Lower bounds for the expected sample size of sequential procedures for selecting and ranking of binomial and Poisson populations

This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a0) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(×) and suitable region R.Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved for the proposed estimator are derived.Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.

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Common threads between sample size recalculation and group sequential procedures

Pharmaceutical Statistics ◽

10.1002/pst.68 ◽

2003 ◽

Vol 2 (4) ◽

pp. 263-271 ◽

Cited By ~ 9

Author(s):

Todd A. Schwartz ◽

Jonathan S. Denne

Keyword(s):

Sample Size ◽

Group Sequential ◽

Sequential Procedures

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Optimized adaptive enrichment designs for three-arm trials: learning which subpopulations benefit from different treatments

Biostatistics ◽

10.1093/biostatistics/kxz030 ◽

2019 ◽

Author(s):

Jon Arni Steingrimsson ◽

Joshua Betz ◽

Tianchen Qian ◽

Michael Rosenblum

Keyword(s):

Sample Size ◽

Disease Severity ◽

Adaptive Design ◽

Type I Error ◽

Type I ◽

Expected Sample Size ◽

Common Control ◽

Enrichment Designs ◽

Adaptive Enrichment Designs ◽

Standard Designs

Summary We consider the problem of designing a confirmatory randomized trial for comparing two treatments versus a common control in two disjoint subpopulations. The subpopulations could be defined in terms of a biomarker or disease severity measured at baseline. The goal is to determine which treatments benefit which subpopulations. We develop a new class of adaptive enrichment designs tailored to solving this problem. Adaptive enrichment designs involve a preplanned rule for modifying enrollment based on accruing data in an ongoing trial. At the interim analysis after each stage, for each subpopulation, the preplanned rule may decide to stop enrollment or to stop randomizing participants to one or more study arms. The motivation for this adaptive feature is that interim data may indicate that a subpopulation, such as those with lower disease severity at baseline, is unlikely to benefit from a particular treatment while uncertainty remains for the other treatment and/or subpopulation. We optimize these adaptive designs to have the minimum expected sample size under power and Type I error constraints. We compare the performance of the optimized adaptive design versus an optimized nonadaptive (single stage) design. Our approach is demonstrated in simulation studies that mimic features of a completed trial of a medical device for treating heart failure. The optimized adaptive design has $25\%$ smaller expected sample size compared to the optimized nonadaptive design; however, the cost is that the optimized adaptive design has $8\%$ greater maximum sample size. Open-source software that implements the trial design optimization is provided, allowing users to investigate the tradeoffs in using the proposed adaptive versus standard designs.

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