1. Overview of Bayesian Methods for Safety Assessment
Karen L. Price, PhD
Eli Lilly and Company
On behalf of the DIA Bayesian Scientific Working Group (BSWG)

2. Outline Brief overview of DIA BSWG
Overview of use of Bayesian methods for safety assessment
Bayesian network meta-analysis with focus in safety data
Bayesian methods for safety trials
Conclusion

3. Who are we?
Group of representatives from Regulatory, Academia, and Industry, engaging in scientific discussion/collaboration
facilitate appropriate use of the Bayesian approach
contribute to progress of Bayesian methodology throughout medical product development

4. Mission
To facilitate the appropriate use of Bayesian methods and contribute to progress by:
Creating a scientific forum for the discussion and development of innovative methods and tools.
Providing education on best practices for Bayesian methods.
Engaging in dialogue with industry leaders, the scientific community, and regulators.
Fostering diversity in membership and leadership.

5. Opportunity Statement
Bayesian methods provide framework to leverage prior information and data from diverse sources.
Bringing together academic, industrial, and regulatory representatives is essential to overcome hurdles.
Provides opportunity to influence proactively by engaging in scientific discussion.
Improved patient outcomes.

6. Safety Subteam Opportunity/Goals 3 initial areas of focus
Current analytical approaches may be oversimplified and knowledge of/experience with proper methods inadequate
Some statistical challenges include: power, multiplicity, complexity of data, continual assessment, signal refinement
Bayes provides great promise
3 initial areas of focus
Meta-analysis/Evidence Synthesis: chair David Ohlssen
Safety Trials: chair Karen Price
Signal Detection: chair Larry Gould
Initial deliverables: white papers, publications, sessions

7. Some Advantages of Bayesian Methods
Ability to incorporate prior information
Natural for evidence synthesis or meta-analysis
Handling multiplicity through borrowing strength and hierarchical modeling
Appealing in dealing with rare events as the model modulates the extremes
Ability to handle complex problems via unified modeling, taking all the uncertainty into account
Allowing direct probability inferences on different scales

8. “Safety assessment is one area where frequentist strategies have been less applicable. Perhaps Bayesian approaches in this area have more promise.” Chi, Hung, and O’Neill; Pharmaceutical Report, “If I were to predict where Bayesian ideas will have great impact in the years ahead I would highlight drug safety – not only during the development of a drug but also post-marketing.” -- Grieve; Pharmaceutical Statistics, 2007

9. Overview of Some Areas of Implementation
Safety signal detection
Safety signal evaluation
Meta-analysis for analyzing adverse event data
Continuously monitor an event of interest in an ongoing trial
Joint modeling for evaluation of safety/efficacy outcomes
Estimating the dose-response relationship of adverse events
Mixed treatment comparisons or network meta-analysis for safety data
Safety Trials

10. Screen shot of Pharmaceutical Statistics Special Issue

11. Recent Publications from DIA BSWG
Pharmaceutical Statistics Special Issue: Bayesian Methods in Medical Product Development and Regulatory Review
The current state of Bayesian methods in medical product development: Survey results and recommendations from the DIA Bayesian Scientific Working Group: Fanni Natanegara, Beat Neuenschwander, John W. Seaman, Nelson Kinnersley, Cory R. Heilmann, David Ohlssen, George Rochester
Bayesian Methods for Design and Analysis of Safety Trials: Karen Price, H Amy Xia, Mani Lakshminarayanan, David Madigan, David Manner, John Scott, James Stamey, Laura Thompson
Guidance on the implementation and reporting of a drug safety Bayesian network meta-analysis: David Ohlssen, Karen Price, H Amy Xia, Hwanhee Hong, Jouni Kerman, Haoda Fu, George Quartey, Cory Heilmann, Haijun Ma, Bradley Carlin
Use of Historical Control Data for Assessing Treatment Effects in Clinical Trials: Kert Viele, Scott Berry, Beat Neuenschwander, Billy Amzal, Fang Chen, Nathan Enas, Brian Hobbs, Joseph G Ibrahim, Nelson Kinnersley, Stacy Lindborg, Sandrine Micallef, Satrajit Roychoudhury, Laura Thompson
Therapeutic Innovation and Regulatory Science, submitted
Methods and Issues to Consider for Detection of Safety Signals from Spontaneous Reporting Databases. Report of the DIA Bayesian Safety Signal Detection Working Group. Larry Gould, Ted Lystig, Yun Lu, Haoda Fu, Haijun Ma, and David Madigan

12. Bayesian Network Meta-analysis with focus in Safety data (based on Ohlssen, et al)

13. Network meta-analysis
Study 1
Study 2
Future study A PL B C
PL vs A: B
PL vs C
Of Interest Cvs A
Additional Studies
AC: Active Comparator 13

14. MTC : Random Effects Model (taken from NICE DSU documents)
kth arm in study I
k=2,..,K
Relative treatment effect between 1st arm and kth arm
First arm in study i
treatment effect of 1st arm
Consistency assumption
between trial standard deviation

15. Network meta-analysis Trelle et al (2011) Cardiovascular safety of non-steroidal anti-inflammatory drugs
Primary Endpoint was myocardial infarction
Data synthesis 31 trials in patients with more than 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: /bmj.c7086

16. b is the control treatment associated with trial i
Poisson network meta-analysis model Based on the work of Lu and Ades (LA) (2006 & 2009)
μi 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

17. 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

18. Key Aspects of Ohlssen, et al.
Summarizes Bayesian network meta-analysis
Extends the Lu and Ades (LA) model via a variety of alternative model parameterizations
Particularly in the context of rare events, estimation of model parameters can be challenging for LA model
Outcomes can be particularly sensitive to the choice of model, emphasizing need for sensitivity analysis and transparency regarding assumptions/limitations
Highlights benefit Bayesian approach provides for decision making (including with multiple outcomes)
Provides reporting guidelines

19. 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; ) a common (though possibly missing) baseline treatment can be assumed for every study (Hong and Carlin; 2012)
Statistical approaches for conducting network
meta-analysis in drug development†
Byron Jones,a* James Roger,b PeterW. Lane,c Andy Lawton,d Chrissie
Fletcher,e Joseph C. Cappelleri,f Helen Tate,g PatrickMoneuse,h and on
behalf of PSI Health Technology Special Interest Group, Evidence
Synthesis sub-team
Modeling between-trial variance structure in mixed
treatment comparisons
GUOBING LU∗, AE ADES
Biostatistics (2009), 10, 4, pp. 792–805
doi: /biostatistics/kxp032
The Use of Two-Way Linear Mixed Models in Multitreatment
Meta-Analysis
H. P. Piepho,1,∗ E. R. Williams,2 and L. V. Madden3
Pharmaceut. Statist. 2011, –531
DIA

20. Reporting Guidelines
Ohlssen et al provides a checklist for use when conducting a safety meta-analysis
Checklist includes four main sections: Introduction, Methods, Results, and Interpretation.
Each main section includes various items relevant to that section
The user of the table should evaluate each item and can utilize the last two columns to confirm whether or not each item has been addressed and to add any relevant comments
The Introduction section includes items that are specific to the intervention being analyzed along with the meta-analysis objective(s), while the Methods section focuses on aspects associated with the planned modeling and analyses to be conducted. The Results section relates to specific summaries of the data that should be provided. Finally, the Interpretation section enables decision makers utilizing the meta-analyses to appropriately evaluate the results.

21. Bayesian methods for design and analysis of safety trials (based on price, et al)

22. Overview of Paper Reviews challenges associated with safety trials
Describes several opportunities for use of Bayesian methods to enhance safety trials
Discusses several case examples

23. Recommendations: Overview of Bayesian Opportunities for Safety Trials
Opportunity
Key References
[1] Bayesian methods to determine sample size
Adcock; Wang and Gelfand; Brutti, De Santis, and Gubbiotti; Gaydos et al.
[2] Frequent interim analyses
Connor and White et al.
[3] Bayesian Meta-analysis
Spiegelhalter et al.;
Stangl and Berry;
Sutton et al.

24. Recommendations: Overview of Bayesian Opportunities for Safety Trials
Opportunity
Key References
[4] Sequential meta-analysis
Cheng and Madigan;
Higgins, Whitehead, Simmonds; Ibrahim et al.;
Zeggini and Ioannidis 
[5] Borrowing historical information
Berry et al.;
Hobbs et al.
[6] Continuous monitoring of events
Xia et al.;
Yao et al.
[7] Hierarchical modeling
Gelman and Hill;
Gelman et al.;
DuMouchel

25. Recommendations: Overview of Bayesian Opportunities for Safety Trials
Opportunity
Key References
[8] Post approval studies/Surveillance studies
FDA Guidance;
Murray, Carlin, and Lystig
[9] Logistical planning related to enrollment rates and landmark event rate
Gajewski, Simon, and Carlson; Bagiella and Heitjan;
Ying and Heitjan;
Donovan, Elliott, and Heitjan
[10] Bayesian interpretations and predictions
Spiegelhalter;
Berry et al.

26. Case Example: Sequential Monitoring of AEs
Sequential Bayesian methods enable regular updating of knowledge as data accumulate
Cheng and Madigan illustrated this approach with Vioxx
Presented a Bayesian sequential meta-analysis of the placebo-controlled trials
The analysis began with a “family of priors”
Proposed a simple graphical summary of the meta-analysis showing the posterior probability over time that the true relative risk of CVT events exceeds two particular thresholds
The following figure shows the posterior probability that the true relative risk exceeds 1.1 over time
Priors ranged from a “skeptical prior” that represents a priori skepticism that Vioxx causes cardiovascular thrombotic (CVT) adverse events, to a “reference prior” the adopts a neutral position, to a “cautious prior” that represents a prior belief that cardiotoxicity is not so implausible.
The specific events are acute myocardial infarction, unstable angina pectoris, sudden and/or unexplained death, resuscitated cardiac arrest, cardiac thrombus, pulmonary embolism, peripheral arterial thrombosis, peripheral venous thrombosis, ischemic cerebrovascular stroke, stroke (unknown mechanism), cerebrovascular venous thrombosis, and transient ischemic attack.

27. Case Example: Sequential Monitoring of AEs, cont.

28. Moving Forward
Safety Meta-analysis guidance from FDA (draft published, opportunity to comment)
Continued growth in use for signal assessment
Opportunities for increased use for safety trials
Expanded use for evaluation of benefit/risk profile (at least for key benefits/risks)

29. Conclusion
Safety assessment is complex with numerous statistical challenges
DIA BSWG is actively working to ensure the use of Bayesian methods in the context of safety are appropriately used by increasing awareness and providing best practice guidelines
Bayesian methods provide advantages in the context of safety signal assessment

30. Thank you!

31. Questions?

32. Backup

33. MTC Case Example: Code (random effects)
proc mcmc data=b missing=ac nmc=10000 diag=ess outpost=o1; parms sd /slice; parms m; parms sd_m /slice; prior sd sd_m ~ uniform(0, 100); prior m ~ normal(0, prec=0.0001); beginnodata; tau = 1 / (sd * sd); tau_phi_prec = 1 / (sd_m * sd_m); endnodata; random mu ~ norm(m, prec=tau_phi_prec) subject = study monitor=(mu); random d2 ~ normal(0, prec=0.0001) subject = trt2 monitor=(d2);

34. MTC Case Example: Code (random effects)
random delta2 ~ norm(d2, prec=tau) subject = study monitor=(delta2); random d3 ~ normal(0, prec=0.0001) subject = trt3 monitor=(d3) zero="0"; if rep eq 3 then do; taud = tau * 2 * 2 / 3; w2 = delta2 - d2; sw3 = w2 / 3; md3 = d3 + sw3; end; else do; md3 = 0; taud = 1; random delta3 ~ norm(md3, prec=taud) subject = trt3 monitor=(delta3) zero="0";

35. MTC Case Example: Code (random effects)
ph = logistic(mu);   /* control arm */
   model r1 ~ binomial(n1, ph);
ph = logistic(mu + delta2);
   model r2 ~ binomial(n2, ph);
   if rep = 3 then do;
      ph = logistic(mu + delta3);
      llike = lpdfbin(r3, n3, ph);
      end;
   else do;
      llike = 0;
   model general(llike);
   run;