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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...

Confidence Interval for Estimating Population Mean

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...

Prediction Intervals

Prediction Intervals

The interval estimate of any variable is known as the prediction interval. It helps decide if a point estimate is dependable.
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.
The...

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Related Experiment Video

Updated: Jul 13, 2026

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

Computation of profile likelihood-based confidence intervals for reference limits with covariates.

A Virtanen¹, E Uusipaikka

¹Central Laboratory, Turku University Central Hospital, Kiinamyllynkatu 4-8, Turku, Finland.

Statistics in Medicine

|August 4, 2007

Summary

This study introduces a new, efficient method for calculating confidence intervals for biochemical reference limits, improving the precision of test result interpretation. The method simplifies calculations for age-dependent reference limits using generalized linear models.

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Area of Science:

Biochemistry
Statistics
Medical Diagnostics

Background:

Biochemical test results often depend on patient age or other covariates.
Accurate reference limits are crucial for physicians to interpret these results correctly.
Estimating reference limits requires assessing their precision using confidence intervals.

Purpose of the Study:

To present a novel method for calculating approximate profile likelihood-based confidence intervals for reference limits.
To provide a more efficient approach to confidence interval calculation compared to standard methods.
To demonstrate the application of the method in real-world biochemical data analysis.

Main Methods:

Modeling biochemical data using generalized linear models (GLMs).
Developing a new method for approximate profile likelihood-based confidence intervals.
Applying the method to immunoglobulin and alpha-fetoprotein data, comparing with existing models and simulations.

Main Results:

The proposed method efficiently calculates confidence intervals for reference limits.
The method was successfully applied to immunoglobulin data within a GLM framework (gamma distribution).
Profile confidence intervals for serum alpha-fetoprotein were compared to regression-based intervals, with confidence levels verified by simulation.

Conclusions:

The new method offers an efficient way to compute confidence intervals for reference limits in biochemical tests.
This approach enhances the precision of interpreting biochemical test results, especially when accounting for covariates.
The method is versatile, applicable to various statistical models including GLMs and linear regression.