Bayesian evidence synthesis in drug development and comparative effectiveness research

1. Bayesian evidence synthesis in drugdevelopment and comparativeeffectiveness research David Ohlssen (Novartis Pharmaceticals Corporation)

2. IntroductionEvidence 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

3. 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

4. Aims of this talkEvidence synthesis • Introduce some basic concepts • Illustration through a series of applications: • Motivating public health example • Meta-analysisand 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

5. Basic conceptsFramework and Notation for evidence synthesis Y1 Y2 YS Y1,..,YSData 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) 2 ? S 1

6. Strategies for HIV screening

7. 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

8. 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!

9. 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

10. 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)

11. Meta-analysis and network meta-analysis

12. 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

13. Bayesian random effects meta-analysis for summary data Carlin JB, Meta-analysis for 2x2 tables: a Bayesian approach. Statistics in Medicine 1992; 11: 141-58 Let yi denote the observed treatment effect in trial iand si2 be the corresponding estimated standard error yi| qi ~ N(qi, si2) qi ~ N(m, t2) • Add prior distributions for unknowns: m~ N(?, ?) • Heterogeneity t~ halfN(0, ?) t ~ Unif(0, ?)

14. 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-

15. 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

16. 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

17. A P A P A P A P A D A D B P B P B P B C B C B D Treatment comparison representation A vs. B vs. C vs. D vs. P

18. A P A P A P A P A D A D B P B P B P B C B C B D Treatment comparison representation A vs. B vs. C vs. D vs. P P C A B D

19. A P A P A P A P A D A D B P B P B P B C B C B D Treatment comparison representation A vs. B vs. C vs. D vs. P P C A B D Network Meta-Analysis (NMA)

20. A P A P A P A P A D A D B P B P B P B C B C B D Treatment comparison representation A vs. B vs. C vs. D vs. P P C A B D Direct comparison Indirect comparison Network Meta-Analysis (NMA)

21. 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.

23. 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

24. Poisson network meta-analysis modelBased on the work of Lu and Ades (LA) (2006 & 2009) b is the control treatment associated with trial i μjis the effect of the baseline treatment b in trial iand δibkis 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

25. Results from Trelle et alMyocardial infarction analysis Relative risk with 95% confidence interval compared to placebo 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.

26. 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

27. Two way layout via MAR assumption • An alternative way to parameterize proposed by Jones et al (2011) and Piephoetalet 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)

28. 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

29. 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

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

31. Discussion of full multivariate meta-analysis model Allows 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

32. Future directions • Network 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

33. Use of Historical controls

34. 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?

35. The Meta-Analytic-Predictive ApproachFramework and Notation Y1,..,YHHistorical control data from H trials 1,…, HControl “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) Y1 Y2 YH 2 1 ? H * Y*

36. Example – meta-analytic predictive approach to form priors Application Random-effect meta-analysis prior information for control group in new study, corresponding to prior sample size n*

37. Bayesian setup-using historical control data Meta Analysis of Historical Data Study Analysis Drug Placebo Observed Control Response Rates Prior Distribution of Control Response Rate Observed Control data Prior Distribution of drug response rate Observed Drug data Historical Trial 1 Historical Trial 2 Bayesian Analysis Historical Trial 3 Predictive Distribution of Control Response Rate in a New Study Historical Trial 4 Meta-Analysis Posterior Distribution of Control Response Rate Posterior Distribution of Drug Response Rate Historical Trial 5 Historical Trial 6 Posterior Distribution of Difference in Response Historical Trial 7 Historical Trial 8

38. Utilization in a quick kill quick win PoC Design ... ≥ 50% ... ≥ 70% ... ≥ 50% Positive PoC if P(d ≥ 0.2)... 1st Interim 2nd Interim Final analysis Negative PoC if P(d < 0.2)... ... ≥ 90% ... ≥ 90% ... > 50% With N=60, 2:1 Active:Placebo, IA’s after 20 and 40 patients With pPlacebo = 0.15, 10000 runs

39. R package available for design investigation

40. Extrapolation Thanks to Roland Fisch

41. 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.

42. Adult data Bayesian meta-analytic predictive approach Model • Mixed effect logistic regression model Yi~ Binomial( Ni, πi )logit( πi) = μ + i+ xiβStudy 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)

43. The Meta-Analytic-Predictive ApproachFramework and Notation σ n * YH μ i x* ni Yrep β yobs yi xi

44. Subgroup analysis Based on Jones, Ohlssen, Neuenschwander, Racine, Branson (2011)

45. 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

46. Challenges with exploratory subgroup analysisrandom high bias -Fleming 2010 Effects of 5-Fluorouracil Plus Levamisole on Patient Survival Presented Overall and Within Subgroups, by Sex and Age* Analysis North Central Intergroup Group Treatment Study Group Study # 0035 (n = 162) (n = 619) All patients 0.72 0.67 Female 0.570.85 Male 0.910.50 Young 0.600.77 Old 0.870.59 Hazard Ratio Risk of Mortality

47. 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 • Unrelated Parameters g1,......, gG(u) Assumes a different treatment effect in each subgroup • Equal Parameters g1=...= gG(c)  Assumes the same treatment effect in each subgroup • Compromise. Effects are similar/related to a certain degree (r)

48. 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

49. 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

50. Graphical model Subgroup analysis involving several studies Y1 Y1,..,YS Data from S studies ? Y2 Y... 2 S 1 YS • Study-specific parameters • 1,…, S • Parameters allow data to be combined from multiple studies g2 gG g1 ? • Subgroup parameters • g1,…, gG • Main parameters of interest • Various modeling structures can be examined