issues in the simulation and analysis of qtc interval data peter l. bonate, phd, fcp ilex oncology...

Issues in the Simulation and Analysis of QTc Interval Data

Peter L. Bonate, PhD, FCP

ILEX Oncology

San Antonio, TX

November 2003

Peter Bonate, ILEX Oncology Nov 2003 2

Objectives• Review issues in the analysis of QTc interval data• Present results of analysis of placebo ECG data

and illustrate the use of Monte Carlo simulation to determine the false-positive rate of common metrics used to assess QTc prolongation– Illustrate pitfalls in the interpretation of model-based

QTc interval analyses

• Illustrate use of Monte Carlo simulation in analysis of the PK-PD relationship of a new drug


Metrics for analysis of QTc interval data from least to most sensitive

• Mean QTc interval• Maximal QTc interval• Area under the QTc interval-time profile• Maximal change from baseline• Maximal QTc interval with baseline as

covariate• Area under the QTc interval-time profile with

baseline as covariate

AboutEqual

Bonate PL: Rank power of metrics used to assess QTc interval prolongation by clinical trial simulation. J Clin Pharmacol 40; 2000: 468-74.

AboutEqual


Guidelines for “Prolonged QTc”

• EMEA, 1997– > 450 msec in males– > 470 msec in males– > 60 msec change from baseline– QTc > 500 msec

• Mean change from baseline during dosing interval– 5 msec = prolonged ???

• No guidelines for AUC-based metrics


Stages of Acceptance

• What QTc effect?

• We have a QTc effect but we’re no worse than other drugs already on the market– Telithromycin, ziprasidone

• We have a QTc effect and we will characterize it


Analysis of Placebo Data From Healthy Normal Volunteers

Experimental Design (1999)• Objective was to characterize the QTc-dose

response relationship• Single-center, randomized, double-blind, placebo-

controlled, 4-way crossover• 40 subjects (20 males and 20 females)

– usual inclusion-exclusion criterion for Phase I study, e.g., 18 to 50, not pregnant, no previous ingestion of study medication, etc.


• 3 doses (10, 30, and 60 mg QD for 7 days)• Placebo day (Day -1) prior to dosing• 1 week washout between periods• Meals were given at breakfast (~1 hour post-dose),

lunch (~5 hours post-dose), dinner (~11 hours post-dose), and snack (~9 PM)

• All ECGs were taken prior to meals, if they were scheduled at the same time

Reference: PL Bonate: Assessment of QTc Interval Prolongation in a Phase I Study Using Monte Carlo Simulation. In: Simulation For Clinical Trials (Kimko HC, Duffull SB, ed.) Marcel Dekker, 2002, pp. 353-367.


ECG Assessments

• 0, 1.5, 3, 6, 9, 12, and 24 h on Day -1 (placebo lead-in), Day 1, and Day 8

• pre-dose on Days 4, 5, 6, and 7• Over-read by a cardiologist blinded to treatment,

time post-dose, and period• QTcB intervals were calculated for each lead• The largest QTcB interval was reported


What is the baseline?

• Average of pre-dose at time 0 prior to dosing– Will fail to correct for natural circadian rhythm– Replicate measurements better than single measurements

• Mean of placebo day– Robust because it is based on many measurements– Also fails to correct for circadian rhythm– Not usually possible with Phase II or III studies

• Point to point with placebo administration– Corrects for circadian rhythm– Not robust because often based on single measurement– Not usually possible with Phase II or III studies– Day -1 or placebo period?


Placebo ECG Model

• Covariates available:– Period, day, and time of ECG– Chest lead– Time of last meal– Sex– Race– Baseline calcium and potassium– Body surface area– Stress (Days with many ECGs more stressful

than days with only 1 ECG)


Population PD Modeling

• Linear mixed effect models were used with NONMEM, version 5

• All models were developed sequentially using LRT

• All factors entered into the model in a linear manner

• All random effects were treated as normally distributed


ECG Results• Total variance of 769 ECGs from 40 subjects

– 449 msec2 (5.1% CV)• Values increased over time (trend effect)• Chest lead IV was greater than other leads• Food increased QTcB intervals:

– breakfast < lunch < dinner

• QTcB intervals were higher on days with intensive sampling (Day 1, 2, and 8)

• Females > Males


Final Placebo Model Parameter Estimates

Parameter Model Component Estimate SE 2 Baseline (E0) E0 = (1) + (1) 389 3.21 147

Trend Effect K = (2) + (2) 0.0225 9.34E-3 8.7E-4

Female Sex Effect

(0=male, 1=female)

SE = (3) * SEX

7.57

4.31

Chest Lead IV Effect

(1 = Lead IV, 0= other)

CE = (8)

9.54

4.33

Rate of Decline in food effect KFE = (7)*exp(3) 0.400 0.208 0.0117

Maximal Food Effect

B: FE = (4) * exp(-KFE * t)

L: FE = (5) * exp(-KFE * t)

D: FE = (6) * exp(-KFE * t)

(4): 10.6 (5): 12.5 (6): 14.7

(4): 2.62 (5): 4.52 (6): 3.90

Day Effect, if Day = {2, 5, 6} DE = (9) -4.02 2.01

Final Model: QTcB = E0 + K*Time + SE + FE + CE + DE + EPS(1)

Inter-Day Variability was < 10 msec2 (removed from model as noninformative)

Residual Variance: 252 msec2 (~16 msec SD)

Peter Bonate, ILEX Oncology Nov 2003 14Time Relative to First Dose (h)

0 2 4 6 8 10 12 14 16 18 20 22 24

QT

cB I

nte

rva

l (m

sec)

380

385

390

395

400

405

410

415

Breakfast Lunch Dinner

Day 1

Peter Bonate, ILEX Oncology Nov 2003 15Time Relative to First Dose (h)

0 24 48 150 200

QT

cB In

terv

al (

mse

c)

380

385

390

395

400

405

410

415


What was the Intrinsic Variability in QTc Intervals?

• Between-subject variability – 147 msec2

– 12 msec SD (~3.1% CV)

• Within-subject variability– 252 msec2

– 16 msec SD (~4.1% CV)– Consists of measurement variance and true unexplained

variance– Future studies should do repeated ECGs at each time

point to assess measurement variability

• IOV was less than 10 msec2

Time (hours) on Day -1

0 5 10 15 20

QT

c In

terv

al (

mse

c)

340

360

380

400

420

440

460


Intrinsic Variability in Time-Averaged QTc AUC

• TA-QTc = AUC calculated over 12 hour/12 h• Linear Mixed Effect Models

– Covariates: period, sex, Ca, K, BSA, race, day– Random intercept model– Simple residual error model– Variance component for group

• No covariates were statistically significant– LS Mean: 400( 2.39) msec– Between-subject variability: 181 msec2

– Residual variability: 59 msec2

– Females may be greater than males (404 vs. 396, p = 0.11)


The Utility of Simulation

• Heuristic tool to increase understanding

• Assist in discovery and formulation of new hypotheses

• Prediction

• Substitute for humans (expert systems)

• Training

• Entertainment


What is Needed for Simulation of QTc Trials?

• What is the primary metric of interest?– What is the variability of this metric in the population

of interest? What is its distribution?– If unknown, what about in healthy volunteers and can

that variability be extrapolated?

• What is the pharmacokinetic model?– Is a pharmacokinetic model needed?

• What is the appropriate concentration-QTc model and what is the variability in those parameter estimates?

• What is the experimental design?


Application of Placebo Model:Food Effects Can Act Like Drug Effects

• Simulated 100 subjects after oral administration of a NCE with same time points as previous study

• Concentration and QTc were independent

• Analyze QTc interval data with Proc Mixed in SAS using a random effects model

Proc mixed; class subject; model QTc = concentration; random intercept concentration / subject=subject type=un;run; quit;


Time (hours)

0 5 10 15 20 25

Sim

ula

ted

QT

c In

terv

al

320

340

360

380

400

420

440

460

480


Time (hours)

0 5 10 15 20 25

Con

cent

ratio

n (n

g/m

L)

0

100

200

300

400

500

1-compartment model Ka = 0.7 per hour Kel = 0.15 per hour Vd = 125 L Dose = 75 mg


p-value for concentration < 0.0001• for every 100 ng/mL in concentration there will be a 2.2 msec in QTc intervals

Drug Concentration (ng/mL)

0 100 200 300 400 500

Obs

erve

d Q

Tc

Inte

rval

(m

sec)

320

340

360

380

400

420

440

460

480


Drug Concentration (ng/mL)

0 100 200 300 400 500

Obs

erve

d C

hang

e F

rom

Bas

elin

ein

QT

c In

terv

al (

mse

c)

-60

-40

-20

0

20

40

60

80

What about using change from baseline where baseline is time 0?

p-value for concentration < 0.0001• for every 100 ng/mL in concentration there will be a 2.2 msec in QTc intervals

Pre-dose QTc values

are inadequate

as a baseline


Application of Placebo Model:What is the false-positive rate?

• Monte Carlo simulation using the placebo model was used to assess– What percent of subjects will have a QTc interval more

than• 470 msec for females,

• 450 msec for males, or

• 500 msec in general?

– What % of subjects will have a change from baseline of 30 to 60 msec, or > 60 msec?

• 5000 subjects sampled at 0, 1, 1.5, 2, 3, 4, 6, 8, 12, and 24 hours


False Positive RateMax(QTc interval)

> 470 msec – females 0.3%

> 450 msec – males 1.5%

> 500 msec 0%

Based on Time 0

> 30 to 60 msec dQTc 49%

> 60 msec dQTc 6.7%

Point to Point Baseline

> 30 to 60 msec dQTc 59%

> 60 msec dQTc 4.0%


Application 3:Modeling Effect of BSA on QTc

• 2-compartment oral with lag time best structural model

• Drug was known to prolong HERG channel• BSA was known to be an important covariate in

the pharmacokinetics of Drug X by affecting Q• Is BSA an important covariate for QTc intervals?

Peter Bonate, ILEX Oncology Nov 2003 28Drug X Concentration (ng/mL)

0 50 100 150 200

Cha

nge

from

Bas

elin

e (P

lace

bo D

ay)

QT

c In

terv

al (

mse

c)

-100

-50

0

50

100

Best fit model was a linear model (no intercept)

– dQTcB=(1)*IPRD (1) = 0.2494(0.0383) msec/ng/mL

– For every 10 ng/mL there is an increase in QTcB intervals of 2.49 msec


Methods• Simulate placebo ECG lead-in day (Day –1)• Simulate concentration-time profile of Drug X for 250 subjects

at steady-state– at doses of 10 to 60 mg QD– over weights 1.2 to 2.2 m2

• Simulate placebo QTc data over dosing interval• Add drug effect to placebo effect• Calculate maximal QTc, maximal dQTc, and average dQTc for

each subject• Compute means by dose and weight• Fit response surface by dose, BSA, and dose by BSA

interaction


0

15

30

45

60

Dose (mg)

1.21.41.61.82.02.2

BSA (m**2)

-1

0

1

2

3

4

5

6

Mean Change From Baseline (Placebo Day –1)Females

Average dQTC = 0.07928*Dose R2 = 0.99

5 msec


Males

0

15

30

45

60

Dose (mg)

1.21.41.61.82.02.2

BSA (m**2)

-1

0

1

2

3

4

5

6

Mean Change From Baseline (Placebo Day –1)

Average dQTC = 0.07928*Dose R2 = 0.99

5 msec


Application 4:Power of a Phase II Study

• Given the following design what is the probability of detecting a exposure-QTc relationship in the population of interest– 10, 20, or 40 mg (1:1:1) once daily for 8 weeks– ECGs collected on Day –1, Week 4, and Week 8 at 0 and 4

h post-dose (0.5 h on Day –1)– Sample size 30 to 120 by 10– Analyze results using linear mixed effect models

class subject sex day time;model qtc = sex day time(day) conc baseline;random intercept conc / subject=subject type=un;

– Repeat simulation 250 times


Power = (# of simulations with p < 0.05)/(Total number of simulations) * 100%

Total Sample Size

20 30 40 50 60 70 80 90 100 110 120 130

Pow

er

0

20

40

60

80

100

ConcentrationDose (continuous)Dose (categorical)


Unresolved Issues

• Choice of covariance matrix– Between-subject (simple, unstructured, CSH)?– Within-subject (simple, spatial, toeplitz)?

• ML or REML

• Best model selection criteria– AIC, AICc, BIC

IWRES

-1.0

-0.5

-0.0

0.5

-1.0

-0.5

-0.0

0.5

-1.0 -0.5 -0.0 0.5

-1.0 -0.5 -0.0 0.5

L1IWRES

L2IWRES

-1.0 -0.5 -0.0 0.5

-1.0 -0.5 -0.0 0.5

L3IWRES

-1.0

-0.5

-0.0

0.5

-1.0

-0.5

-0.0

0.5

L4IWRES

-1.0

-0.5

-0.0

0.5

-1.0 -0.5 -0.0 0.5


Summary

• Many Phase 1 studies where pre-dose ECGs are used as a baseline may show an artifactual relationship to drug concentrations simply because of the food effect on QTc intervals

• There will be a false-positive rate– What are we willing to live with?

• Simulation can be a powerful to help interpret results and to plan studies


Opinion

• QTc is no different than other laboratory parameters

• How do we measure it?– Slavic devotion to outdated correction formula

• Bazett

• What is clinically relevant?

issues in the simulation and analysis of qtc interval data peter l. bonate, phd, fcp ilex oncology...

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