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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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Related in: MedlinePlus

Prior densities for pC,pE and θ elicited from two individuals (labelled experts A and B) and the densities of the consensus prior distributions agreed by the 15 participating experts as representing their collective opinion. All prior densities were elicited without reference to the MYCYC data. Expert A's distributions were defined by the following responses to the elicitation questions: (i) 0.65, (ii) 0.45, (iii) 0.63 and (iv) 0.05. Expert B's distributions were defined by the following answers: (i) 0.85, (ii) 0.65, (iii) 0.2 and (iv) 0.4.
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fig02: Prior densities for pC,pE and θ elicited from two individuals (labelled experts A and B) and the densities of the consensus prior distributions agreed by the 15 participating experts as representing their collective opinion. All prior densities were elicited without reference to the MYCYC data. Expert A's distributions were defined by the following responses to the elicitation questions: (i) 0.65, (ii) 0.45, (iii) 0.63 and (iv) 0.05. Expert B's distributions were defined by the following answers: (i) 0.85, (ii) 0.65, (iii) 0.2 and (iv) 0.4.

Mentions: Once each expert had completed the questionnaire, they had a one-to-one meeting with a statistical facilitator who fed back plots of the fitted probability density functions (PDFs) and summaries of the marginal prior distributions, including 90% credibility intervals, measures of location (mode and mean) and the strength of prior opinion (standard deviations and prior effective sample sizes (ESSs)). When providing feedback, emphasis was placed on the pC and pE prior distributions, recognising that log-odds ratios can be challenging to interpret. In an attempt to overcome these difficulties, we interpreted the PDF of θ informally in terms of a prior distribution for pE assuming pC is fixed at the individual's prior mode stipulated by question (i) (e.g. Figure 2(d)).


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)

Prior densities for pC,pE and θ elicited from two individuals (labelled experts A and B) and the densities of the consensus prior distributions agreed by the 15 participating experts as representing their collective opinion. All prior densities were elicited without reference to the MYCYC data. Expert A's distributions were defined by the following responses to the elicitation questions: (i) 0.65, (ii) 0.45, (iii) 0.63 and (iv) 0.05. Expert B's distributions were defined by the following answers: (i) 0.85, (ii) 0.65, (iii) 0.2 and (iv) 0.4.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

fig02: Prior densities for pC,pE and θ elicited from two individuals (labelled experts A and B) and the densities of the consensus prior distributions agreed by the 15 participating experts as representing their collective opinion. All prior densities were elicited without reference to the MYCYC data. Expert A's distributions were defined by the following responses to the elicitation questions: (i) 0.65, (ii) 0.45, (iii) 0.63 and (iv) 0.05. Expert B's distributions were defined by the following answers: (i) 0.85, (ii) 0.65, (iii) 0.2 and (iv) 0.4.
Mentions: Once each expert had completed the questionnaire, they had a one-to-one meeting with a statistical facilitator who fed back plots of the fitted probability density functions (PDFs) and summaries of the marginal prior distributions, including 90% credibility intervals, measures of location (mode and mean) and the strength of prior opinion (standard deviations and prior effective sample sizes (ESSs)). When providing feedback, emphasis was placed on the pC and pE prior distributions, recognising that log-odds ratios can be challenging to interpret. In an attempt to overcome these difficulties, we interpreted the PDF of θ informally in terms of a prior distribution for pE assuming pC is fixed at the individual's prior mode stipulated by question (i) (e.g. Figure 2(d)).

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