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Related Concept Videos

Bootstrapping01:24

Bootstrapping

The term "bootstrap" originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is small or...
Confidence Interval for Estimating Population Mean01:25

Confidence Interval for Estimating Population Mean

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...
Confidence Intervals01:21

Confidence Intervals

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 confidence...
Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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...
Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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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Related Experiment Video

Updated: Jun 24, 2026

Inverse Probability of Treatment Weighting (Propensity Score) using the Military Health System Data Repository and National Death Index
06:55

Inverse Probability of Treatment Weighting (Propensity Score) using the Military Health System Data Repository and National Death Index

Published on: January 8, 2020

Improving Variance and Confidence Interval Estimation in Small-Sample Propensity Score Analyses: Bootstrap Versus

Baoshan Zhang1,2, Sean M O'Brien1,2, Yuan Wu1

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

Statistics in Medicine
|June 23, 2026
PubMed
Summary
This summary is machine-generated.

For propensity score (PS) methods, sandwich variance estimators perform poorly in small samples. A stratified bootstrap approach is recommended for reliable treatment effect estimation in non-randomized studies with limited data.

Keywords:
bootstrapinverse probability of treatment weightingpropensity scorevariance estimation

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An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

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Last Updated: Jun 24, 2026

Inverse Probability of Treatment Weighting (Propensity Score) using the Military Health System Data Repository and National Death Index
06:55

Inverse Probability of Treatment Weighting (Propensity Score) using the Military Health System Data Repository and National Death Index

Published on: January 8, 2020

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Area of Science:

  • Biostatistics
  • Epidemiology
  • Clinical Trials

Background:

  • Propensity score (PS) methods are crucial for estimating treatment effects in non-randomized studies.
  • Standard variance estimation methods include sandwich and bootstrap, with differing assumptions about PS estimation.
  • Small sample sizes, common in rare disease research and external control trials, challenge the validity of traditional asymptotic methods.

Purpose of the Study:

  • To compare the performance of bootstrap versus sandwich variance and confidence interval (CI) estimators for PS methods.
  • To evaluate the impact of treating PS as fixed versus re-estimating it.
  • To assess estimator performance under various conditions, including small sample sizes and differing prevalences.

Main Methods:

  • Conducted Monte Carlo simulations to compare bootstrap and sandwich estimators.
  • Utilized inverse probability of treatment weighting (IPTW) and augmented inverse probability of treatment weighting (AIPW) estimators.
  • Systematically varied sample sizes, outcome prevalences, and treatment prevalences.

Main Results:

  • Sandwich estimators demonstrated poor performance in small sample sizes.
  • Treating PS as fixed was not consistently conservative.
  • A stratified bootstrap method effectively avoided quasi-separation and showed good performance.

Conclusions:

  • Sandwich estimators are unreliable in small samples when using PS methods.
  • Fixed PS methods do not guarantee conservative estimates.
  • Stratified bootstrap offers a robust alternative for variance estimation in PS methods, especially in small samples.