# Intra-Class Correlation (ICC)

In planning group-randomized studies, we typically assume that the measurements between any pair of people in the same group have the same correlation, the intra-class correlation or ICC.
## Estimating ICC

Sometimes you can get an estimate of the ICC from a previous publication or if you need to estimate it from your preliminary data, there are several possible approaches:
- You can use analysis of variance (ANOVA) and estimate the ICC using the mean squares within and between groups.
- You can also fit a clustered-data model assuming compound symmetry with a generalized estimating equation approach and use the working correlation.

The more correlated the people in a group, the bigger the ICC. And the less information each new person in the same group will add to the study! We can calculate this effect using the variance inflation factor (VIF).
The variance inflation factor (VIF) tells how much larger a sample size you will need because of within-group correlation. You have to know how many people per group (call this number m) and the ICC. The formula for the VIF is:
**VIF = 1 + (m-1)x(ICC)**

Suppose that you have a lot of physicians, each of whom sees about 20 patients with Type II diabetes.
You find an intraclass correlation (ICC) of 0.05 between outcomes for patients with the same doctor.

The VIF will then be:

**VIF = 1 + (20-1)x0.05**

**= 1 + 0.95 = 1.95.**

You will need almost twice as many people enrolled in your study as you would have required if they were not clustered and similar in physician practices.