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Related Concept Videos

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 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.
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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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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.
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5-Number Summary01:04

5-Number Summary

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In a dataset, the 5-number summary includes the minimum data value, the data value of the first quartile, the median data value or data value of the second quartile, the data value of the third quartile, and the maximum data value. These 5 data values can be visualized as a box and whisker plot.
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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 Construction for Causally Generalized Estimates With Target Sample Summary Information.

Yi Chen1, Guanhua Chen1, Menggang Yu2

  • 1Department of Biostatistics and Medical Informatics, University of Wisconsin, Madison, Wisconsin, USA.

Statistics in Medicine
|January 22, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a new method to estimate the average treatment effect (ATE) in target populations, even with covariate shift. The approach uses summary data to build confidence intervals, improving causal inference in biomedical research.

Keywords:
causal generalizationconfidence intervalentropy balancing weightsresampling‐based perturbationsummary‐level data

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Causal Inference

Background:

  • Generalizing causal findings like the average treatment effect (ATE) across populations is crucial in biomedical research.
  • Covariate shift, or differences in treatment effect modifiers' distributions, can cause ATEs to vary between source and target populations.
  • Existing weighting methods to estimate target ATEs using summary data face limitations in statistical inference due to reliance on individual-level data for variance calculation.

Purpose of the Study:

  • To propose a novel resampling-based perturbation method for constructing confidence intervals for the estimated target ATE.
  • To enable accurate statistical inference for the target ATE when only summary-level information is available.
  • To address the limitations of previous methods that require individual-level data for variance estimation.

Main Methods:

  • Developed a resampling-based perturbation technique for confidence interval construction.
  • Utilized additional summary-level information from the target sample.
  • Applied the method in both simulation studies and real-world data analyses.

Main Results:

  • The proposed method effectively constructs confidence intervals for the target ATE using only summary-level data.
  • Demonstrated the approach's validity and effectiveness in simulation settings.
  • Validated the method's performance on real-world datasets, confirming its practical applicability.

Conclusions:

  • The resampling-based perturbation method offers a viable solution for statistical inference of the target ATE under covariate shift when only summary data is accessible.
  • This approach overcomes the limitations of prior methods by avoiding the need for individual-level target data.
  • The findings enhance the ability to generalize causal findings in biomedical research using readily available summary statistics.