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Related Concept Videos

Sample Size Calculation01:19

Sample Size Calculation

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...
Testing a Claim about Population Proportion01:24

Testing a Claim about Population Proportion

A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...
Margin of Error01:27

Margin of Error

The margin of error is also called the maximum error of an estimate. The margin of error is the maximum possible or expected difference between the observed sample parameter value and the actual population parameter value. For proportion, it is the maximum difference between the value of sample proportion obtained from the data and the true value of population proportion. As the true value of the population parameter is not known, the margin of error is calculated using the sample statistic.
Sample Proportion and Population Proportion01:20

Sample Proportion and Population Proportion

Collecting samples or responses from an entire population takes significant time and effort, so a researcher collects responses from only a sample of that population. Suppose a study needs to collect information about a specific mobile application. After sample collection, the researcher analyzes the data and discovers that most individuals in the sample use that specific mobile application. The sample proportion measures the number of individuals in a sample who either use or don't use the...
Binomial Probability Distribution01:15

Binomial Probability Distribution

A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
Bonferroni Test01:10

Bonferroni Test

The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...

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Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems
07:41

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

Published on: July 30, 2019

Bayesian sample size calculation for estimation of the difference between two binomial proportions.

Hamid Pezeshk1, Nader Nematollahi, Vahed Maroufy

  • 11School of Mathematics, Statistics and Computer Science and Center of Excellence in Biomathematics, University of Tehran, Tehran, Iran.

Statistical Methods in Medical Research
|March 26, 2011
PubMed
Summary
This summary is machine-generated.

This study presents a Bayesian method for determining optimal clinical trial sample sizes with binary outcomes. It uses dependent prior distributions to enhance the analysis of success probabilities.

Keywords:
Dirichlet distributionbinomial distributionclinical trialexpected net benefitfully Bayesian approachsample size determination

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Decision Theory

Background:

  • Sample size determination is crucial for efficient clinical trials.
  • Traditional methods may not fully incorporate prior knowledge or account for dependencies.
  • Bayesian approaches offer a flexible framework for sample size optimization.

Purpose of the Study:

  • To develop a decision-theoretic (Bayesian) approach for sample size calculation in clinical trials with binary responses.
  • To extend existing Bayesian methods by incorporating dependent prior distributions for success probabilities.
  • To optimize trial size by maximizing an expected net benefit function.

Main Methods:

  • Utilized a fully Bayesian framework for sample size determination.
  • Modeled binary responses using two binomial distributions.
  • Employed a Dirichlet distribution to represent prior knowledge of success probabilities (p1 and p2).
  • Defined the parameter of interest as the difference in success probabilities (p = p1 - p2).
  • Optimized sample size by maximizing the expected net benefit function.

Main Results:

  • The proposed methodology provides a robust approach to sample size calculation.
  • Incorporating dependent prior distributions offers a more nuanced analysis compared to independent priors.
  • The expected net benefit function guides the selection of an optimal trial size.

Conclusions:

  • The Bayesian decision-theoretic approach offers a valuable tool for sample size optimization in clinical trials.
  • The assumption of dependent priors enhances the accuracy and relevance of sample size recommendations.
  • This method contributes to more efficient and informative clinical trial designs.