A Bayesian sequential design using alpha spending function to control type I error

Self Cite

Several researchers have proposed solutions to control type I error rate in sequential designs. The use of Bayesian sequential design becomes more common; however, these designs are subject to inflation of the type I error rate. We propose a Bayesian sequential design for binary outcome using an alpha-spending function to control the overall type I error rate. Algorithms are presented for calculating critical values and power for the proposed designs. We also propose a new stopping rule for futility. Sensitivity analysis is implemented for assessing the effects of varying the parameters of the prior distribution and maximum total sample size on critical values. Alpha-spending functions are compared using power and actual sample size through simulations. Further simulations show that, when total sample size is fixed, the proposed design has greater power than the traditional Bayesian sequential design, which sets equal stopping bounds at all interim analyses. We also find that the proposed design with the new stopping for futility rule results in greater power and can stop earlier with a smaller actual sample size, compared with the traditional stopping rule for futility when all other conditions are held constant. Finally, we apply the proposed method to a real data set and compare the results with traditional designs.

Section: Review Of Bayesian Sequential Designs With Alpha Spending Fumentioning

confidence: 99%

α_{1} (t^{*}) = 2 - 2 normalΦ (z_{\frac{α}{2}} / \sqrt{t^{*}}),

where Φ is the standard normal distribution function. Pocock alpha‐spending function:

α_{2} (t^{*}) = α normall normalo normalg {1 + (e - 1) t^{*}} .

Power alpha‐spending function:

α_{3} (t^{*}) = {(t^{*})}^{γ} α,

where γ is the power. When γ =1, α 3 ( t ∗ ) is also called the uniform alpha‐spending function.…”

Section: Review Of Bayesian Sequential Designs With Alpha Spending Fumentioning

confidence: 99%

“…

P_{u} false(t_{j}^{*} false)

is the critical value that depends on t j and pre‐specified type I error rate. Zhu and Yu() provide an algorithm to calculate

P_{u} false(t_{j}^{*} false)

that uses an alpha‐spending functions to control the overall type I error rate. Stopping for futility: If

P r e false(μ_{T} > μ_{C} false| {\overset{X}{true}}_{T j}, {\overset{X}{true}}_{C j}, n false) ⩽ P_{l}

Section: Review Of Bayesian Sequential Designs With Alpha Spending Fumentioning

confidence: 99%

Section: Review Of Bayesian Sequential Designs With Alpha Spending Fumentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Bayesian sequential design with binary outcome

Zhu

Mercante

2017

Self Cite

A Bayesian sequential design with adaptive randomization for 2‐sided hypothesis test

Zhu

2017

Self Cite

Bayesian sequential and adaptive randomization designs are gaining popularity in clinical trials thanks to their potentials to reduce the number of required participants and save resources. We propose a Bayesian sequential design with adaptive randomization rates so as to more efficiently attribute newly recruited patients to different treatment arms. In this paper, we consider 2-arm clinical trials. Patients are allocated to the 2 arms with a randomization rate to achieve minimum variance for the test statistic. Algorithms are presented to calculate the optimal randomization rate, critical values, and power for the proposed design. Sensitivity analysis is implemented to check the influence on design by changing the prior distributions. Simulation studies are applied to compare the proposed method and traditional methods in terms of power and actual sample sizes. Simulations show that, when total sample size is fixed, the proposed design can obtain greater power and/or cost smaller actual sample size than the traditional Bayesian sequential design. Finally, we apply the proposed method to a real data set and compare the results with the Bayesian sequential design without adaptive randomization in terms of sample sizes. The proposed method can further reduce required sample size.

Probability of success and group sequential designs

Grieve

2023

In this article, I extend the use of probability of success calculations, previously developed for fixed sample size studies to group sequential designs (GSDs) both for studies planned to be analyzed by standard frequentist techniques or Bayesian approaches. The structure of GSDs lends itself to sequential learning which in turn allows us to consider how knowledge about the result of an interim analysis can influence our assessment of the study's probability of success. In this article, I build on work by Temple and Robertson who introduced the idea of conditional probability of success, an idea which I also treated in a recent monograph.