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Related Concept Videos

Sampling Plans01:23

Sampling Plans

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Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
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Cluster Sampling Method01:20

Cluster Sampling Method

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Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
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Sample Size Calculation01:19

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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

One-Way ANOVA: Equal Sample Sizes

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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.
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Estimating Population Mean with Unknown Standard Deviation01:22

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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...
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Sample size calculation in three-level cluster randomized trials using generalized estimating equation models.

Jingxia Liu1,2, Graham A Colditz1

  • 1Division of Public Health Sciences, Department of Surgery, Washington University School of Medicine (WUSM), St. Louis, Missouri, USA.

Statistics in Medicine
|July 29, 2020
PubMed
Summary
This summary is machine-generated.

This study extends generalized estimating equations (GEE) for three-level cluster randomized trials (CRTs) with nested data. It provides methods to accurately estimate treatment effects and accounts for unequal cluster sizes, improving implementation science research.

Keywords:
bias-corrected sandwich estimatorcluster randomized trialgeneralized estimating equationnested correlation structurerelative efficiency

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Area of Science:

  • Implementation Science
  • Biostatistics
  • Health Services Research

Background:

  • Three-level cluster randomized trials (CRTs) are increasingly used in implementation science, generating complex nested data structures.
  • Existing methods, like generalized estimating equations (GEE) with a nested exchangeable correlation structure, address two-level clustering but require extension for three levels.

Purpose of the Study:

  • To extend GEE models for analyzing continuous, binary, or count data in three-level CRTs.
  • To derive and evaluate bias-corrected sandwich estimators for improved treatment effect estimation in three-level CRTs.
  • To assess the impact of unequal provider and practice sizes on statistical efficiency and propose adjustments.

Main Methods:

  • Utilized generalized estimating equations (GEE) with a nested exchangeable correlation structure for three-level CRTs.
  • Derived asymptotic variances for treatment effect estimators across different outcome types.
  • Extended two bias-corrected sandwich estimators to the three-level CRT context.
  • Conducted simulation studies to evaluate estimator performance under various provider and practice size distributions.

Main Results:

  • Provided formulas for asymptotic variances and bias-corrected sandwich estimators in three-level CRTs.
  • Quantified the relative efficiency (RE) loss due to unequal provider and practice sizes.
  • Demonstrated the performance of the proposed methods across different size distribution scenarios through simulations.

Conclusions:

  • The proposed GEE-based methods and bias-corrected estimators enhance the analysis of three-level CRTs.
  • Understanding and accounting for unequal cluster sizes is crucial for accurate treatment effect estimation and efficient study design.
  • A method for proposing an increased number of practices to compensate for efficiency loss is presented.