OPC

1
OPC

• Koustenis, Breiter

2
General Comments

• Surrogate for Control Group
• Benchmark for Minimally Acceptable Values
• Not a Control Group
• Driven by Historical Data
• Requires Pooling of Different Investigations

3
(continued)

• Periodical Re-Evaluation and Updating the OPCs
• Policy not yet formalized
• Specific Guidance on Methodology to Derive an OPC
• Is urgently needed

4
Bayesian Issues in Developing OPC

• Objective means?
• Derived from (conditionally?) exchangeable
  studies
• Non-informative hyper-prior
• For new Bayesian trials should the OPC be
  expressed as a (presumably tight) posterior
  distribution rather than a fixed number?
• E.g. logit(opc) normal(?,?), etc

5
Does OPC Preempt an Informative Prior?

• An objective informative prior would be derived
  from some of the same trials used to set the OPC.
• This could be dealt with by computing the joint
  posterior distribution of opc and pnew. But this
  would be extremely burdensome to implement for
  anything but an in-house OPC (Breiter).
• A non-informative prior might be least
  burdensome.

6
Bayesian Endpoints

• Superiority
• P(pnew lt opc New Data)
• Non-inferiority
• P(pnew lt opc D New Data)
• PP(pnew lt kopc New Data)

7
OPC as an Agreed upon Standard

• Historical Data ???
• Are evaluated to produce an agreed upon OPC as a
  fixed number with no uncertainty.
• Can I used some of these same data to develop an
  informative prior?
• Probably yes but needs work. The issue is what
  claim will be made for a successful device trial.

8
The prior depends on the Claim

• Claim The complication rate (say) of the new
  device is not larger than (say) the median of
  comparable devices D.
• If the new device is exchangeable with a subset
  of comparable devices then the correct prior
  for the new device is the joint distribution of
  (pnew, opc) prior to the new data.
• If the new device is not exchangeable with any
  comparable devices, then a non-informative prior
  should be used.

9
(continued)

• Claim The complication rate of the new device
  is not greater than a given number (opc D).
• The prior can be based on device trials that are
  considered exchangeable with the planned trial
  (e.g. in house).

10
Logic Chopping?

• Not necessarily. Consider
• The average male U of IA professor is taller
  than the average male professor.
• vs
• The average male U of IA professor is taller than
  511
• How you or I arrived at the 511 is not relevant
  to the posterior probability.

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But perhaps thats a bit disingenuous

• The regulatory goal is clearly to set an OPC that
  will not permit the reduction of average safety
  or efficacy of a class of devices.
• Of necessity, it has to be related to an estimate
  of some sort of average.
• So a claim of superiority or non-inferiority to
  an opc is clearly made at least indirectly with
  reference to a control

12
Would it Make sense to Express the OPC as a PD?

• If the OPC is derived from a hierarchical
  analysis of exchangeable device trials it would
  be possible to compute the predictive
  distribution of xnew.
• Could inferiority (superiority) be defined as the
  observed xnew being below the 5th (above the
  95th) percentile of the predictive distribution?

13
Poolability

• Roseann White

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Binary Response Setup

• i arm (T or C) j center k Ss
• Response variable yijk bernoulli(pij)
• logit(pCj) gj logit(pTj) gj t dj
• Primary t gt -D
• Secondary djs are within clinical tolerance

15
Specify Secondary Goal ?

• If the difference between the treatment group
  varies more than twice the non-inferiority
  margin D
• Possible interpretations
• Random CxT interaction sd lt 2D
• Multiple comparisons max dj dk lt 2D

16
(continued)

• Modify ... Liu et. al...
• Center j is non-inferior t dj gt -kt
• All centers must be non-inferior?
• ID the inferior centers?

17
Why Bootstrap Resample?

• To increase n of Ss in clusters? --- Probably
  invalid
• To generate a better approximation of the null
  sampling distribution? --- OK, but what are the
  details? Do you combine the two arms and
  resample?
• Why not use random-effects Glimmix if you want to
  stick to frequentist methods.

18
Bayesian Analysis

• Ad-hoc pooling is not necessary
• Can produce the posterior distribution of any
  function of the parameters.
• Can use non-informative hyper-priors, so is
  objective data driven.
• Will have the best frequentist operating
  characteristics (which could be calculated by
  simulation.)

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Bayesian Setup

• Define tj t dj (logit of p in the T arm)
• (gj, tj) iid N((mg,mt),S)
• m, S have near non-informative priors
• Primary goal P(mt gt -D Data) (or t-bar)
• Secondary goal(s) ??
• P(st lt 2D Data) (or st )
• For each (j,j) P(tj tj lt 2D Data)
• For each j P(tj mt lt 2D Data)
• For each j P(tj gt -kmt Data)

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Bayes Could Use the Original Metric

• pCj 1/(1exp(-gj)) pTj 1/(1exp(-gj-tj))
• pC 1/(1exp(-mg)) pT 1/(1exp(-mg-mt))
• Primary P(pT pC gt D Data)
• Secondary
• e.g. P(pTj pCj gt k(pT pC ) Data)