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OPC

OPC. Koustenis, Breiter. General Comments. Surrogate for Control Group Benchmark for Minimally Acceptable Values Not a Control Group Driven by Historical Data Requires Pooling of Different Investigations. (continued). Periodical Re-Evaluation and Updating the OPC’s

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OPC

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  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 OPC’s • 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 < opc | New Data) • Non-inferiority • P(pnew < opc + D | New Data) • PP(pnew < k∙opc | 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 5’11” • How you or I arrived at the 5’11” is not relevant to the posterior probability.

  11. But perhaps that’s 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

  14. Binary Response Setup • i = arm (T or C) j = center k = S’s • Response variable yijk ~ bernoulli(pij) • logit(pCj) = gj logit(pTj) = gj + t+ dj • Primary: t> -D • Secondary: dj’s 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 < 2D • Multiple comparisons: max |dj – dk| < 2D

  16. (continued) • “Modify ... Liu et. al...” Center j is non-inferior: t + dj > -kt All centers must be non-inferior? ID the inferior centers?

  17. Why Bootstrap Resample? • To increase n of S’s 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.)

  19. 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 > -D | Data) (or t-bar) • Secondary goal(s): ?? • P(st < 2D | Data) (or st ) • For each (j,j’) P(|tj – tj’| < 2D | Data) • For each j P(|tj –mt| < 2D | Data) • For each j P(tj > -kmt | Data)

  20. Bayes Could Use the Original Metric • pCj = 1/(1+exp(-gj)) pTj = 1/(1+exp(-gj-tj)) • pC = 1/(1+exp(-mg)) pT = 1/(1+exp(-mg-mt)) • Primary: P(pT – pC > D | Data) • Secondary: • e.g. P(pTj – pCj > k(pT – pC ) | Data)

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