SciStat

# Sample size: Precision of regression-based reference limits

## Description

With this procedure you can calculate the required sample size for the estimation of regression-based reference limits, such as Age-related reference limits, with a specified relative precision (Bellera & Hanley, 2007).

## Required input

• Reference limit (%): the p% reference limit of interest, for example the 95% reference limit.
• Confidence interval (%): the A% confidence interval (two-sided) of the reference limit of interest, for example a 95% confidence interval.
• Reference range (%): the B% reference range, used for the calculation of the relative margin of error. The reference range encompasses the middle B% of the y values at any value of the covariate (age for example).
• Relative margin of error Δ (%): this is the margin of error relative to the reference range. It is defined as the ratio of the desired width of the confidence interval of the reference limit to the width of the reference range at any value of the covariate.
For example, look at the following output from a Age-related reference interval study:
The 95% reference range at age 25 is 67.9618−56.3196 = 11.6422. A relative margin of error (Δ) of 10% corresponds with a width of the confidence interval of 10% of 11.6422 or about 1.2.
• Distribution: the distribution of the covariate in the sample.
• Uniform distribution: select this option when the covariate follows a uniform distribution.
• Low-Median-High groups: select this option when the covariate is grouped into 3 groups where one-third of the sample were taken at one age extreme, one-third are taken at the midpoint, and one-third are taken from the other extreme.
• Normal distribution: select this option when the covariate follows a normal distribution.
• Average age value: select this option if you are only interested in the reference limit at the average age value.

## Example

You plan a study to obtain a 95% reference limit of blood pressure at different ages. For a 90% confidence interval, the desired relative margin of error is 10% compared with a 95% reference range (the middle 90% of observations). The distribution of age of the subjects is uniform.

You enter 95 for reference limit, 90 for confidence interval, 95 for reference range and 10 for relative margin of error. For distribution, you select Uniform distribution.

Click Calculate.

The minimum required sample size is 377.

## Literature

• Bellera CA, Hanley JA (2007) A method is presented to plan the required sample size when estimating regression-based reference limits. Journal of Clinical Epidemiology 60:610-615.