and obtain predicted drug concentrations for the QT observation times.
2. Build base PD model
•
Fit nonlinear mixed-effect model to baseline data, with only time of the day as a covariate. This effect
of diurnal variation was usually represented in a truncated Fourier series as follows:
 2  t  1  
 2  t  2  
 2  t  3  
f (t )  A1 cos 
  A2 cos 
  A3 cos 

24
12
6






where t represents time of the day, and parameters Ai and i are amplitude and acrophase parameters
for periods of 24, 12 and 6 hours, to the extent required. The baseline model was then as follows:
QTc(base)  0  f t   
•
Add active treatment data and estimate placebo and active treatment effects. Fit nonlinear mixedeffect model to all the data by adding a drug effect, f(Cp), a function of the individually predicted
drug concentrations.
QTc  0  f t   f (Cp)  
Provided that concentration is associated with prolongation of QT-interval, the functional form of the
drug effect term is dependent on the data, with the two most common terms being linear (left) or
sigmoid Emax (right). In our experience, the linear model was usually more appropriate.

max
1


50
As part of each of the above steps, demographic covariates were tested to determine their significance
on baseline and concentration-effect. For covariate inclusion-exclusion, a stepwise forward addition
(α = 0.05), backward elimination (α = 0.01) process was used, based on -2*log-likelihood.
f Cp     Cp
•
•
E * Cp
f  Cp  
EC  Cp
Determination of the error structure is an important aspect of model building. It was assumed that the
residual error, e, is normally distributed. Baseline (β0) and drug effect (β1) are the random effects.
When the study had a cross-over design, it was assumed both random effects have a more complex
nested structure, with the first level measuring variation among periods within an individual and the
second level measuring variation between individuals.
The structural model for QTc was kept similar to the one described in Methods – Modeling Steps section
Conclusions: There was no evidence of potential for QTc prolongation.
1000
1200
46 0
44 0
44 0
QTcF
38 0
40 0
42 0
42 0
800
1000
1200
Bazett
Fridericia
420
400
360
380
400
QTcF
420
440
RR
440
RR
1400
36 0
36 0
1400
Slope
vs.1400
Cp relationship
with
CI
1000 for QTc
1200
800
1000 95%1200
800
40 0
38 0
QTcF
440
380
400
420
Figure 3. Comparison of correction
methods using baseline data. Points
represent all individual measurements,
lines are the smoothed fit showing an
overall trend. In this particular case,
neither Bazett nor Fridericia provided an
adequate correction. As a result, a linear
mixed-effects model was constructed to
obtain the most appropriate power for
each individual’s QT correction (S-PLUS
function lme was employed).
360
360
380
400
QTpred
420
440
Indiv. Correction
6
8
10
12
14
16
0
18
500
1000
1500
2000
2500
3000
C onc C S-917 (ng/mL)
Time of the day at bas eline (h)
Figure 8. QTcF seems to show a slight diurnal pattern at baseline but does not seem to show any
significant relationship with predicted drug concentration
Case 7 – Anti-platelet Agent
AP1 is a novel antiplatelet agent.
1400
RR
QTcB
2.0
Objectives of the Analysis: Quantitatively evaluate whether AP1 exposure results in QTc prolongation in
healthy volunteers.
Figure4. Slope characterizing QT and
FQ2 exposure relationship with 95%
CI for different QT correction methods
2.00
1.81
Model Development:
Fridericia’s correction proved good enough to correct for heart rate. The structural model was described by the
following set of equations:
AP1
1.69
1.5
10
12
14
Simulation of QTc Prolongation: The final popPK and QTc models were used to simulate likely QTc interval
prolongation as a function of FQ1 dose, day, infusion duration, and subject covariates. For each such
combination, a distribution of Cmax values was computed. For each Cmax value, the final QTc model was used
to calculate a corresponding ΔΔQTcF (equivalent to the maximum ΔΔQTcF value because FQ1 Cmax values
were used). The mean maximum ΔΔQTcF value and the corresponding 90% confidence bound (the upper
bound corresponding to a 95% one-sided confidence interval) were then computed. Simulations were
completed assuming a single individual or a study population comprised of 16 or 60 individuals.
Simulations of maximum ΔΔQTcF values based on populations consisting of 60 individuals were then used to
predict the likely QTc outcome for studies based on the FQ1 dosing regimens of interest. QTc outcomes were
classified as per the FQ1 QTc Outcome Criteria outlined above.
Conclusions: The final QTc model suggested that QTc prolongation increases with Cmax (proportional to
dose) in an approximately linear fashion over a dose range of 200 mg IV QD to 2000 mg IV QD. The
presence of a term for day in the model may represent the effect of a metabolite. Prolongation effects were
predicted to be negligible at doses of 200 mg IV QD. A modest effect was predicted for doses of 400 mg IV
QD such that an E-R model predicted an acceptable QTc study outcome for 400 mg IV QD doses with
infusion durations of 1 hour or longer irrespective of the dosing duration. A comparable outcome was
predicted for 600 mg IV QD provided the infusion duration was 2 hours or greater and the dosing duration did
not exceed 7 days. All simulated 800 mg dosing regimens were predicted to result in “Ambiguous” QTc
outcomes, while all higher doses and associated regimens were predicted to result in an “Unacceptable” QTc
outcome.
Case 2 – Pre-clinical to Clinical
Fluoroquinolone #2 (FQ2) is a broad-spectrum fluoroquinolone with demonstrated activity against a wide
array of medically important Gram positive and Gram negative bacteria.
Data: Two pharmacokinetic studies of oral and IV FQ2 administrations in cynomolgus monkeys; 3 monkeys
following a single IV dose and 3 monkeys following single oral FQ2 administration. QT study in 4
cynomolgus monkeys administered a single IV dose of FQ1 and QT study in 4 cynomolgus monkeys
administered a single IV dose of FQ2.
Objective of the Analysis: Characterize the magnitude of QTc prolongation by FQ2 in humans based on
preclinical data from FQ1 and FQ2 and clinical data from FQ1.
Model Development: Analysis of FQ1 monkey and human QTc prolongation and exposures was used to derive
a potency scaling factor for predicting human QTc prolongation from monkey data. Major assumptions: the
magnitude of effect on QTcB is the same as on QTcF; FQ2 does not have an active metabolite as was
postulated for FQ1, and therefore the day of the study has no effect on QTcF magnitude; baseline QTcF value
of 400 msec.
1) Derive FQ2 pharmacokinetic model for monkey data
2) Derive a potency scaling factor for FQ1 based on monkey and human QTc prolongation and exposures
3) Based on FQ2 monkey PK and potency and QTc scaling for FQ1, adjust the slope of FQ1 and QTc
relationship accordingly. Assume that FQ2 does not have an active metabolite.
Simulations: The FQ2 popPK model was used to simulate PK profiles for an average 70 kg man. PK
parameters for humans and monkey were assumed to have comparable uncertainty. This uncertainty was
included in the PK simulations. The PK model was linked to the final FQ2 QTc model by simulated Cmax
exposures. For generated concentration profiles, maximum ΔΔQTcF effect was simulated.
Results: Doses and regimens for FQ2 were classified according to the schema used previously for FQ1 in
Case 1. Regions where QTc prolongation would be expected to be dose-limiting were identified prior to any
actual ECGs data for FQ2 in clinical trials.
Epilogue: After FIM SAD trial was analyzed for FQ2, modeling projections were compared to the E-R model
from FIM results. The scaling-based point estimate of 2.5 [msec/(mg/L)] was within 33% of the FIM
estimate of 1.7 [90% CI: (1, 2.4)].
440
460
420
8
A c tiv e treatment group
Baseline measurements
600
800
No Correction
1000
1200
1400
Indiv. Correction
440
360
6
P l ac ebo group
40
420
400
340
4
Conclusions: One-sided 95% CI would exceed 10 msec at the higher end of the dose range tested; however,
this is several-fold higher than the expected therapeutically active dose.
QTc QTCf
(msec)
2
The placebo effect component had a statistically significant impact on the overall fit and varied as time
passed. Based on the final QTc model, at the maximum observed plasma concentration the QTc prolongation
was 20 msec at the highest dose.
AD1 is a anti-diabetic compound.
Data: Two Phase I and two Phase II studies that comprised the dataset for the existing population PK model
were used to develop the E-R model for the QTc effect of AD1. The E-R analysis was dominated by a single
Phase I study which had serial triplicate ECGs taken during periods with substantial drug concentrations while
the other three studies had ECG measurements taken ≥48 hrs post-dose.
Objectives of the Analysis: Characterize the magnitude of QTc prolongation, if any, and provide guidance for
dose selection as required by the results of the E-R study.
Model Development and Results:
1) Fridericia’s correction did not prove adequate to correct for heart rate, thus an individual correction factor
(α=0.24 on the average) was derived based on a mixed-effects linear model (see Figure 5).
2) Error structure was structured to take into account crossover study design.
3) Time-of-day effects on baseline were modeled via a truncated Fourier series .
4) The central estimate of the slope was negative (Figure 6) and well-characterized, indicating no concern for
QT prolongation with this compound.
440
-50
  6  Conc
420
0
AP1
400
50
Case 4 – Agreement with TQT
Eff
380
15
360
10
 2  t   3  
Base  Q1  QTcbase   6  

12


PCB   4   5  log TreatmentDay 
QTCf
QTc (msec)
5
Figure 2. Smoothing plots
showing
the
relationship
between FQ1 concentrations
and day of the study and
ΔΔQTcF (baseline and placebo
adjusted based on baseline and
placebo fit)

QTc  Base  PCB  Eff
1.0
0
400
50
QTcF
380
2.5
QTc
20
380
360
delta QTc [msec]
RR
Model Development:
Data: Data from one Phase I study conducted in healthy volunteers was used to conduct the analyses.
Day of the study
3
800
100
100
QT
QTcF 

 CONC *CONC  DAY *log  DAY 
Predicted Cp (mg/L)
Figure1. Schematic representation
of normal ECG trace.

RR
0
Appropriate correction of QT interval for changes in HR is an essential element of the evaluation of druginduced QT prolongation, and the first step in E-R modeling. Since the 1920s, researchers have attempted to
find a formula that would make the corrected QT interval independent of HR.
Most of the investigators today use either the Bazett (QTcB) or the Fridericia (QTcF) correction[1]:
RR
FQ1
-50
Methods
QT
QTcB 
Eff
delta-delta QTcF (msec)
Figure 1 shows the interval typically measured on an ECG. QT
interval is a measure of the time between the start of the Q-wave and
the end of the T wave in the heart's electrical cycle and represents the
time required for both ventricular depolarization and repolarization to
occur, and therefore it roughly estimates the duration of an average
ventricular action potential. This interval can range from 0.2 to 0.5
seconds, depending upon heart rate.
The QT interval obviously shortens with a shorter RR interval
(equivalently, a faster heart rate), thus RR interval is one of the main
sources of QT variability.
Other sources of variability affecting QT include the following:
genetic differences, food intake (increases of 16-23 msec have been
observed during the hour following a meal), circadian rhythm, sex
(females tend to have 8-10 msec longer intervals than males at
baseline), obesity (more than 5 msec increase per 10 kg increase in fat
mass), physical activity, electrolyte disturbances, blood glucose level,
blood pressure, alcoholism, age, and presence of U-wave.[1]
QTcF  Base  PCB  Eff

No Correction
3) The effect of FQ1 (see Figure 2) was statistically significant and could be modeled best by a simple linear
function. Day of the study had a significant impact on the active treatment as well and was modeled as an
additive component. Weight, age, sex, race and time of the day did not have a statistically significant impact
on placebo or on drug effect. The final form of the model was an additive combination of baseline, placebo,
active treatment and residual variability (ε) components.
FQ1
Objectives of the Analysis: Develop E-R models to predict effects on QTc interval of MB2 plasma
concentration (Cp).

Where ή0(ID) and ή0(PERIOD in ID) are normally distributed first and second-level random effects attributed to
random variation in ID and among periods within each individual respectively.
Conclusions: Modeling QTcF and QTcB values (as opposed to individually corrected QTc) leads to a
seemingly more precise estimate of the slope, but the QTcF and QTcB estimates are biased upwards. Thus,
using QTcF or QTcB instead of individual correction would lead to an overestimation of prolongation and, as
a result, unnecessary restrictions on dose selection.
340
320
Bazett
Fridericia
440
-20
0
400
-60
340
0
1000
1200
1400
50
100
150
200
Figure 6. Negative slope indicates no QTc prolongation
Comparison to Completed TQT: A thorough QT study was completed after the studies used to build the PK
and E-R models. The TQT study was negative, indicating agreement with the E-R model.
Case 5 – Anti-coagulant
FXa1 is a direct Factor Xa inhibitor (FXa).
Data: Data from seven Phase I and one Phase IIa study, consisting of 307 healthy volunteers (276 males, 31
females) and 603 surgical patients (253 males, 350 females).
Objectives of the Analysis: Evaluate whether FXa1 exposure results in clinically significant QTc prolongation
in healthy volunteers and surgical patients.
Model Development:
1) Fridericia’s correction proved adequate for correcting QT for heart rate
2) The structural model for QTc was kept similar to the one described in Methods section
Conclusions: Based on the final QTc model, at the maximum observed plasma concentration the QTc
prolongation was 2.5 msec. This observation was in a healthy volunteer, and it corresponds to a steady-state
BID dose three-fold higher than the expected therapeutic dose. Thus, the results of this analysis show that
FXa1 exposure does not significantly prolong QTc interval neither in healthy volunteers nor in surgical
patients.
Figure 7. Smoothing plot showing the
relationship between FXa1 plasma
concentrations and baseline
and placebo adjusted QTc (ΔΔQTc).
Red line is a smooth. Dashed lines
represent ΔΔQTc of 5 msec and 20
msec, respectively.
0
2
4
Predicted log Conc (ng/mL)
6
0
20
40
60
80
100
Time s i nc e medi c ati on (hr)
Pooling of QTc data from multiple studies may increase the power and improve the
predictivity of the QTc risk assessment (either at one stage of development or in the NDA).
•
Conclusions from a compound’s exposure-response model established from the pooled Phases
I/II data aligned with conclusions from a completed “negative” thorough-QTc study.
•
Individual correction, when possible, can provide a more reliable correction of QT for HR.
•
For an anti-infective drug, the predictions made based on allometric and cross-compound
scaling of non-clinical data were similar to results obtained from a subsequent FIM study.
•
E-R may extrapolate the QTc effect to drug exposures that were not tested (or could not be
tested) in the TQT study. This may be relevant for risk assessment in vulnerable subsets of
patients with the target indication.
References
1.
2.
4.
5.
6.
7.
Piotrovsky V. Pharmacokinetic-pharmacodynamic modeling in the data analysis and interpretation of druginduced QT/QTc prolongation. AAPS J. 2005 Oct 24;7(3):E609-24.
Food and Drug Administration, HHS. International Conference on Harmonization; guidance on E14 Clinical
Evaluation of QT/QTc Interval Prolongation and Proarrhythmic Potential for Non-Antiarrhythmic Drugs;
availability. Notice. Fed Regist. 2005 Oct 20;70(202):61134-5.
Bonate PL , Russell T . Assessment of QTc prolongation for noncardiac-related drugs from a drug
development perspective. J Clin Pharmacol . 1999 ; 39 : 349 - 358 .
Bonate PL . Assessment of QTc interval prolongation in a phase 1 study using Monte Carlo simulation. In:
Kimko H , Duffull S, eds. Simulation in Clinical Trials . New York, NY : Marcel Dekker ; 2003 :353- 367.
Shah RR . Drug-induced QT dispersion: does it predict the risk of torsade de pointes? J Electrocardiol . 2005 ;
38 : 10 - 18 .
Bazett HC. An analysis of the time relations of electrocardiograms. Heart . 1920 ; 7 : 353 - 370 .
Fridericia LS. Die systolendauer im elektrokardiogramm bei normalen Menchen und bei Herzkranken. Acta
Med Scand . 1920 ; 53 : 469 – 486.
8.
Bhattaram VA, Bonapace C, Chilukuri DM, et al.: Impact of pharmacometric reviews on new drug approval
and labeling decisions – a survey of 31 New Drug Applications submitted between 2005 and 2006. Clin
Pharmacol Ther (2007) 81:213-221.
9.
Powell JR, Gobburu JVS. Pharmacometrics at FDA: Evolution and Impact on Decisions Clin Pharm Ther
(2007) 82, 97 - 102
-100
0
-20
•
3.
100
100
Pharmacokinetic and exposure-response models were able to characterize the relationship
between drug exposure in plasma and the potential for QTc prolongation across a variety of
compounds and therapeutic areas.
Predicted AD1 Concentrations [ng/mL]
200
80
•
250
RR [msec]
Figure 5. Individual QT correction proved superior.
60
Conclusions
360
800
40
-20
380
600
20
Figure 9. Time dependent decline in QTcF
-40
320
0
Time s i nc e medi c ati on (hr)
420
delta-delta QTcF (msec)
Background
PCB  PCB0  PCBSTUDY
Data: Data from four Phase I and two Phase II studies in 144 diabetic subjects (79 male, 65 female) receiving
DB1 or placebo were used to conduct the E-R analysis.
 CONC  1 ID  1 PERIOD in ID * CONC
380
The evidence that multiple classes of noncardiac drugs significantly prolong the QT interval of the surface
ECG and have cardiotoxic potential, leading to life-threatening arrhythmias has been accumulating since the
1980s. In general, there is a qualitative relationship between QT prolongation and the risk of torsades de
pointes (TdP), especially for drugs that cause substantial prolongation of the QT interval. Most drugs that have
caused TdP clearly increase the QT interval as well. Documented cases of TdP (both fatal and nonfatal)
associated with the use of a drug have resulted in the withdrawal from the market of several drugs and
relegation of other drugs to second-line status. Because prolongation of the QT interval is the ECG finding
associated with the increased susceptibility to these arrhythmias, an adequate nonclinical and clinical
investigation of the safety of a new pharmaceutical agent should include rigorous characterization of its
effects on the QT interval. Once proarrhythmic safety of a new drug has been established in early
development, large Phase III studies and post marketing surveillance can be limited to less intensive and
laborious designs (e.g., a smaller number of ECGs involved in patient monitoring, less emphasis on the QT
correction for heart rate).
Eff
FQ 2
360
Introduction
2) Once the baseline model was established, baseline visit data was grouped with the data from the active
treatment visit. The placebo effect (i.e., post-baseline versus baseline) had a statistically significant impact on
the overall fit and varied in its magnitude from one study to another.

DB1 is a prodrug intended to control and reduce hyperglycemia in type 2 diabetes.
QTc(base)  0  0 ID  0 PERIOD in ID  f  t 
QT [msec]
• Characterize the relationship between drug exposure and potential for prolongation of the QTc interval.
• Quantitatively characterize the sources of variability in the QTc interval, including subject demographics,
twenty-four hour time-of-day, study, occasion, individual, and measurement.
• Compare the conclusions from a compound’s exposure-response model for QTc to conclusions from a
completed thorough-QTc study.
• Determine the potential impact of using different methods to correct QT interval for differences in heart rate.
• Analyze the adequacy of first-in-man QTc predictions made based on allometric and cross-compound
scaling methods using nonclinical in vitro/in vivo exposure and in vivo QTc data.
QTc(base)   0     f t    AGE   AGE  29  FEMALES  STUDY
Data: FIM Phase I study to investigate safety, tolerability and pharmacokinetics of FQ2 in healthy adult
volunteers. The study consisted of two cohorts of 12 healthy volunteers that each received FQ2 and placebo.
Objectives of the Analysis: Characterize the magnitude of QTc prolongation and provide dose
recommendation for Phase II/III studies.
Model Development:
1) Fridericia’s correction did not prove adequate to correct for heart rate, thus an individual correction factor
(α=0.2 on the average) was derived based on mixed-effects linear model (see Figure 3).
2) The structural model for QTc and FQ2 was kept similar to the one described in Case 1 (sans day effect). As
suspected, FQ2 did not have a day effect.
3) Different error structure was utilized to take into account the crossover study design.
QT
Objectives
Fluoroquinolone #1 (FQ1) is a new antibacterial agent that exhibits a marked activity against multidrugresistant staphylococci, streptococci, and enterococci, including strains resistant to other marketed
quinolones.
Data: The data for exposure-QTc response analysis came from five placebo-controlled Phase I studies. 192
healthy subjects (148 males, 44 females) received an IV infusion every 24h for 10 to 15 days. In three studies
serial ECG readings were performed at approximately the same time of day across different visits in order to
minimize any effects of a diurnal rhythm in QT interval when comparing on-drug QT measurements to
baseline measurements. To minimize the intrinsic variability of QT interval measurement, a triplicate ECG
(three readings not more than two minutes apart) was taken in two out of five studies. For the QTc E-R
analysis, only baseline and active period visit data were utilized.
Objectives of the Analysis: Provide dose recommendation for Phase II/III studies based on FQ1 exposure-QTc
response analysis in conjunction with the exposure-efficacy response analysis.
QTc Outcome Criteria for FQ1: QTc Outcome Criteria for FQ1 were defined prior to completion of the
exposure-QTc prolongation analysis. Outcome criteria were based on the upper bound of the 95% 1-sided
confidence interval (estimate of largest mean placebo-subtracted QTc effect for a study population) and were
defined as follows: ≤ 8 msec, >8 msec but ≤ 15 msec, and >20 msec constituted “Negative”, “Acceptable”,
and “Unacceptable” outcomes, respectively, while 15-20 msec represented an “Ambiguous” outcome.
Model Development:
1) Age, gender, time of the day and study effect were found to be significant modifiers of baseline QTc.
Case 3 – Individual QT Correction Case 6 – Anti-diabetic Agent
QTcB
Concentration/Exposure-response (E-R) modeling of QTc prolongation has been conducted for multiple
compounds currently in clinical development in different therapeutic areas. Data from available single and
multiple ascending dose (SAD/MAD) studies were pooled to construct a population E-R model, with post-hoc
predictions of concentration provided by a pharmacokinetic model. All SAD and MAD studies employed a
customized robust QTc assessment with time-matched triplicate ECGs and centralized manual QTc reading.
Sources of variability were characterized, and the relationship between covariates and model parameters was
explored, with a particular emphasis on correcting QT interval for heart rate and modeling the diurnal
variation using a truncated Fourier series. Where applicable, all detectable metabolites of the administered
compound were examined for a potential relationship with QTc interval. The results of population prediction
of QTc prolongation were compared to available thorough QTc (TQT) study results, and the E-R model was
evaluated to determine whether it could establish the QTc prolongation relationship without the TQT results.
Several benefits of the modeling approach were found. (1) Extrapolation of pre-clinical models in cynomolgus
monkeys to humans using allometric scaling and potency scaling between two novel fluoroquinolones
provided predictions for the QTc results of the first-in-human SAD study which compared well with the later
observations. (2) Negative TQT study results confirmed the negative simulation results from a Phase 1/2 E-R
model. (3) The superiority of individual correction of QT for heart rate was shown where typical population
correction methods would have substantially overstated the E-R relationship and could have led to
unnecessary restrictions on dose selection. E-R modeling should be implemented as a standard part of
modeling and simulation at different phases of drug development and used in conjunction with other data that
influence the need and/or the timing of a TQT study.
Case 1 – Phase II Dose Selection
delta-delta QTcF (msec)
Abstract