# When do I use two-way mixed, two way random and one way random for the Intraclass correlation coefficient?

I have a question about the intraclass correlation coefficient. I have 62 patients for whom I calculated the breast tumor volume. The surgeon who resected the tumors did the same thing, but without seeing my calculations. Now I want to know something about the inter-observer agreement for this group by using the ICC. Can someone help me: should I use the two-way mixed, two-way random or one-way random method?

## 2 Answers

Your question has been downvoted with no explanation as to why, which is not very helpful in my opinion, as you don't get any hints on how to improve your question to get an appropriate answer.

Anyway, the question as to which ICC to use depends on 3 things (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4913118/):

1. The "Model” (e.g., 1-way random effects, 2-way random effects, or 2-way mixed effects);

2. The "Type” (e.g., for decision-making, will you use the average of the measurements produced by the surgeon and yourself or just the measurement produced by the surgeon);

3. The “Definition” of relationship considered to be important (i.e., consistency in measurements between the surgeon and yourself OR absolute agreement between the surgeon and yourself in terms of measurements).

Please read the article and see if you can figure out what the answer is - then you can come back with a more pointed question here.

The two-way mixed and two-way random methods will yield identical ICC values, so this choice will likely be inconsequential. The only difference is in interpretation: The two-way mixed model treats rater as a fixed effect, the two-way random model treats it as a random effect. The estimated ICCs will however be the same, see e.g., Table 4 in McGraw & Wong (1996).

The one-way random approach assumes that there is only a random effect of patient. As your question indicates that there are two raters, most likely you will want to model this rater effect, so a two-way (mixed or random) method seems most appropriate.

McGraw, K. O., & Wong, S. P. (1996). Forming inferences about some intraclass correlation coefficients. Psychological methods, 1(1), 30. https://doi.org/10.1037/1082-989X.1.1.30