Company Confidential

© 2014 Eli Lilly and Company

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)

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

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

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.

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.

Safety Subteam

• Opportunity/Goals • 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

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

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• “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, 2002

“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

Overview of Some Areas of Implementation

1. Safety signal detection2. Safety signal evaluation3. Meta-analysis for analyzing adverse event data4. Continuously monitor an event of interest in an

ongoing trial5. Joint modeling for evaluation of safety/efficacy

outcomes6. Estimating the dose-response relationship of

adverse events7. Mixed treatment comparisons or network meta-

analysis for safety data8. Safety Trials

Screen shot of Pharmaceutical Statistics Special Issue

www.diahome.org 10

Recent Publications from DIA BSWGPharmaceutical 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

BAYESIAN NETWORK META-ANALYSIS WITH FOCUS IN SAFETY DATA(BASED ON OHLSSEN, ET AL)

Network meta-analysis

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Study 1 Study 2Future study

A PL B A CPL C

PL vs A: BPL vs C

Of Interest Cvs A

Additional Studies

AC: Active Comparator

MTC : Random Effects Model(taken from NICE DSU documents)

1 1 11 ,μ μ +i i i iki t ik t t t

~ ( , ) μ log1ik ik ik

pr binomial n p

p

First arm in study i

kth arm in study Ik=2,..,K

Relative treatment effect between 1st arm and kth arm

treatment effect of 1st arm

1μ ~N(0,1000)

it

1 1

2, ,~ ( , )

i ik i ikt t t tN d

23 13 12

24 14 12

( 1), 1 1, 1

...

s s s s

d d d

d d d

d d d

Consistency assumptionbetween trial standard deviation

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

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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)

• 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

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b is the control treatment associated with trial i

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

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

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

BAYESIAN METHODS FOR DESIGN AND ANALYSIS OF SAFETY TRIALS (BASED ON PRICE, ET AL)

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

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.

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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

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Recommendations: Overview of Bayesian Opportunities for Safety Trials

Opportunity Key References[8] Post approval

studies/Surveillance studiesFDA 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.

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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

Case Example: Sequential Monitoring of AEs, cont.

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)

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

Thank you!

Questions?

Backup

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);  

   

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;

      end;

random delta3 ~ norm(md3, prec=taud) subject = trt3 monitor=(delta3) zero="0"; 

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;      end;   model general(llike);   run;