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Related Concept Videos

Sample Size Calculation01:19

Sample Size Calculation

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Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
The sample size for the given experiment or sampling effort is fundamental to any study design. Sample size decides the number of...
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One-Way ANOVA: Unequal Sample Sizes01:15

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One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:
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One-Way ANOVA: Equal Sample Sizes01:15

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One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...
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Estimating Population Mean with Known Standard Deviation01:16

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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Wald-Wolfowitz Runs Test II01:17

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The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and...
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Estimating Population Standard Deviation01:26

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Updated: May 20, 2025

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Sample Size and Power Calculations With Win Measures Based on Hierarchical Endpoints.

Huiman Barnhart1,2, Yuliya Lokhnygina1,2, Roland Matsouaka1,2

  • 1Department of Biostatistics and Bioinformatics, Duke University Medical Center, Durham, North Carolina, USA.

Statistics in Medicine
|May 19, 2025
PubMed
Summary
This summary is machine-generated.

New formulas simplify sample size and power calculations for clinical trials analyzing hierarchical endpoints using win measures. This approach reduces reliance on complex simulations and difficult-to-obtain data for accurate study planning.

Keywords:
DOORhierarchical endpointsnet benefitsample size and powerwin oddswin ratio

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Statistical Methods

Background:

  • Win measures (win ratio, win odds, net benefit, DOOR) are increasingly used for hierarchical endpoints in clinical studies.
  • Current sample size and power calculations often rely on cumbersome simulations or hard-to-elicit parameters.
  • Investigator-specified clinically significant win measures and tie probabilities are challenging to determine from existing literature or preliminary data.

Purpose of the Study:

  • To develop novel formulas for sample size and power calculations for four common win measures.
  • To provide methods for computing overall win measures and tie probabilities from readily available marginal specifications.
  • To enable more accessible and justifiable sample size and power estimations for hierarchical endpoints.

Main Methods:

  • Derivation of sample size and power calculation formulas for four win measures.
  • Development of formulas to translate marginal win measures and tie probabilities into overall measures.
  • Extensive simulation studies to validate the accuracy of the derived formulas.

Main Results:

  • The proposed formulas provide accurate power estimations comparable to simulation results for various correlated hierarchical endpoints.
  • The method allows for the evaluation of power based on the number, ordering, and types of endpoints.
  • Formulas are effective across different types of hierarchical endpoints, with slight discrepancies in very high correlation scenarios.

Conclusions:

  • The developed formulas offer a practical and robust alternative to simulation-based calculations for win measures in hierarchical endpoint analysis.
  • These formulas facilitate meaningful and justifiable specification of win measures and tie probabilities.
  • The approach enhances the efficiency and accuracy of sample size and power calculations in clinical trial design.