# Presentation: 035219

## Issues in the Simulation and Analysis of QTc Interval Data

- Peter L. Bonate, PhD, FCP
- ILEX Oncology
- San Antonio, TX
- November 2003

## 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

- About
- Equal

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

- About
- Equal

## 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

- 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

## Breakfast  Lunch        Dinner

- Day 1

## Slide 15

## 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

## 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;

## Slide 21

## 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

## 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 Rate

| Max(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?

## 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

## Females

- Average dQTC = 0.07928*Dose  R2 = 0.99

- 5 msec

## Males

- 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%

## 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

## Slide 35

## 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?