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Sampling: comparison of two ROC curves

Command:    

 Sampling
Next selectComparison of two ROC curves

Description

Calculates the required sample size for the comparison of the areas under two ROC curves (derived from the same cases). The sample size takes into account the required significance level and power of the test (see Sampling: Introduction).

Required input

  • Type I error - alpha: the probability of making a Type I error (Alpha-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 (Beta-level), i.e. the probability of accepting the null hypothesis when in fact it is false.
  • Area under ROC curve 1: hypothesized area for the first ROC curve.
  • Area under ROC curve 2: hypothesized area for the second ROC curve.
  • Correlation in positive group: the hypothesized rank correlation coefficient in the positive group (abnormal cases)
  • Correlation in negative group: the hypothesized rank correlation coefficient in the negative group (normal cases)

Example

You are interested to show that the discriminating power of two assays (performed on the same cases), with an area under the ROC curve of 0.825 and 0.9, is significant different. From previous studies you know that the rank correlation between the two assays is 0.4 in both positive and negative cases.

You enter the values 0.825 and 0.9 for Area under ROC curve 1 and Area under ROC curve 2. Next you enter 0.4 for Correlation in positive group and Correlation in negative group. For Alpha-level you select 0.05 and for Beta-level you select 0.10.

After you click the Calculate button the program will display the required sample size. In our example this is 198, meaning that you need 198 normal subjects (negative group) and 198 abnormal subjects (positive group), assuming equal numbers of normal and abnormal subjects. So in fact a total of 396 subjects is required.

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

References

  • Hanley JA, McNeil BJ (1982) The meaning and use of the area under a receiver operating characteristic (ROC) curve. Radiology, 143:29-36.
  • Hanley JA, McNeil BJ (1983) A method of comparing the areas under receiver operating characteristic curves derived from the same cases. Radiology, 148:839-843.

See also