# Sample size: Area under ROC curve

## Description

Calculates the required sample size for the comparison of the area under a ROC curve with a null hypothesis value. The sample size takes into account the required significance level and power of the test.

## Required input

- Type I error - alpha: the probability of making a Type I error (α-level, two-sided), i.e. the probability of rejecting the null hypothesis when in fact it is true.
- Type II error - beta: the probability of making a Type II error (β-level), i.e. the probability of accepting the null hypothesis when in fact it is false.
- Area under ROC curve: the hypothesized Area under the ROC curve (the AUC expected to be found in the study).
- Null hypothesis value: the null hypothesis AUC.
- Ratio of sample sizes in negative / positive groups: enter the desired ratio of negative and positive cases. If you desire both groups to have an equal number of cases you enter 1; when you desire twice as many cases in the negative than in the positive group, enter 2.

## Example

You want to show that the AUC of 0.725 for a particular test is significant from the null hypothesis value 0.5 (meaning no discriminating power), then you enter 0.725 for Area under ROC curve and 0.5 for Null Hypothesis value.

You expect to include twice as many negative cases than positive cases, so for the Ratio of sample sizes in negative / positive groups you enter 2.

For α-level you select 0.05 and for β-level you select 0.20 (power is 80%).

## Results

After you click the OK button the program displays the required sample size. In the example 19 cases are required in the positive group and 38 in the negative group, giving a total of 57 cases.

A table shows the required sample size for different Type I and Type II Error levels.

## Reference

- Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology 143:29-36.