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Related Concept Videos

Poisson Probability Distribution01:09

Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
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...
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...
One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

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:
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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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Related Experiment Video

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Sample size calculations for noninferiority trials with Poisson distributed count data.

Kathrin Stucke1, Meinhard Kieser

  • 1Institute of Medical Biometry and Informatics, University of Heidelberg, Im Neuenheimer Feld 305, D-69120 Heidelberg, Germany.

Biometrical Journal. Biometrische Zeitschrift
|February 13, 2013
PubMed
Summary

New sample size formulas accurately estimate required participants for clinical trials using Poisson data, ensuring reliable noninferiority testing for conditions like multiple sclerosis and migraine.

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Medical Statistics

Background:

  • Clinical trials frequently utilize Poisson distributed count data for primary outcomes, such as relapse counts or attack frequency.
  • Noninferiority testing is crucial for evaluating new treatments against established ones in various medical fields.

Purpose of the Study:

  • To develop and validate approximate sample size formulas for noninferiority tests with Poisson outcomes.
  • To consider unequal follow-up schemes and noninferiority margins expressed as differences or ratios.

Main Methods:

  • Utilized asymptotic tests based on restricted or unrestricted maximum likelihood estimators for Poisson rates.
  • Evaluated exact Type I error rates and powers of the proposed tests.
  • Examined the accuracy of the approximate sample size formulas across different scenarios.

Main Results:

  • The test statistic using restricted maximum likelihood estimators (for difference tests) and log-transformed maximum likelihood estimators (for ratio tests) demonstrated favorable Type I error control.
  • Approximate sample size formulas exhibited high accuracy, even for small sample sizes.
  • The formulas provided power values close to the desired levels, confirming their utility.

Conclusions:

  • Recommended test statistics offer reliable Type I error control for practical noninferiority trials with Poisson data.
  • The developed approximate sample size formulas are accurate and efficient, aiding in the design of clinical studies.
  • These methods are applicable to diverse clinical trial settings, including anesthesia studies.