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Related Concept Videos

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...
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,...
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...
Confidence Coefficient01:24

Confidence Coefficient

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 both the...
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...
Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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 't,' or...

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An R-Based Landscape Validation of a Competing Risk Model
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An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Corrected profile likelihood confidence interval for binomial paired incomplete data.

Vivek Pradhan1, Sandeep Menon, Ujjwal Das

  • 1Boston Scientific, 100 Boston Scientific Way, Marlborough, MA 01752, USA.

Pharmaceutical Statistics
|January 9, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces a new profile likelihood method for confidence intervals with incomplete paired binomial data. The new method offers better coverage and shorter intervals compared to existing approaches.

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Area of Science:

  • Biostatistics
  • Clinical Trials
  • Statistical Methods

Background:

  • Clinical trials frequently utilize paired binomial data for endpoints.
  • Confidence intervals are standard for estimating treatment efficacy.
  • Existing methods for incomplete paired binomial data can be overly conservative.

Purpose of the Study:

  • To develop a more accurate confidence interval method for incomplete paired binomial data.
  • To improve upon the methods proposed by Tang et al. (2009).
  • To address issues of overly conservative intervals and large expected confidence interval widths (ECIW).

Main Methods:

  • A profile likelihood-based method was developed.
  • A Jeffreys' prior correction was incorporated.
  • Extensive simulations were used to evaluate performance.
  • Real-world datasets were analyzed for comparison.

Main Results:

  • The proposed method demonstrated improved coverage probability.
  • The new approach resulted in shorter expected confidence interval widths (ECIW).
  • The profile likelihood method with Jeffreys' prior correction outperformed existing methods.

Conclusions:

  • The profile likelihood-based method with Jeffreys' prior correction is a superior approach for confidence intervals with incomplete paired binomial data.
  • This method provides a better balance between coverage and interval width.
  • SAS code is provided for implementation.