Bayesian evidence synthesis in drugdevelopment and comparativeeffectiveness research

David Ohlssen (Novartis Pharmaceticals Corporation)

Introduction Evidence synthesis in drug development

The ideas and principles behind evidence synthesis date back to the work of Eddy et al; 1992

However, wide spread application has been driven by the need for quantitative health technology assessment:• cost effectiveness • comparitive effectiveness

Ideas often closely linked with Bayesian principles and methods:• Good decision making should ideally be based on all relevant

information• MCMC computation

Recent developments in comparative effectiveness

Health agencies have increasing become interested in health technology assessment and the comparative effectiveness of various treatment options

Statistical approaches include extensions of standard meta-analysis models allowing multiple treatments to be compared

FDA Partnership in Applied Comparative Effectiveness Science (PACES) -including projects on utilizing historical data in clinical trials and subgroup analysis

Aims of this talkEvidence synthesis

Introduce some basic concepts Illustration through a series of applications:

• Motivating public health example• Meta-analysis and Network meta-analysis• Using historical data in the design and analysis of clinical trials• Extrapolation• Subgroup analysis

Focus on principles and understanding of critical assumptions rather than technical details

Basic conceptsFramework and Notation for evidence synthesis

Y1 Y2 YS Y1,..,YS Data from S sources

1,…, SSource-specific parameters/effects of interest(e.g. a mean difference)

Question related to 1,…, S

(e.g. average effect, or effect in a new study)

1

2

S?

Strategies for HIV screening

Ades and Cliffe (2002)

HIV: synthesizing evidence from multiple sources

Aim to compare strategies for screening for HIV in pre-natal clinics:• Universal screening of all women, • or targeted screening of current injecting drug users (IDU) or women

born in sub-Saharan Africa (SSA)

Use synthesis to determine the optimal policy

Key parametersAdes and Cliffe (2002)

a- Proportion of women born in sub-Saharan Africa (SSA)

b Proportion of women who are intravenous drug users (IDU)

c HIV infection rate in SSA

d HIV infection rate in IDU

e HIV infection rate in non-SSA, non-IDU

f Proportion HIV already diagnosed in SSA

g Proportion HIV already diagnosed in IDU

h Proportion HIV already diagnosed in non-SSA, non-IDU

NO direct evidence concerning e and h!

A subset of some of the data used in the synthesisAdes and Cliffe (2002)

HIV prevalence, women not born in SSA,1997-8

[db + e(1 − a − b)]/(1 − a) 74 / 136139

Overall HIV prevalence in pregnant women, 1999

ca + db + e(1 − a − b) 254 / 102287

Diagnosed HIV in SSA women as a proportion of all diagnosed HIV, 1999

fca/[fca + gdb + he(1 − a − b)] 43 / 60

Implementation of the evidence synthesisAdes and Cliffe (2002)

The evidence was synthesized by placing all data sources within a single Bayesian model

Easy to code in WinBUGS

Key assumption – consistency of evidence across the different data sources

Can be checked by comparing direct and indirect evidence at various “nodes” in the graphical model (Conflict p-value)

Meta-analysis and network meta-analysis

Why use Bayesian statistics for meta-analysis?

Natural approach for accumulating data / meta-analysis

Unified modelling and the ability to explore a wide range of modelling structure • Synthesis of evidence from multiple sources / multiple treatments

Formal incorporation of other sources of evidence by utilizing prior distributions for modelling unknowns. e.g.• Ability to incorporate prior information regarding background event

rates• Ability to model between-study variability properly in random effects

models

Probability statements about true effects of treatment easier to understand than confidence intervals and p-values

Bayesian random effects meta-analysis for summary data

Let yi denote the observed treatment effect in trial i and si2 be the corresponding estimated standard error

yi | i ~ N(i, si2)

i ~ N(m, t2)

Add prior distributions for unknowns:

m ~ N(?, ?)• Heterogeneity

t ~ halfN(0, ?)

t ~ Unif(0, ?)

Carlin JB, Meta-analysis for 2x2 tables: a Bayesian approach. Statistics in Medicine 1992; 11: 141-58

Bayesian method - extending the basic model

Characterizing heterogeneity and prediction (See Higgins et al; 2009)• Heterogeneity: quantification – but not homogeneity test• Mean effect: important, but incomplete summary• Study effect: maybe of interest, if studies distinguishable• Prediction: effect in new study most relevant and complete

summary (predictive distribution)

Flexibility• Alternative scales and link function - see Warn et al (2002)• Flexible random effects distributions – see Lee et al (2007) and

Muthukumarana (2012)• Combining individual patient data with aggregate data - see Sutton

et al (2008)• Subgroup analysis – see Jones et al (2011)• Multiple treatments and network meta-analysis-

Motivation for Network Meta-Analysis

There are often many treatments for health conditions

Published systematic reviews and meta-analyses typically focus on pair-wise comparisons• More than 20 separate Cochrane reviews for adult smoking

cessation• More than 20 separate Cochrane reviews for chronic asthma in

adults

An alternative approach would involve extending the standard meta-analysis techniques to accommodate multiple treatment

This emerging field has been described as both network meta-analysis and mixed treatment comparisons

15

Bayesian Network Meta-Analysis

Systematic reviews are considered standard practice to inform evidence-based decision-making regarding efficacy and safety

Bayesian network meta-analysis (mixed treatment comparisons) have been presented as an extension of traditional MA by including multiple different pairwise comparisons across a range of different interventions

Several Guidances/Technical Documents recently published

Treatment comparison representation

17

A PA PA PA PA DA D

B PB PB PB CB CB D

A vs. B vs. C vs. D vs. P

Treatment comparison representation

18

A PA PA PA PA DA D

B PB PB PB CB CB D

A B

D

CP

A vs. B vs. C vs. D vs. P

Treatment comparison representation

19

A PA PA PA PA DA D

B PB PB PB CB CB D

A B

D

CP

Network Meta-Analysis(NMA)

A vs. B vs. C vs. D vs. P

Treatment comparison representation

20

A PA PA PA PA DA D

B PB PB PB CB CB D

A B

D

CP

Network Meta-Analysis(NMA)

A vs. B vs. C vs. D vs. P

Indirect comparisonDirect comparison

Network meta-analysis – key assumptions

Three key assumptions (Song et al., 2009):

Homogeneity assumption – Studies in the network MA which compare the same treatments must be sufficiently similar.

Similarity assumption – When comparing A and C indirectly via B, the patient populations of the trial(s) investigating A vs B and those investigating B vs C must be sufficiently similar.

Consistency assumption – direct and indirect comparisons, when done separately, must be roughly in agreement.

Network meta-analysisTrelle et al (2011) - Cardiovascular safety of non-steroidal anti-inflammatory drugs:

Primary Endpoint was myocardial infarction

Data synthesis 31 trials in 116 429 patients with more than 115 000 patient years of follow-up were included.

A Network random effects meta-analysis were used in the analysis

Critical aspect – the assumptions regarding the consistency of evidence across the network

How reasonable is it to rank and compare treatments with this technique?

Trelle, Reichenbach, Wandel, Hildebrand, Tschannen, Villiger, Egger, and Juni. Cardiovascular safety of non-steroidal anti-inflammatory drugs network meta-analysis. BMJ 2011; 342: c7086. Doi: 10.1136/bmj.c7086

Poisson network meta-analysis modelBased on the work of Lu and Ades (LA) (2006 & 2009)

μj is the effect of the baseline treatment b in trial i and δibk is the trial-specific treatment effect of treatment k relative to treatment to b (the baseline treatment associated with trial i)

Note baseline treatments can vary from trial to trial Different choices for µ’s and ’s. They can be: common (over studies),

fixed (unconstrained), or “random”

Consistency assumptions required among the treatment effects

Prior distributions required to complete the model specification

b is the control treatment associated with trial i

Results from Trelle et alMyocardial infarction analysis

25

Treatment RR estimate lower limit upper limitCelecoxib 1.35 0.71 2.72Diclofenac 0.82 0.29 2.20Etoricoxib 0.75 0.23 2.39Ibuprofen 1.61 0.50 5.77

Lumiracoxib 2.00 0.71 6.21Naproxen 0.82 0.37 1.67Rofecoxib 2.12 1.26 3.56

Authors' conclusion: Although uncertainty remains, little evidence exists to suggest that any of the investigated drugs are safe in cardiovascular terms. Naproxen seemed least harmful.

Relative risk with 95% confidence interval compared to placebo

Comments on Trelle et al

Drug doses could not be considered (data not available).

Average duration of exposure was different for different trials.

Therefore, ranking of treatments relies on the strong assumption that the risk ratio is constant across time for all treatments

The authors conducted extensive sensitivity analysis and the results appeared to be robust

Two way layout via MAR assumption An alternative way to parameterize proposed by Jones et al (2011) and Piephoetal et

al (2012) uses a classical two-way (TW) linear predictor with main effects for treatment and trial.

Both papers focus on using the two-way model in the classical framework. By using the MAR property a general approach to implementation in the Bayesian framework can be formed

All studies can in principle contain every arm, but in practice many arms will be missing. As the network meta-analysis model implicitly assume MAR (Lu and Ades; 2009) a common (though possibly missing) baseline treatment can be assumed for every study (Hong and Carlin; 2012)

Comments on implementation and practical advantages

In WinBUGS include every treatment in every trial with missing outcome cells for missing treatments

Utilize a set of conditional univariate normal distributions to form the multivariate normal (this speeds up convergence)

The parameterization has several advantages when forming priors:• In the Lu and Ades model, default “non-informative” priors must be used

as the trial baseline parameters are nuisance parameters with no interpretation

• In the two-way model an informative prior for a single treatment baseline treatment can be formed as each trial has the same parameterization

• In the two way model there is much greater control over non-informative priors. This can be valuable when you have rare safety events asymmetry in prior information can potentially lead to a bias

Full multivariate meta-analysis

Instead of associating a concurrent control parameter with each study, an alternative approach is to place random effects on every treatment main effect

This creates a so called multivariate meta-analysis

29

MI and stroke results from Trelle et alComparing LA FE RE model with the TW RE model and MV RE

Discussion of full multivariate meta-analysis modelAllows borrowing of strength across baseline as every treatment is considered random

Therefore, in rare event meta-analysis, incorporates trials with zero total events through the random effects

No consistency relations to deal with!

Priors on the variance components can be formed using inverse Wishart or using Cholesky decomposition

Breaks the concurrent control structure so automatically will introduce some confounding

Future directionsNetwork meta-analysis with multiple outcomes

•Sampling model (multinomial?)•Borrow strength across treatment effects•Surrogate outcome meta-analysis combined with a network meta-analysis

Network meta-analysis with subgroup analysis

Combining network meta-analysis; meta-analysis of subgroups and multivariate meta-analysis

More work on informative priors for variance components and baseline parameters

Use of Historical controls

IntroductionObjective and Problem Statement

Design a study with a control arm / treatment arm(s)

Use historical control data in design and analysis

Ideally: smaller trial comparable to a standard trial

Used in some of Novartis phase I and II trials

Design options

• Standard Design: “n vs. n”

• New Design: “n*+(n-n*) vs. n” with n* = “prior sample size”

How can the historical information be quantified?

How much is it worth?

The Meta-Analytic-Predictive ApproachFramework and Notation

Y1 Y2 YH

Y1,..,YH Historical control data from H trials

1,…, H

Control “effects” (unknown)

?‘Relationship/Similarity’ (unknown)no relation… same effects

*Effect in new trial (unknown)Design objective: [ * | Y1,…,YH ]

Y*Data in new study(yet to be observed)

1

2

H?

*

Y*

Example – meta-analytic predictive approach to form priors Application

prior information for control group in new study, corresponding to prior sample size n*

Random-effect meta-analysis

Bayesian setup-using historical control data

Meta Analysis of Historical Data Study AnalysisObserved Control Response

Rates

Historical Trial 1

Historical Trial 2

Historical Trial 3

Historical Trial 4

Historical Trial 5

Historical Trial 6

Historical Trial 7

Historical Trial 8

Meta-Analysis

Predictive Distribution of Control Response Rate in a

New Study

Bayesian Analysis

Observed Control

data

Observed Drugdata

Prior Distribution of Control Response

Rate

Prior Distribution

of drug response

rate

Placebo Drug

Posterior Distribution of Difference in Response

Posterior Distribution of Control Response Rate

Posterior Distribution of Drug Response Rate

Utilization in a quick kill quick win PoC Design

With pPlacebo = 0.15, 10000 runs

Scenario

First interim Second interim Final Overall power

Stop for efficacy

Stop for futility

Stop for efficacy

Stop for futility

Claim efficacy

Fail  

d = 0 1.6% 49.0% 1.4% 26.0% 0.2% 21.9% 3.2%

d = 0.2 33.9% 5.1% 27.7% 3.0% 8.8% 21.6% 70.4%

d = 0.5 96.0% 0.0% 4.0% 0.0% 0.0% 0.0% 100.0%

1st Interim

... ≥ 90%

2nd Interim

... ≥ 90%

Final analysis

... > 50%Negative PoC if P(d < 0.2)...

... ≥ 70% ... ≥ 50% ... ≥ 50%Positive PoC if

P(d ≥ 0.2)...

With N=60, 2:1 Active:Placebo, IA’s after 20 and 40 patients

R package available for design investigation

Extrapolation

Thanks to Roland Fisch

General Background: EMA Concept Paper on Extrapolation

EMA produced a “Concept paper on extrapolation of efficacy and safety in medicine development”:

A specific focus on Pediatric Investigation Plans : ‘Extrapolation from adults to children is a typical example ...’

Bayesian methods mentioned:• ‘could be supported by 'Bayesian' statistical approaches’

Alternative Approaches:- No extrapolation: full development program in the target population. - Partial extrapolation: reduced study program in target population

depending on magnitude of expected differences and certainty of assumptions.

- Full extrapolation: some supportive data to validate the extrapolation concept.

Adobe Acrobat Document

Adult data Bayesian meta-analytic predictive approachModel

Mixed effect logistic regression model

Yi ~ Binomial( Ni , πi )logit( πi ) = μ + i + xi β

Study i, Yi = number of events, Ni = number of patients, πi = event rate

•μ: intercept• i ~ N(0, σ2): random study effect

•xi : design matrix (Study level covariates)

The Meta-Analytic-Predictive ApproachFramework and Notation

YH

σ

β

μ i

yi

*

xi

x* ni

n

Yrepyobs

Subgroup analysis

Based on Jones, Ohlssen, Neuenschwander, Racine, Branson (2011)

Introduction to Subgroup analysis

For biological reasons treatments may be more effective in some populations of patients than others• Risk factors• Genetic factors • Demographic factors

This motivates interest in statistical methods that can explore and identify potential subgroups of interest

45

Challenges with exploratory subgroup analysisrandom high bias - Fleming 2010

Hazard Ratio Risk of Mortality Analysis North Central Intergroup Group Treatment Study Group Study # 0035 (n = 162) (n = 619)

All patients 0.72 0.67

Female 0.57 0.85Male 0.91 0.50

Young 0.60 0.77Old 0.87 0.59

Effects of 5-Fluorouracil Plus Levamisole on PatientSurvival Presented Overall and Within Subgroups, by Sex and Age*

Assumptions to deal with extremesJones et al (2011)

Similar methods to those used when combining historical data

However, the focus is on the individual subgroup parameters g1,......,gG rather than the prediction of a new subgroup

1) Unrelated Parameters g1,......,gG (u) Assumes a different treatment effect in each subgroup

2) Equal Parameters g1=...= gG (c)

Assumes the same treatment effect in each subgroup

3) Compromise. Effects are similar/related to a certain degree (r)

Comments on shrinkage estimation

This type of approach is sometimes called shrinkage estimation

Shrinkage estimation attempts to adjust for random high bias

When relating subgroups, it is often desirable and logical to use structures that allow greater similarity between some subgroups than others

A variety of possible subgroup structures can be examined to assess robustness

Subgroup analysis– Extension to multiple studies Data summary from several studies

• Subgroup analysis in a meta-analytic context

• Efficacy comparison T vs. C

• Data from 7 studies

• 8 subgroups• defined by 3 binary base-

line covariates A, B, C

• A, B, C high (+) or low (-)

• describing burden of disease (BOD)

• Idea: patients with higher BOD at baseline might show better efficacy

Graphical model Subgroup analysis involving several studies

g1

g2gG?

12 S

?Y1

Y2

YS

Y...

Y1,..,YS Data from S studies

Subgroup parametersg1,…, gG

• Main parameters of interest• Various modeling structures can be

examined

Study-specific parameters1,…, S

• Parameters allow data to be combined from multiple studies

Extension to multiple studiesExample 3: sensitivity analyses across a range of subgroup structures

51 | Evidence synthesis in drug development

• 8 subgroups• defined by 3 binary base-line covariates

A, B, C

• A, B, C high (+) or low (-)

• describing burden of disease (BOD)

SummarySubgroup analysis

Important to distinguish between exploratory subgroup analysis and confirmatory subgroup analysis

Exploratory subgroup analysis can be misleading due to random high bias

Evidence synthesis techniques that account for similarity among subgroups will help adjust for random high bias

Examine a range of subgroup models to assess the robustness of any conclusions

Overall Conclusions

• There is general agreement that good decision making should be based on all relevant information

• However, this is not easy to do in a formal/quantitative way

• Evidence synthesis

- offers fairly well-developed methodologies

- has many areas of application

- is particularly useful for company-internal decision making (we have used and will increasingly use evidence synthesis in our phase I and II trials)

- has become an important tool when making public health policy decisions

References

Evidence Synthesis/Meta-Analysis DerSimonian, Laird (1986). Meta-analysis in clinical trials. Controlled Clinical Trials, 7;

177-88Gould (1991). Using prior findings to augment active-controlled trials and trials with

small placebo groups. Drug Information J. 25 369--380.Normand (1999). Meta-analysis: formulating, evaluating, combining, and reporting

(Tutorial in Biostatistics). Statistics in Medicine 18: 321-359.See also Letters to the Editor by Carlin (2000) 19: 753-59, and Stijnen (2000) 19:759-761

Spiegelhalter et al. (2004); see main referenceStangl, Berry (eds) (2000). Meta-analysis in Medicine in Health Policy. Marcel DekkerSutton, Abrams, Jones, Sheldon, Song (2000). Methods for Meta-analysis in Medical

Research. John Wiley & Sons

Trelle et al., “Cardiovascular safety of non-steroidal anti-inflammatory drugs: network non-steroidal anti-inflammatory drugs: network meta-analysis,” BMJ 342 (January 11, 2011): c7086-c7086.

Meta-analysis and network meta-analysisCarlin J. Meta-analysis for 2 2 tables: A Bayesian approach. Statistics in Medicine 1992; 11(2):141–158, doi:10.1002/sim.4780110202.

Smith TC, Spiegelhalter DJ, Thomas A. Bayesian approaches to random-effects meta-analysis: A comparative study. Statistics in Medicine 1995; 14(24):2685–2699, doi:10.1002/sim.4780142408.

Warn D, Thompson S, Spiegelhalter D. Bayesian random effects meta-analysis of trials with binary outcomes: methods for the absolute risk difference and relative risk scales. Statistics in Medicine 2002; 21(11):1601–1623, doi:10.1002/sim.1189.

Lambert PC, Sutton AJ, Burton PR, Abrams KR, Jones DR. How vague is vague? a simulation study of the impact of the use of vague prior distributions in MCMC using WinBUGS. Statistics in Medicine 2005; 24(15):2401–2428, doi:10.1002/sim.2112.

Turner RM, Davey J, Clarke MJ, Thompson SG, Higgins JP. Predicting the extent of heterogeneity in meta-analysis, using empirical data from the Cochrane Database of Systematic Reviews. International journal of epidemiology 2012; 41(3):818–827.

Sutton A, Kendrick D, Coupland C. Meta-analysis of individual-and aggregate-level data. Statistics in Medicine 2008; 27(5):651–669, doi:10.1002/sim.2916.

Turner R, Spiegelhalter D, Smith G, Thompson S. Bias modelling in evidence synthesis. Journal of the Royal Statistical Society: Series A(Statistics in Society) 2009; 172:21–47.

Lee K, Thompson S. Flexible parametric models for random-effects distributions. Statistics in Medicine 2007; 27(3):418–434.

Muthukumarana S, Tiwari RC. Meta-analysis using Dirichlet process. Statistical Methods in Medical Research Jul 2012; doi:10.1177/0962280212453891.

Jones HE, Ohlssen DI, Neuenschwander B, Racine A, Branson M. Bayesian models for subgroup analysis in clinical trials. Clinical Trials Apr 2011; 8(2):129–143, doi:10.1177/1740774510396933.

Turner RM, Davey J, Clarke MJ, Thompson SG, Higgins JP. Predicting the extent of heterogeneity meta-analysis, using empirical data from the Cochrane Database of Systematic Reviews. Internationalj ournal of epidemiology 2012; 41(3):818–827.

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Historical Controls

Ibrahim, Chen (2000). Power prior distributions for regression models.Statistical Science, 15: 46-60

Neuenschwander, Branson, Spiegelhalter (2009). A note on the power prior. Statistics in Medicine, 28: 3562-3566

Neuenschwander, Capkun-Niggli, Branson, Spiegelhalter. (2010). SummarizingHistorical Information on Controls in Clinical Trials. Clinical Trials, 7: 5-18

Pocock (1976). The combination of randomized and historical controls in clinical trials. Journal of Chronic Diseases, 29: 175-88

Spiegelhalter et al. (2004); see main referenceThall, Simon (1990). Incorporating historical control data in planning phase II

studies. Statistics in Medicine, 9: 215-28

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a three-level hierarchical mixture model. Biometrics, 60: 418-26Davis, Leffingwell (1990). Empirical Bayes estimates of subgroup effects in clinical trial.

Controlled Clinical Trials, 11: 37-42Dixon, Simon (1991). Bayesian subgroup analysis. Biometrics, 47: 871-81Fleming (2010), “Clinical Trials: Discerning Hype From Substance,” Annals of Internal

Medicine 153:400 -406.Hodges, Cui, Sargent, Carlin (2007). Smoothing balanced single-error terms Analysis of

Variance. Technometrics, 49: 12-25Jones, Ohlssen, Neuenschwander, Racine, Branson (2011). Bayesian models for subgroup

analysis in clinical trials. Clinical Trials Clinical Trials 8 129 -143Louis (1984). Estimating a population of parameter values using Bayes and empirical Bayes

methods. JASA, 79: 393-98

Pocock, Assman, Enos, Kasten (2002). Subgroup analysis, covariate adjustment and baseline comparisons in clinical trial reporting: current practic eand problems. Statistics in Medicine, 21: 2917–2930

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Acknowledgements

Stuart Bailey ,Björn Bornkamp, Roland Fisch, Beat Neuenschwander, Heinz Schmidli, Min Wu, Andrew Wright