sample

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240

6

0 500 1000 1500 2000 2500

int.hat-2.5

-1.0

0.5 plac.hat-1

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000 slp1.hat0.

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0 500 1000 1500 2000 2500

omega[1,1]0.00

200.

0045

omega[2,2]

0.02

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omega[3,3]

9.6

10.0

sigma

Figure 1. History Plots of Fixed and Random Effect Parameters

HIERARCHICAL BAYESIAN EXPOSURE-RESPONSE ANALYSIS AND STATISTICAL ASSESSMENT OF HEART RATE-CORRECTED QT INTERVAL (QTC) FOR TORCETRAPIBS. Riley, Pfizer Global Research and Development, New London, CT.

RESULTSModel Diagnostics• History plots (Figure 1) suggest that the parameters values are being sampled from a stable

posterior distribution• Kernel density (Figure 2A) plots show that the marginal posterior distribution of each

parameter is approximately normal • Autocorrelation plots (Figure 2B) show minimal correlation within chains beyond lag = 1

STUDY DESIGN/DATA• 389 healthy subjects

• T/A 60/20 mg, 240/80 mg, or PBO QD x 21 days or PBO QD x 20 days + open-label MOXI 400 mg on Day 21

• PK/ECG Collection• Day 0 (ECG only): 24, 22, 20, 18, 16, and 12 hours pre-dose• Day 1: 0, 2, 4, 6, and 8 hours post-dose• Day 21: 0, 2, 4, 6, 8, 12, hours post-dose

• Database for ER analysis included 2722 baseline (pre-dose) QTcF values, 1697 torcetrapib/BTFMBA-QTcF pairs, and 1529 QTcF records on PBO

METHODS• Posterior Predictive Check (PPC) was performed using the observed mean,

median, and maximum QTcF by time, study day, and dose as test statistics

NONMEM Model

WinBUGS Model• Stage 1 – Data Model

• Stage 2 – Intersubject Variability model

• Stage 3 – Prior Distributions

WinBUGS code inside model statementfor(i in 1:nsub) # Loop over subjects

theta[i, 1:3] ~ dmnorm(theta.mean[i, 1:3], omega.inv[1:3, 1:3])theta.mean[i, 1] <- int.hat + sex.hat*isex[i] # Mean Intercepttheta.mean[i, 2] <- slp1.hat # Mean torcetrapib slopetheta.mean[i, 3] <- slp2.hat # Mean BTFMBA slope

int[i] <- theta[i,1] # Individual interceptslp1[i] <- theta[i,2] # Individual torcetrapib slopeslp2[i] <- theta[i,3] # Individual BTFMBA slope

for(j in 1:nobs) # Loop over observations

qtc[j] ~ dnorm(qtc.mean[j],qtc.tau)

# qtc.mean[j] is similar to NONMEM IPREDqtc.mean[j] <- int[subject[j]] + plac.hat*plac[j] + slp1[subject[j]]*cpar[j] + slp2[subject[j]]*cmet[j]

# Sample from posterior distribution (conditioned on observed data) [3]# Provides distribution of future observations from subjects in current study# Can use these samples to generate output for posterior predictive check (Figure 3)qtc.cond[j] ~ dnorm(qtc.mean[j],qtc.tau)

# Specify Priorsint.hat ~ dnorm(402, 1.0E-5)plac.hat ~ dnorm(-0.715,1.0E-5)sex.hat ~ dnorm(-12,1.0E-5)slp1.hat ~ dnorm(-0.00846,1.0E-5)slp2.hat ~ dnorm(0.118,1.0E-5)

omega.inv[1:3, 1:3] ~ dwish(omega.inv.prior[1:3, 1:3], 3)omega[1:3, 1:3] <- inverse(omega.inv[1:3, 1:3])

sigma ~ dunif(0,1000)qtc.tau <- 1/(sigma*sigma)

SUMMARY• A Bayesian model was implemented to quantify the relationship between torcetrapib and BTFMBA

concentrations and QTcF interval• Parameter estimates and model predictions were similar across the maximum likelihood and

Bayesian approaches• PPC using observed mean, median, and maximum QTcF by time, day, and dose as test statistics all

showed similarly inconsistent predictive performance• Implementing a Bayesian model circumvents the need for additional procedures to assess

confidence in parameter estimates and predictive performance, potentially reducing overall computational time and resources needed to implement those procedures

ABSTRACTObjectives: Torcetrapib is a cholesteryl ester transfer protein inhibitor previously in Phase 3 testing in combination with atorvastatin for treating dyslipidemias and altering the progression of atherosclerosis*. The primary objective of this study was to demonstrate a lack of effect of torcetrapib/atorvastatin (T/A) fixed dose combinations on change in QTc, using Fridericia’s correction method (QTcF). Another objective was to characterize the exposure-response relationship between plasma concentrations of torcetrapib and the M1 metabolite (BTFMBA) and QTc. The per protocol analysis results have been reported previously [1]. The objective of this communication is to evaluate a hierarchical Bayesian approach using Markov Chain Monte Carlo (MCMC) methods for analysis of QTc data.Methods: This was a double-blind, randomized, multisite, parallel group, multidose thorough QT study in healthy subjects. Subjects were given T/A 60/20 mg, 240/80 mg, or placebo (PBO) daily for 21 days. A fourth group received PBO for 20 days then open-label moxifloxacin (MOXI) 400 mg on Day 21 to confirm study sensitivity. The per protocol analyses were an analysis of variance (ANOVA) using SAS PROC MIXED with treatment, sex, and site as fixed effects and an exposure-response (ER) model implemented using maximum likelihood (ML) methods in NONMEM V with fixed effects for baseline, PBO, and sex on intercept and both torcetrapib and BTFMBA concentrations on slope. Simulation and nonparametric bootstrap procedures were employed to assess the predictive performance of the NONMEM model and to generate confidence intervals (CI) about the parameter estimates and the expected QTc response. The NONMEM model was translated into a Bayesian framework implemented in WinBUGS 1.4.3 [2]. Inferences about parameter estimates and predictive performance of the model can be made from the joint posterior distribution generated during the estimation process.Results: Mean (90% CI) Placebo-Corrected Change from Baseline QTcF Interval Estimates at 4 hours (T/A) and 2 hours (MOXI) on Day 21 from the Per Protocol (ANOVA and NONMEM) and WinBUGS analyses

Conclusions: Statistical analysis and exposure-response modeling support a lack of effect of T/A 60/20 mg and 240/80 mg on QTcF prolongation at the torcetrapib historical Tmax on Day 21. Employing hierarchical Bayesian methods affords some process efficiencies over maximum likelihood approaches for model evaluation and making inferences based upon the model results.

*All clinical development of torcetrapib was halted after the independent Data and Safety Monitoring Board monitoring the ILLUMINATE morbidity and mortality study for torcetrapib recommended terminating the study because of a statistically significant imbalance in all-cause mortality between patients receiving torcetrapib/atorvastatin and those receiving atorvastatin alone. Full details of the cause of this imbalance have yet to be determined.

T/A MOXI Analysis Method 60/20 mg 240/80 mg 400 mg

ANOVA -0.662 (-3.46, 2.13)

-0.750 (-3.25, 1.75)

6.14 (3.62, 8.65)

NONMEM ER Model -0.406 (-1.05, 0.258)

-0.830 (-3.18, 1.58) -

WinBUGS ER Model

-1.12 (-3.01, 0.777)

-3.28 (-9.85, 3.43) -

REFERENCES1. Riley SP, LaBadie R, Terra SG, Kolluri S, Thuren T, Shear C, Russell T, Benincosa LJ, Gibbs M. Mixed Effects

Exposure-Response Analysis and Statistical Assessment of Heart Rate-Corrected QT Interval (QTc) for Torcetrapib. Clin Pharmacol Ther 81 (Suppl1): Abstract PII-74, S73, 2007.

2. Lunn, D.J., Thomas, A., Best, N., and Spiegelhalter, D. (2000) WinBUGS -- a Bayesian modelling framework: concepts, structure, and extensibility. Statistics and Computing, 10:325--337.

3. Gillespie, William R,. (2007) Introduction to Bayesian PK-PD Modeling & Simulation. Class notes. Metrum Institute, Tariffville, CT

( ) ( )~ , ~ 0, ; 1,...,389; 1,...,ij i i ij ijy f N i j nobsε ε τ+ = =θ X

( )1~ ,i iMVN −θ θX Ω

( )( )

( )

1

2

~ , 1.0 5, where is a identity matrix

~ , , where is a scale matrix

~ 0,1000 3

P P

P

MVN E P P

Wi

U P

ν ν ν

σ τ σ ν

−

−

= × − ×

×

= = =

θ µ C C I I

Ω R R

METHODS• Data processing, graphical evaluations, and WinBUGS execution

were performed using R Version 2.5.1

• Initial estimates for chains were overdispersed random samples based upon parameter estimates from an lme fit to the data in R

• Priors for parameters in the model were uninformative

• Three Markov chains of 50,000 samples each were run with a burn-in period of 25,000 iterations. Inferences and diagnostic plots were based upon a thin rate of 10 (7500 total iterations)

1 2 3θ θ θ η= + × + × + Intercepti i i iIntercept PBO SEX

,

4torcetrapibto rcetrapib Slope

i iS lope θ η= +

5BTFMBABT FM BA Slope

i iS lope θ η= +,

, , , ,torcetrap ib torcetrapib B TF M B A B TF M BA

i j i i i j i i j i jQ Tc Intercept S lope C p S lope Cp ε= + × + × +

Definitions: PBO = placebo

,i jQTc = observed QTc at the jth observation for the ith individual.

iIn tercept = typical value of QTc for the ith individual not on active treatment

1θ = typical value of the baseline QTc for female subjects on active treatment

2θ = typical value of the additive effect of placebo treatment on the intercept relative to the baseline QTc

3θ = typical value of the additive difference in QTc for males relative to females

4 5,θ θ = typical values of slope for QTc versus torcetrapib and BTFMBA concentrations, respectively

( )2~ 0,i Nη ω = interindividual deviation from the typical values for the ith individual

( )2, ~ 0,i j Nε σ = random residual error of the jth observation for the ith individual

Chain 1Chain 2Chain 3

Predictive Comparison• In general, the Bayesian analysis predicted similar expected change from baseline QTcF values as the

other methods, but with less precision, as suggested by the wider credible intervals at most time points• The increased magnitude and lower precision of the estimate of torcetrapib concentration on the slope

resulted in wider credible intervals when torcetrapib concentrations were highest (2-8 hours post-dose)

Parameter Effective N Parameter Estimate Mean (%RSD)

90% Central Credible Interval

Intercept [msec] Baseline (int.hat) 6999 402 (0.285) (400,404)

Placebo (plac.hat) 7707 -1.12 (33.6) (-1.73, -0.503) Sex (sex.hat) 7610 -12.2 (12.2) (-14.7, -9.72)

IIVInterceptb (omega[1,1]) 7313 13.9 (7.59)c (13.0, 14.7)

Slope

Torcetrapib (slp1.hat)[msec/(ng/mL)] 7605 -0.0123 (35.5) (-0.0196, -0.00516)

IIVslp1.hatb (omega[2,2]) 7141 0.0571 (11.0)c (0.0522, 0.0624)

BTFMBA (slp2.hat)[msec/(µg/mL)] 5312 0.126 (17.7) (0.0894, 0.163)

IIVslp2.hatb (omega[3,3]) 3699 0.183 (23.0)c (0.150, 0.218)

Residual Error (sigma) [msec] 7500 9.86 (0.976) (9.70, 10.0) a Percent relative standard deviation (%RSD) calculated as marginal posterior standard deviation/|marginal posterior mean| * 100 b IIV = interindividual variability estimates expressed as standard deviations such that the reported values have the same units as the structural model parameters with which they are associated c %RSD of variance estimate

Table 1. Summary of Marginal Posterior Distributions of Model Parameters

BA

Figure 3. Boxplots of Observed QTcF Interval Plus Median, 90%, and 50% Posterior Prediction Intervals by Dose and Time (Panel A) and Posterior Density of Predicted Mean and Observed Mean (dashed red line) QTcF Interval by Time on Day 21 in the 240/80 mg T/A Dose Group

Time Post-Dose (hr)

Obs

erve

d an

d P

redi

cted

QTc

F In

terv

al (m

ec)

350

400

450

0 2 4 6 8 12

3.2% 3.2% 6.3% 5.3% 5.3% 2.1%

7.4% 4.2% 9.5% 3.2% 7.4% 5.3%0 mg

0 2 4 6 8 12

3.2% 5.4% 3.2% 3.2% 5.4% 2.2%

8.6% 3.2% 1.1% 1.1% 2.2% 3.3%240 mg

350

400

450

3.3% 2.2% 4.3% 2.2% 6.5% 3.3%

10.9% 8.7% 7.6% 5.4% 5.4% 5.4%60 mg

90% Posterior Prediction Interval50% Posterior Prediction IntervalMedian Posterior Prediction

Values represent the % of observations above the upper bound of the 90% posterior prediction interval

Values represent the % of observations below the lower bound of the 90% posterior prediction interval

QTcF Interval (msec)

Den

sity

0.05

0.10

0.15

0.20

390 395 400 405

P(pred > obs) = 0.025

0 hrP(pred > obs) = 0.153

2 hr

390 395 400 405

P(pred > obs) = 0.834

4 hr

P(pred > obs) = 0.542

6 hr

390 395 400 405

P(pred > obs) = 0.697

8 hr

0.05

0.10

0.15

0.20

P(pred > obs) = 0.846

12 hr

Parameter Estimates• Mean parameter estimates were all within 20% of those resulting from the maximum likelihood

(NONMEM) analysis reported previously [1] except for slp1.hat and omega[2,2], which were 32% and 91% greater, respectively

• Precision of the slp1.hat estimate was ~ 3-fold lower than in the NONMEM analysis

Figure 2. Marginal Posterior Density (Panel A) and Autocorrelation Plots (Panel B) of Fixed and Random Effect Parameters

A B

RESULTSPosterior Predictive Check• Samples drawn from a stable posterior distribution can be used to perform various posterior

predictive checks as shown in Figure 3• PPC using observed mean, median, and maximum QTcF by time, day, and dose as test statistics

all showed similarly precise but biased predictive performance

A

0 2 4 6 8 10 12

-10

-50

5

Day 21 Expected Value (WinBUGS Model)Day 21 Expected Value (E-R Model)Day 21 Expected Value (Statistical Analysis)90% Credible Interval (WinBUGS Model)90% CI (E-R Model)90% CI (Statistical Analysis)

Time Post-Dose (hr)

Cha

nge

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TcF

Inte

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c)

0 2 4 6 8 10 12

010

000

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BA C

once

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020

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060

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etra

pib

Con

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n (n

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L)

Fig 4. Mean Concentrations (Panel A) and Expected Change from Baseline QTcF Interval and 90% Confidence/Credible Intervals from the NONMEM, ANOVA, and WinBUGS analyses (Panel B) on Day 21 in the 240/80 mg T/A Dose Group

BChain 1Chain 2Chain 3