Table 1

Hypothetical data showing that the size of the intraclass correlation (ICC) calculated by the simulation method⁶ in a multilevel logistic model depends of the prevalence of the outcome (that is, the predicted probability). We present 11 cases, all with the same area variance V_A but with different outcome prevalence (p_I)

Prevalence p_I of the outcome (probability scale)	Prevalence of the outcome on the logistic scale (intercept M_C)	Area variance V_A on the logistic scale	Area variance converted to the probability scale*	Individual variance**	Intraclass correlation ICC = /(+**)
To convert the area level variance to the probability scale, we simulated 100000 area level residuals E_C–A based on the area level variance V_A, and calculated the predicted probability in each of these 100000 simulated area as p = exp (M_C+E_C-A) /[1+exp (M_C+E_C-A)]. We computed the area level variance on the probability scale as the variance of these predicted probabilities. *The overall individual level variance is computed as the mean of the individual level variances computed as p (1−p) for each of the 100000 simulated values.
0.01	−4.6	0.2	0.00003	0.0108	0.002 (ie, 0.2%)
0.1	−2.2	0.2	0.00185	0.0936	0.019 (ie, 1.9%)
0.2	−1.4	0.2	0.00519	0.1589	0.032 (ie, 3.2%)
0.3	−0.8	0.2	0.00872	0.2079	0.040 (ie, 4.0%)
0.4	−0.4	0.2	0.01063	0.2304	0.044 (ie, 4.4%)
0.5	0.0	0.2	0.01136	0.2386	0.045 (ie, 4.5%)
0.6	0.4	0.2	0.01062	0.2305	0.044 (ie, 4.4%)
0.7	0.8	0.2	0.00872	0.2080	0.040 (ie, 4.0%)
0.8	1.4	0.2	0.00518	0.1590	0.032 (ie, 3.2%)
0.9	2.2	0.2	0.00185	0.0936	0.019 (ie, 1.9%)
0.99	4.6	0.2	0.00003	0.0108	0.002 (ie, 0.2%)