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Confidence Intervals

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...

Interpretation of Confidence Intervals

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...

Uncertainty: Confidence Intervals

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...

Confidence Coefficient

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...

Finding Critical Values for Chi-Square

Finding Critical Values for Chi-Square

Consider a curve representing sample data drawn randomly from a normally distributed population. One must construct confidence intervals to estimate or to test a claim regarding the population standard deviation. For example, a 95% confidence interval covers 95% of the area under the curve, and the remaining 5% is equally distributed on either side of the curve. To achieve such confidence intervals, one must determine the critical values. The critical values are simply the values separating the...

Margin of Error

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.

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An R-Based Landscape Validation of a Competing Risk Model

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Confidence intervals for the risk ratio under inverse sampling.

M Tian¹, M L Tang, H K T Ng

¹The School of Statistics, Renmin University of China, Beijing 100872, China.

Statistics in Medicine

|December 12, 2007

Summary

This study compares confidence intervals for risk ratios using inverse sampling. The saddlepoint approximation (SA) method demonstrated superior performance in simulations for risk ratio estimation.

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Establishing a Competing Risk Regression Nomogram Model for Survival Data

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Last Updated: Jul 9, 2026

An R-Based Landscape Validation of a Competing Risk Model

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Published on: September 16, 2022

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

Area of Science:

Biostatistics
Statistical Inference
Epidemiology

Background:

Inverse sampling is frequently used in clinical and epidemiological studies.
Accurate confidence intervals for the risk ratio are crucial for interpreting study findings.

Purpose of the Study:

To evaluate existing and develop new confidence intervals for the risk ratio under inverse sampling.
To compare the performance of different confidence intervals using Monte Carlo simulations.

Main Methods:

Review of existing confidence intervals (Fieller's theorem, delta method, F-statistic).
Development of new confidence intervals (score, likelihood ratio, saddlepoint approximation).
Monte Carlo simulations to assess coverage probabilities and interval widths.

Main Results:

The saddlepoint approximation (SA)-based confidence interval showed generally superior performance.
Comparative analysis revealed differences in coverage and width across methods.
Illustrative examples using real-world data from drug comparison and congenital heart disease studies.

Conclusions:

The SA-based confidence interval is recommended for risk ratio estimation under inverse sampling.
The study provides valuable insights for statistical analysis in relevant research areas.
Practical application demonstrated through real data analysis.