The Proportional Closeness and the Expected Sample Size of Sequential Procedures for Estimating Tail Probabilities in Exponential Distributions

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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Bias, Precision, and Accuracy of Skewness and Kurtosis Estimators for Frequently Used Continuous Distributions

Symmetry ◽

10.3390/sym12010019 ◽

2019 ◽

Vol 12 (1) ◽

pp. 19 ◽

Cited By ~ 7

Author(s):

Roser Bono ◽

Jaume Arnau ◽

Rafael Alarcón ◽

Maria J. Blanca

Keyword(s):

Social Sciences ◽

Monte Carlo Simulation ◽

Sample Size ◽

Mean Square ◽

Exponential Distributions ◽

Continuous Distributions ◽

Monte Carlo Simulation Study ◽

Normal Distributions ◽

Precision And Accuracy ◽

Skewness And Kurtosis

Several measures of skewness and kurtosis were proposed by Hogg (1974) in order to reduce the bias of conventional estimators when the distribution is non-normal. Here we conducted a Monte Carlo simulation study to compare the performance of conventional and Hogg’s estimators, considering the most frequent continuous distributions used in health, education, and social sciences (gamma, lognormal and exponential distributions). In order to determine the bias, precision and accuracy of the skewness and kurtosis estimators for each distribution we calculated the relative bias, the coefficient of variation, and the scaled root mean square error. The effect of sample size on the estimators is also analyzed. In addition, a SAS program for calculating both conventional and Hogg’s estimators is presented. The results indicated that for the non-normal distributions investigated, the estimators of skewness and kurtosis which best reflect the shape of the distribution are Hogg’s estimators. It should also be noted that Hogg’s estimators are not as affected by sample size as are conventional estimators.

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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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Comparison of a Two-Stage and Three-Stage Interim-Analysis Procedure

Psychological Reports ◽

10.2466/pr0.1992.71.1.3 ◽

1992 ◽

Vol 71 (1) ◽

pp. 3-14 ◽

Cited By ~ 1

Author(s):

John E. Overall ◽

Robert S. Atlas

Keyword(s):

Sample Size ◽

Interim Analysis ◽

Type I Error ◽

Substantial Reduction ◽

Error Rates ◽

Sampling Plan ◽

Type I ◽

Two Stage ◽

Expected Sample Size ◽

Analysis Strategy

A statistical model for combining p values from multiple tests of significance is used to define rejection and acceptance regions for two-stage and three-stage sampling plans. Type I error rates, power, frequencies of early termination decisions, and expected sample sizes are compared. Both the two-stage and three-stage procedures provide appropriate protection against Type I errors. The two-stage sampling plan with its single interim analysis entails minimal loss in power and provides substantial reduction in expected sample size as compared with a conventional single end-of-study test of significance for which power is in the adequate range. The three-stage sampling plan with its two interim analyses introduces somewhat greater reduction in power, but it compensates with greater reduction in expected sample size. Either interim-analysis strategy is more efficient than a single end-of-study analysis in terms of power per unit of sample size.

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