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Related Concept Videos

Confidence Intervals01:21

Confidence Intervals

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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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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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Prediction Intervals01:03

Prediction Intervals

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The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y. 
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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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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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Related Experiment Video

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An R-Based Landscape Validation of a Competing Risk Model
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Precise confidence intervals of regression-based reference limits: Method comparisons and sample size requirements.

Gwowen Shieh1

  • 1Department of Management Science, National Chiao Tung University, Hsinchu, 30010, Taiwan, ROC.

Computers in Biology and Medicine
|November 4, 2017
PubMed
Summary
This summary is machine-generated.

This study introduces exact confidence intervals for regression-based reference limits, offering superior accuracy over approximate methods. New sample size procedures are also presented for precise interval estimation in biological and medical research.

Keywords:
PercentilePrecisionQuantileReference limitSample size

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Area of Science:

  • Biostatistics
  • Medical Informatics
  • Quantitative Biology

Background:

  • Covariate-dependent reference limits are crucial for interpreting quantitative measurements in biology and medicine.
  • Existing methods for regression-based reference limits often involve simplifications and have limited applicability.
  • Accurate confidence intervals and sample size determination are essential for reliable reference limit studies.

Purpose of the Study:

  • To develop and present exact confidence intervals for regression-based reference limits.
  • To compare the performance of exact intervals against commonly used approximate methods.
  • To introduce novel, optimal sample size procedures for precise interval estimation in diverse regression-based studies.

Main Methods:

  • Derivation of exact confidence intervals for regression-based reference limits.
  • Comparative analysis of exact versus approximate interval methods across various model configurations.
  • Development of sample size procedures based on the ratio of confidence interval width to reference interval width, incorporating covariate features.

Main Results:

  • Approximate interval methods, particularly those assuming normal distribution, yield inaccurate confidence limits.
  • Exact confidence intervals demonstrate superior one- and two-sided coverage performance compared to approximate methods.
  • The proposed sample size procedures effectively integrate key factors, including covariate characteristics, for optimized precision.

Conclusions:

  • Exact interval estimation offers significant theoretical and practical advantages over approximate methods for regression-based reference limits.
  • The developed sample size procedures are suitable for a wide range of regression-based reference limit studies with varying configurations.
  • The study provides practical tools and algorithms to enhance data analysis and research design in this field.