In contrast to Pearson's correlation in which the relationship between two variables (measures such as the height and body weight of a person) is concerned, intraclass correlation (ICC) is defined as the correlation of one variable (measure) between two or more members within groups. Applied to the context of brain imaging, ICC can be used as an indicator of scanning reliability or consistency across sessions/days/sites, for example, and, defined as the proportion of variability across subjects relative to the total variability in the data.

Here we provide a program, 3dICC, to calculate the ICC on brain volume data instead of ROI data typically seen in the literature. If there is one random factor (e.g., session) other than subject, the ICC is typically calculated in a two-way random-effects ANOVA model as shown in the classical notation of ICC(2,1) [Shrout and Fleiss (1979), Psychological Bulletin, Vol. 86, No.2, 420-428]. In the same token, here I've extended the definition of ICC to two random factors in addition to subject in a three-way random-effects ANOVA.

Program 3dICC

3dICC, written in R, can be run on all major platforms such as unix-based systems and Windows, and requires R installation. First, create a text file model.txt in the following format which stores all the information about output file name, the input files, etc.:

Output:OutputFileName            <-- Optional: prefix only, and no view (e.g., tlrc) needed                 
MASK:../data/Mask+tlrc.BRIK      <-- Optional: a mask will significantly reduce runtime   
Clusters:4                       <-- Optional: number of parallel jobs; default is 1 if this line is not provided
Subj     Session         Site            InputFile
Jim      one             site1           Jim1+tlrc
Jim      two             site1           Jim2+tlrc
Jim      one             site2           Jim3+tlrc
Jim      two             site1           Jim4+tlrc
Carol    one             site1           Carol1+tlrc
......                           <-- don't put these dots in the file as it's meant to show incompletion

As indicated in the table above exemplifying a 3-way random-effects ANOVA, the first 3 lines are optional, but the 4th line is mandatory with two keywords, Subj and InputFile in the title are reserved.

Once model.txt is available, execute the following command at the prompt in the directory where file model.txt exists:

3dICC.R MyOutput &

Or if you run it remotely:

nohup 3dICC.R MyOutput &

You can open file MyOutput to check the running progress.

There will have 2 sub-bricks in the output for two-way random-effects ANOVA: one for subject (ICC), and one for the other factor (some people call it within-subject variation coefficient, WSC). For the case of three-way random-effects ANOVA, 6 sub-bricks will be in the output: one for subject (ICC), one for each of the other two factors (WSC's), and one for each of three two-way interactions. Theoretically speaking, ICC and WSC should be within [0,1], but in rare cases they may become negative when the assumptions about the ANOVA model are vilated.

Useful links

1. Wikipedia: Intraclass correlation

Acknowledgements

I'd like to thank Yang Wang for motivating me writing the program and for providing testing data and feedback, and thank Geon-Ho Jahng and Tom Liu for concept clarification.