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A curtailed selection procedure for comparing Bernoulli outcomes with a control.

Pinyuen Chen1, Lifang Hsu2

  • 1Department of Mathematics, Syracuse University, Syracuse, NY, USA.

Journal of Biopharmaceutical Statistics
|May 15, 2020
PubMed
Summary

This study introduces a sequential selection procedure for comparing Bernoulli populations based on success probability. The new method efficiently identifies the best population or a subset containing it, using fewer observations than fixed-sample methods.

Keywords:
Indifference zone approachexpected sample sizeintegrated formulationleast favorable configurationsubset selection approachworst configuration

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Area of Science:

  • Statistics
  • Probability Theory
  • Experimental Design

Background:

  • Comparing multiple experimental populations is crucial in scientific research.
  • Traditional fixed-sample-size procedures can be inefficient, requiring a large number of observations.
  • Selecting the best performing population or a subset containing it is a common goal.

Purpose of the Study:

  • To propose a novel sequential selection procedure for comparing Bernoulli populations.
  • To integrate indifference zone and subset selection formulations for robust selection.
  • To develop a procedure that is statistically sound and sample-efficient.

Main Methods:

  • A sequential sampling approach is employed, taking observations one at a time.
  • Populations are eliminated if they are no longer comparable based on success probabilities.
  • The procedure continues until the best population is identified or an upper bound on observations is reached.

Main Results:

  • The proposed sequential procedure meets the same probability requirements as fixed-sample-size procedures.
  • The expected sample size per population is significantly reduced compared to fixed-sample methods.
  • The procedure effectively selects the best Bernoulli population or a subset containing it.

Conclusions:

  • The developed sequential selection procedure offers a more efficient alternative to fixed-sample methods for comparing Bernoulli populations.
  • This method optimizes resource allocation by minimizing the required number of observations.
  • The procedure provides a statistically valid framework for identifying superior experimental populations.