Model-Based Meta-Analysis with NONMEM Jae Eun Ahn, Ph.D. College - PowerPoint PPT Presentation

Longitudinal Aggregate Data Model-Based Meta-Analysis with NONMEM Jae Eun Ahn, Ph.D. College of Pharmacy, Kangwon National University 7 Sep 2012 WCoP, Seoul, Korea

Acknowledgments • Department of Pharmacometrics, Pfizer, Inc. • Jonathan French, Sc.D., Metrum Research Group Ahn and French, Longitudinal aggregate data model-based meta-analysis with NONMEM: approaches to handling within treatment arm correlation, JPKPD (2010) 37: 147-201 2

Negative study results from PoC study in acute schizophrenia (Change From Baseline) PANSS Total Better Visit (week) PANSS: Positive & Negative Syndrome Scale Ahn et al., ASCPT 2012 3

How is the placebo response in the literature? Mean Change from BS in PANSS Total Score at 6 Weeks for Acute Subjects Study Author, Year Delta PANSS Total + 95%CI Delta PANSS Total SE N NDA 20-825 study 1,2001 -0.40 [ -4.58 , 3.78 ] -0.4 2.1 83 Cutler et al.,2006 -5.30 [ -9.36 , -1.24 ] -5.3 2.1 88 McEvoy et al.,2007 -2.38 [ -6.04 , 1.28 ] -2.4 1.9 108 Marder SR-3,2007 -7.59 [ -12.20 , -2.98 ] -7.6 2.4 110 Potkin SG study 3-5,2008 -7.6 1.5 160 -7.60 [ -10.61 , -4.59 ] Potkin SG study 2-4,2008 -3.5 1.6 156 -3.50 [ -6.55 , -0.45 ] Organon Study 041021-30,2009 -11.1 1.6 100 -11.10 [ -14.24 , -7.96 ] Vanda Study ILP3000ST-48,2009 -4.10 [ -8.29 , 0.09 ] -4.1 2.1 127 Organon Study 041004-29,2009 -5.30 [ -9.81 , -0.79 ] -5.3 2.3 59 Organon Study 041023-33,2009 -10.8 1.6 123 -10.80 [ -13.94 , -7.66 ] Organon Study 041022-31,2009 -10.10 [ -13.43 , -6.77 ] -10.1 1.7 93 Canuso CM-4,2009 -25.50 [ -29.76 , -21.24 ] -25.5 2.2 80 Vanda Study ILPB202-50,2009 -18.40 [ -24.84 , -11.96 ] -18.4 3.3 35 Sunovion Study D1050231-45,2010 -15.20 [ -18.53 , -11.87 ] -15.2 1.7 116 Sunovion Study D1050196-42,2010 -5.50 [ -9.75 , -1.25 ] -5.5 2.2 90 Sunovion Study D1050229-43,2010 -14.70 [ -17.84 , -11.56 ] -14.7 1.6 127 C. M. Canuso-3,2010 -10.80 [ -14.52 , -7.08 ] -10.8 1.9 95 Sunovion Study D1050049-41,2010 -12.3 2.3 72 -12.30 [ -16.85 , -7.75 ] Sunovion Study D1050006-39,2010 -6.2 2.7 50 -6.20 [ -11.57 , -0.83 ] RE Model for All Studies -9.25 [ -11.96 , -6.55 ] -85 -75 -65 -55 -45 -35 -25 -15 -5 5 15 25 PANSS Total Change from BS at Week 6 Courtesy: Sima Ahadieh and Vikas Kumar, Pfizer, Inc . PANSS Total change from baseline at week 6 in placebo group

Comparison of the Placebo Response Model Simulation (90% PI) with Overlaid Observed Placebo 10 Change from Baseline in PANSS Total 0 -10 -20 Courtesy: Sima Ahadieh and Vikas Kumar Pfizer, Inc . -30 0 1 2 3 4 Time (Weeks) Mean change from baseline PANSS Total in placebo group seems to be greater than model estimated mean from the literature meta-analysis but within 90% PI

Meta-Analysis • A quantitative review and synthesis of results from related but independent studies (Normand, 1999) Meta-analysis estimate = weighted average • More precise inferences (pooling data) • Point of reference for in-licensing opportunities • Relationship b/w early (Phase 1, 2) and later (Phase 3) endpoints • Quantitative predictions of the probability of a successful phase 3 study 6

Model-Based Meta-Analysis • Incorporates parametric model to describe dose- response, time effects, etc. Drug & Disease Trial Performance Models Metrics Model-Based Drug Competitor Info. Quantitative Development & Meta-Analysis Decision Criteria Design & Trial Data Analysis Execution Models Model Lalonde RL et al., Clin Pharmacol Ther 2007;82:21-32 7

Benefits and Challenges • Publication bias • Address uncertainty and heterogeneity of studies • Incomplete description of • Increase statistical power trial design and methods • Combining aggregate • Improve estimates of data (AD) and individual treatment effect patient-level data (IPD) • Lead to new knowledge • Appropriately accounting • Formulate new questions for the correlation between time points within each study Lalonde RL et al., Clin Pharmacol Ther 2007;82:21-32 8

Longitudinal Aggregate Data Response variable = • Observations within a study Mean outcome over time within an arm are correlated – Because the patients come from a common population – Use the study as ID (the grouping factor for the first level random effects) • Mean observations over time within a treatment arm are correlated – Because they are based on the same set of patients  Need to account for more than two-level random effects 9

How to handle within-treatment arm correlation? 1. IOV Random Population PK Analysis with Meta-Analysis* Effects IOV Study 1 st Level Individual (ID) (Inter-Individual Variability, (Inter-Study Variability, ISV) IIV) Treatment arm 2 nd Level Occasions (Inter-Occasion Variability, (Inter-Arm Variability, I A V) IOV) RUV Usually assumed to be Can be correlated independent * Modified from Laporte-Simitsidis et al. Inter-Study Variability in Population Pharmacokinetic Meta-Analysis: When and Howe to Estimate It? J of Pharm Sci 89: 155-167 (2000) 10

How to handle within-treatment arm correlation? 2. L2 • L1 (=ID): group together the data records of the same realization of etas • L2: group together the data records of the same realization of epsilons – Within a L1 observation, the L2 random effects can be made to be correlated between L2 observations • A way to handle correlation of multivariate observations within individual records – PK and PD – Parent and metabolite – Replicates S. L. Beal, L. B. Sheiner, and A. J. Boeckmann (Eds.). NONMEM Users Guides, ICON Development Solutions, Ellicott City, MD, 1989-2006 11

What if ignoring the correlation? - Simulation Experiments 12

Impact On • Estimating the drug effect • Predicting the outcome of interest in a future study – E.g., what is the probability that the observed mean difference from placebo is at least c 2 , for a given design?     P Y Y c ik i 0 2

Simulation Model and Study Design  E Dose             MAX Y E exp( k time ) ( ) w w = 1/sqrt(n)  0 0 s p ED Dose 50 Parameters Correlation Low Med High ID Phase Sample Size Doses Time Points (per dose) E0 30 1 2 50 0, 50, 100, 200, 400 0, 1, 2, 4 EMAX 10 2 2 50 0, 100, 300, 500, 1000 0, 1, 2, 4 ED50 250 3 2 50 0, 100, 200, 300, 400 0, 2, 4, 8, 12 K0 0.1 OMGS (inter-study variability) 1 1 1 4 2 50 0, 300, 400, 500, 600 0, 2, 4, 8, 12 OMGP (inter-patient variability) 3 9 27 5 3 100 0, 200, 400 0, 4, 8, 12 SIG (residual unexplained 9 9 9 6 3 100 0, 400, 600 0, 4, 8, 12 variability) Correlation = 0.25 0.5 0.75 7 3 100 0, 200, 600 0, 4, 8, 12 OMGP/(OMGP+SIG) 8 3 250 0, 200, 400 0, 4, 8, 12 TV (total variance = 1.12 1.18 1.36 OMGS+(OMGP+SIG)/n) 9 3 250 0, 400, 600 0, 4, 8, 12 100 mg Effect 2.86 10 3 250 0, 200, 600 0, 4, 8, 12 500 mg Effect 6.67 500 simulations per design; NONMEM VI (level 1.2) 14

Estimation Models • A1: Inter-study on E0, Inter-arm on E0 (=simulation model) • A2: Inter-study on E0 with correlated residual errors (L2) • A3: Inter-study on with uncorrelated residual errors (ID=Study) • A4: Inter-arm on E0 with uncorrelated residual errors(ID=Arm) 15

Results - Parameter Estimates Inter-Study Inter-Arm Residual Total Var 200 500 150 Hardly any bias in the 150 150 400 L 100 100 100 300 fixed effect parameter o 50 50 50 200 estimates 0 0 0 w 100 -50 (mean estimation error: -1 ~ 7%) 0 -100 -100 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 A1 A2 A3 A4 ISV IAV RUV TOTVAR When the within arm 200 correlation was ignored 500 150 150 150 M 400 (A3), residual variability 100 100 100 300 e was inflated 50 50 50 200 d 0 0 0 100 -50 When the study effects 0 -100 -100 were ignored (A4), inter- 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 ISV IAV RUV TOTVAR patient variability is under- 200 500 estimated 150 150 H 150 400 100 100 100 (close to the true first level 300 i 50 50 50 200 random effects) g 0 0 0 100 h -50 0 -100 -100 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 ISV IAV RUV TOTVAR 16

Standard Error *: 95% CI for High Dose Effects Low Medium High Low Medium High W idth of 95% CI ↑ for 4.0 4.0 4.0 A1 A1- A3 as correlation ↑ 3.5 3.5 3.5 A1 3.0 3.0 3.0 Information from longitudinal measurements ↓ , as 2.5 2.5 2.5 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 correlation ↑ simulation # simulation # simulation # 4.0 4.0 4.0 Not A4 A3 3.5 3.5 3.5 A3 3.0 3.0 3.0 2.5 2.5 2.5 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 simulation # simulation # simulation # 4.0 4.0 4.0 3.5 3.5 3.5 A4 A4 3.0 3.0 3.0 *Delta method to approximate the 2.5 2.5 2.5 SE using variances and covariance 0 100 200 300 400 500 0 100 200 300 400 500 0 100 200 300 400 500 of EMAX and ED50 simulation # simulation # simulation # White line = True value 17