Projection from previous studies: A Bayesian and frequentist compromise

Brown, Barry W.; Herson, Jay; Atkinson, E. Neely; Rozell, M. Elizabeth

doi:10.1016/0197-2456(87)90023-7

Cited by 54 publications

(52 citation statements)

References 4 publications

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“…In addition, there will also be uncertainty about the likely magnitude of intervention e ect; allowance for this through speciÿcation of a prior distribution has been discussed in the context of individually randomized trials by many authors (for example [6,7,37]). To incorporate this additional uncertainty, the intervention e ect in expression (6) can be supplied with a prior distribution rather than assumed known, and the resulting distribution for power may be used and summarised as before.…”

Section: Discussionmentioning

confidence: 99%

“…The corresponding distribution for power is then obtained from (5). When constructing a distribution for the future observed ICCˆ 2 and the corresponding power from the distribution for , we would again base the variance ofˆ 2 on , as in (6).…”

Section: Multiple Previous Icc Estimatesmentioning

confidence: 99%

“…This approach to power calculation, which is labelled 'hybrid Neyman-Pearson and Bayesian' by Spiegelhalter et al [5], has been considered in other trial settings [6][7][8][9], and brie y by Spiegelhalter [10] in the context of cluster randomized trials. The uncertainty about the ICC in the planned trial is expressed in the form of a parametric distribution, which results in an estimated distribution for the power of any particular trial design.…”

Section: Introductionmentioning

confidence: 99%

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Allowing for imprecision of the intracluster correlation coefficient in the design of cluster randomized trials

Turner

Prevost

Thompson

2004

Statistics in Medicine

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The sample size required for a cluster randomized trial depends on the magnitude of the intracluster correlation coefficient (ICC). The usual sample size calculation makes no allowance for the fact that the ICC is not known precisely in advance. We develop methods which allow for the uncertainty in a previously observed ICC, using a variety of distributional assumptions. Distributions for the power are derived, reflecting this uncertainty. Further, the observed ICC in a future study will not equal its true value, and we consider the impact of this on power. We implement calculations within a Bayesian simulation approach, and provide one simplification that can be performed using simple simulation within spreadsheet software. In our examples, recognizing the uncertainty in a previous ICC estimate decreases expected power, especially when the power calculated naively from the ICC estimate is high. To protect against the possibility of low power, sample sizes may need to be very substantially increased. Recognizing the variability in the future observed ICC has little effect if prior uncertainty has already been taken into account. We show how our method can be extended to the case in which multiple prior ICC estimates are available. The methods presented in this paper can be used by applied researchers to protect against loss of power, or to choose a design which reduces the impact of uncertainty in the ICC.

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Section: Discussionmentioning

confidence: 99%

Section: Multiple Previous Icc Estimatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Allowing for imprecision of the intracluster correlation coefficient in the design of cluster randomized trials

Turner

Prevost

Thompson

2004

Statistics in Medicine

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show abstract

“…We can consider the difference, aPOW NI − aPOW Sup , between the two powers as the gain from the simultaneous testing of both hypotheses using the S-NI design compared with the design to test for superiority only. The relative gain, , is then defined as From another perspective, Brown et al [16] suggested the use of average power, which for the non-inferiority test is defined as follows:…”

Section: Evaluation Of Powermentioning

confidence: 99%

A hybrid Bayesian‐frequentist approach to evaluate clinical trial designs for tests of superiority and non‐inferiority

Shao

Mukhi

Goldberg

2007

Statistics in Medicine

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Specification of the study objective of superiority or non-inferiority at the design stage of a phase III clinical trial can sometimes be very difficult due to the uncertainty that surrounds the efficacy level of the experimental treatment. This uncertainty makes it tempting for investigators to design a trial that would allow testing of both superiority and non-inferiority hypotheses. However, when a conventional single-stage design is used to test both hypotheses, the sample size is based on the chosen primary objective of either superiority or non-inferiority. In this situation, the power of the test for the secondary objective can be low, which may lead to a large loss of resources. Potentially low reproducibility is another major concern for the single-stage design in phase III trials, because significant findings of confirmatory trials are required to be reproducible. In this paper, we propose a hybrid Bayesian-frequentist approach to evaluate reproducibility and power in single-stage designs for phase III trials to test both superiority and non-inferiority. The essence of the proposed approach is to express the uncertainty that surrounds the efficacy of the experimental treatment as a probability distribution. Then one can use Bayes formula with simple graphical techniques to evaluate reproducibility and power adequacy.

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“…8 Calculating the sample size necessary for a Bayesian RCT depends on the decision scheme that is to be followed after completion of the trial. Several different methods have been proposed, including hybrid frequentist-Bayesian, [9][10][11][12] fully decision theoretic [13][14][15][16] and interval-length based approaches. [17][18][19] Whitehead et al 8 have advocated a variant of the latter which is comparable in simplicity to the frequentist sample size calculation (equation (1)) and includes an analogy to frequentist type I and II errors.…”

Section: Introductionmentioning

confidence: 99%

Bayesian sample size re-estimation using power priors

Brakenhoff

Roes

Nikolakopoulos

2018

Stat Methods Med Res

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The sample size of a randomized controlled trial is typically chosen in order for frequentist operational characteristics to be retained. For normally distributed outcomes, an assumption for the variance needs to be made which is usually based on limited prior information. Especially in the case of small populations, the prior information might consist of only one small pilot study. A Bayesian approach formalizes the aggregation of prior information on the variance with newly collected data. The uncertainty surrounding prior estimates can be appropriately modelled by means of prior distributions. Furthermore, within the Bayesian paradigm, quantities such as the probability of a conclusive trial are directly calculated. However, if the postulated prior is not in accordance with the true variance, such calculations are not trustworthy. In this work we adapt previously suggested methodology to facilitate sample size re-estimation. In addition, we suggest the employment of power priors in order for operational characteristics to be controlled.

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Projection from previous studies: A Bayesian and frequentist compromise

Cited by 54 publications

References 4 publications

Allowing for imprecision of the intracluster correlation coefficient in the design of cluster randomized trials

Allowing for imprecision of the intracluster correlation coefficient in the design of cluster randomized trials

A hybrid Bayesian‐frequentist approach to evaluate clinical trial designs for tests of superiority and non‐inferiority

Bayesian sample size re-estimation using power priors

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