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Bayesian methods for the design and interpretation of clinical trials in very rare diseases.

Hampson LV, Whitehead J, Eleftheriou D, Brogan P - Stat Med (2014)

Bottom Line: For such studies, the sample size needed to meet a conventional frequentist power requirement is clearly infeasible.A systematic elicitation from clinicians of their beliefs concerning treatment efficacy is used to establish Bayesian priors for unknown model parameters.As sample sizes are small, it is possible to compute all possible posterior distributions of the two success rates.

View Article: PubMed Central - PubMed

Affiliation: Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K.

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Posterior densities for pC and θ given two hypothetical datasets: (1) (SE = 14,FE = 6,SC = 14, FC = 6); (2)(SE = 7,FE = 13,SC = 14,FC = 6).
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fig04: Posterior densities for pC and θ given two hypothetical datasets: (1) (SE = 14,FE = 6,SC = 14, FC = 6); (2)(SE = 7,FE = 13,SC = 14,FC = 6).

Mentions: The face validity of the prior densities in Figure 3 as representations of the group's beliefs after learning the MYCYC data was reviewed. Prior ESSs were presented, calculated using a similar approach to that described in the Appendix. Uncertainty about the relevance of the MYCYC data for learning about pC and p E means that their contribution to the prior distributions of pC and θ is discounted. The ESS of the prior for log{ pC/( 1 − pC)} incorporating the MYCYC data is 17 patients, whereas for θ, the prior ESS is 48 patients on MMF and CYC. Comparing these with the ESSs of the day 1 priors, we see that the 70 MYCYC observations on MMF and CYC have been discounted to 12 and 9 observations for log{ pC/( 1 − pC)} and θ, respectively. Experts were given the option to discard the MYCYC data entirely from their prior distributions, but they chose to retain it. The posterior densities that would result from observing (S E = 14, F E = 6, S C = 14, F C = 6), (S E = 7, F E = 13, S C = 14, F C = 6) and (S E = 7, F E = 3, S C = 7, F C = 3) were presented to the experts to show the impact of hypothetical datasets on their priors. Figure 4 shows posteriors for two of these datasets. The meeting concluded with the experts agreeing to adopt the prior distributions for pE,pC and θ shown in Figure 3 as their consensus priors for the MYPAN trial.


Bayesian methods for the design and interpretation of clinical trials in very rare diseases.

Hampson LV, Whitehead J, Eleftheriou D, Brogan P - Stat Med (2014)

Posterior densities for pC and θ given two hypothetical datasets: (1) (SE = 14,FE = 6,SC = 14, FC = 6); (2)(SE = 7,FE = 13,SC = 14,FC = 6).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4260127&req=5

fig04: Posterior densities for pC and θ given two hypothetical datasets: (1) (SE = 14,FE = 6,SC = 14, FC = 6); (2)(SE = 7,FE = 13,SC = 14,FC = 6).
Mentions: The face validity of the prior densities in Figure 3 as representations of the group's beliefs after learning the MYCYC data was reviewed. Prior ESSs were presented, calculated using a similar approach to that described in the Appendix. Uncertainty about the relevance of the MYCYC data for learning about pC and p E means that their contribution to the prior distributions of pC and θ is discounted. The ESS of the prior for log{ pC/( 1 − pC)} incorporating the MYCYC data is 17 patients, whereas for θ, the prior ESS is 48 patients on MMF and CYC. Comparing these with the ESSs of the day 1 priors, we see that the 70 MYCYC observations on MMF and CYC have been discounted to 12 and 9 observations for log{ pC/( 1 − pC)} and θ, respectively. Experts were given the option to discard the MYCYC data entirely from their prior distributions, but they chose to retain it. The posterior densities that would result from observing (S E = 14, F E = 6, S C = 14, F C = 6), (S E = 7, F E = 13, S C = 14, F C = 6) and (S E = 7, F E = 3, S C = 7, F C = 3) were presented to the experts to show the impact of hypothetical datasets on their priors. Figure 4 shows posteriors for two of these datasets. The meeting concluded with the experts agreeing to adopt the prior distributions for pE,pC and θ shown in Figure 3 as their consensus priors for the MYPAN trial.

Bottom Line: For such studies, the sample size needed to meet a conventional frequentist power requirement is clearly infeasible.A systematic elicitation from clinicians of their beliefs concerning treatment efficacy is used to establish Bayesian priors for unknown model parameters.As sample sizes are small, it is possible to compute all possible posterior distributions of the two success rates.

View Article: PubMed Central - PubMed

Affiliation: Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, U.K.

Show MeSH
Related in: MedlinePlus