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Related Concept Videos

Confidence Intervals01:21

Confidence Intervals

9.1K
An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...
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Critical Values01:31

Critical Values

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A critical value is a definite value obtained from a particular probability distribution at a predecided confidence level (or a predecided significance level) for a given population parameter. The critical value provides demarcation that separates the sample statistics that are likely to occur from the ones that are unlikely to occur based on the given probability distribution and the population parameter to be estimated. The critical value for normal distribution is obtained from the z...
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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
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Confidence Coefficient01:24

Confidence Coefficient

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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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Exact confidence limits after a group sequential single arm binary trial.

Chris J Lloyd1

  • 1Melbourne Business School, University of Melbourne, Carlton, Victoria, Australia.

Statistics in Medicine
|March 2, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces new exact methods for confidence limits in sequential trials, improving upon existing techniques for treatment efficacy inference. An R-package is available for practical application in nonadaptive designs.

Keywords:
Buehler limitsadaptive trialssufficiency principle

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Statistical Inference

Background:

  • Group sequential single arm designs are frequently used in Phase II trials, attribute testing, and acceptance sampling.
  • Post-trial, full inference on treatment efficacy is desired, particularly when trials recommend further investigation.
  • Exact confidence limits for binary responses are crucial for accurate efficacy assessment.

Purpose of the Study:

  • To develop and evaluate novel exact methods for constructing confidence limits in group sequential single arm designs.
  • To ensure consistency between confidence limits and hypothesis test results, addressing a gap in existing literature.
  • To compare proposed methods against established techniques like Jennison and Turnbull (1983) and Fisher's combination test.

Main Methods:

  • Development of new general results within the theory of exact confidence limits.
  • Proposal of two novel exact methods based on the minimal sufficient statistic.
  • Investigation of methods based on inverting Fisher's combination test and a tie-breaking variant.
  • Performance evaluation across 10 selected nonadaptive sequential designs.

Main Results:

  • The proposed exact methods outperform the Jennison and Turnbull method across various designs.
  • A preferred method is identified based on practical and theoretical advantages.
  • Inverting Fisher's combination test and its variant did not offer sufficient efficiency gains to warrant deviating from the sufficiency principle.

Conclusions:

  • New exact confidence limit methods offer improved performance for sequential single arm trials.
  • The recommended method provides a statistically sound and practically applicable approach for treatment efficacy inference.
  • An R-package is provided to facilitate the application of these methods in nonadaptive sequential designs.