Assessing intraindividual variability for a binary variable

[confooseddesi89]

Hello,

I have repeated-measures data of about 590 adolescents. Each variable is measured once per day, with 3 to 10 days per teen. One variable is caffeine consumption, which I have coded as 0 (none) or 1 (some).  I want to calculate a measure of intraindividual variability for caffeine consumption, analogous to the intraclass correlation coefficient (ICC) that is used on continuous variables. ICC for continuous variables is calculated as random effect variance / total variance, where the random effect is the individual. Does anyone have knowledge of an analogous measure for a binary variable, and how to calculate this measure in SAS? This measure should have guidelines for what is poor, moderate, and high intraindividual consistency. For example, ICC values less than 0.5, between 0.5 and 0.75, between 0.75 and 0.9, and greater than 0.90 are indicative of poor, moderate, good, and excellent reliability, respectively (Koo & Lee, 2016).

Thanks!

[StatDave · Accepted solution]

One option would be to fit a GEE model with this binary variable as the response and using the exchangeable correlation structure. This will report a measure of the correlation among the repeated measures over the clusters (subjects) in the data. For example:

proc gee;
class id;
model caffeine = / dist=bin;
repeated subject=id / type=exch;
run;

No global evaluation of the correlation can ever be very useful since this is highly dependent on the subject area and details of the study. 

[confooseddesi89]

You said this correlation wouldn't be "useful" - would you say the same of an ICC?

My goal of obtaining the analogous measure for the binary variable is to report that there is at least moderate intraindividual variation in caffeine per person across the repeated measurements - which would justify examining the within-person effect.

[StatDave]

I didn't say the correlation wouldn't be useful... I said a global evaluation of it like "less than .5 is poor, .5 to .75 is moderate ..." is not useful. What is "poor", "moderate", "good", etc, is highly dependent on the subject area and details of the phenomenon being studied. You will have to decide for your situation what implications the value obtained has on your analytic goals.

[confooseddesi89]

Okay, I understand. I have seen papers use a cutoff for the ICC, and I'll follow those guidelines in my manuscript (even if they're a bit arbitrary).

EDIT: For others interested in using such a measure in a publication, I suggest citing the following paper, which discusses assessing correlations within individuals in repeated-measures data:

Liang K-Y, Zeger SL. Longitudinal data analysis using generalized linear models. Biometrika 1986; 73(1): 13-22.