Compute sample size for an intra-class correlation (ICC)

#1
We want to compare three different methods to measure blood haemoglobin levels. So, as we are speaking about continous variables, we thought that intra-class correlation coefficient would be an addequate option.

In order to calculate the sample size that we will need, we discovered a Stata module called sampicc (https://ideas.repec.org/c/boc/bocode/s456978.html).

So we used it to calculate the sample size for an expected ICC of 0.6 and allowing for a variability among 0.45 and 0.75 (width: 0.15). We applied the sintaxis and we got the following result:

Code:
. sampicc 0.6 3, width(0.15) ci

  ****************************************************************
     Sample Size for the Width of a Confidence Interval for ICC
  ****************************************************************

   Given:
                     Expected Value (P1):  0.60
                    Number of Replicates:    3
                                CI level:   95%
                         Specified Width:  0.15

  ****************************************************************

                Esimtated sample size is:  177

  ****************************************************************
But we wanted to give it a try to a higher ICC, and we ran the sintax again:

Code:
. sampicc 0.8 3, width(0.15) ci

  ****************************************************************
     Sample Size for the Width of a Confidence Interval for ICC
  ****************************************************************

   Given:
                     Expected Value (P1):  0.80
                    Number of Replicates:    3
                                CI level:   95%
                         Specified Width:  0.15

  ****************************************************************

                Esimtated sample size is:   63

  ****************************************************************
Surprisingly, the sample size needed to reach a higher agreement is smaller.

Does anyone know why we are getting this result? If we specify higher ICCs, we get smaller sample sizes.

Thanks in advance.
 

spunky

Can't make spagetti
#2
We want to compare three different methods to measure blood haemoglobin levels. So, as we are speaking about continous variables, we thought that intra-class correlation coefficient would be an addequate option.

In order to calculate the sample size that we will need, we discovered a Stata module called sampicc (https://ideas.repec.org/c/boc/bocode/s456978.html).

So we used it to calculate the sample size for an expected ICC of 0.6 and allowing for a variability among 0.45 and 0.75 (width: 0.15). We applied the sintaxis and we got the following result:

Code:
. sampicc 0.6 3, width(0.15) ci

  ****************************************************************
     Sample Size for the Width of a Confidence Interval for ICC
  ****************************************************************

   Given:
                     Expected Value (P1):  0.60
                    Number of Replicates:    3
                                CI level:   95%
                         Specified Width:  0.15

  ****************************************************************

                Esimtated sample size is:  177

  ****************************************************************
But we wanted to give it a try to a higher ICC, and we ran the sintax again:

Code:
. sampicc 0.8 3, width(0.15) ci

  ****************************************************************
     Sample Size for the Width of a Confidence Interval for ICC
  ****************************************************************

   Given:
                     Expected Value (P1):  0.80
                    Number of Replicates:    3
                                CI level:   95%
                         Specified Width:  0.15

  ****************************************************************

                Esimtated sample size is:   63

  ****************************************************************
Surprisingly, the sample size needed to reach a higher agreement is smaller.

Does anyone know why we are getting this result? If we specify higher ICCs, we get smaller sample sizes.

Thanks in advance.
Because the ICC is a parameter estimate and the larger it is, the easier it is to be detected. In general, if your parameter estimate is well-defined in the population, it will always be the case that larger parameter estimates need smaller sample sizes to be detected. Not just true of ICCs but most statistics.
 
#3
Thank you, Spunky

Your explanation makes sense to me... but, what is the purpose of calculating a sample size, then? In general you need to calculate sample sizes to ensure a statistically significant result and to no waste resources (or damage people).
I understand that the best way to proceed here is to use as many patients as possible and cross the fingers to get a relible result.
Am I wrong?
Thank you, again