Hi Statalist,

I'm hoping to calculate the intraclass correlation (with confidence intervals) from a three level accelerated failure time model using mestreg and the lognormal distribution option.

I found this blog post from Stata to be very useful: https://www.stata.com/stata-news/new...-correlations/

But it only specifies how to calculate the individual level variance component for the Weibull distribution, where the level 1 variance =(pi / (6+p^2)) and p is the ancillary parameter of the Weibull AFT model

I am not sure how to calculate the equivalent individual level variance component for the lognormal AFT model, and couldn't work it out from the referenced Rodríguez, G. 2010. Parametric Survival Models. http://data.princeton.edu/pop509/ParametricSurvival.pdf.

Code and output from Stata 17 on a Mac:

mestreg i.var1 c.var2 i.var3 ||level3var: ||level2var:, distribution(lognormal) time tr

----------------------------------------------------------------------------------------------
_t | Time ratio Std. err. z P>|z| [95% conf. interval]
-----------------------------+----------------------------------------------------------------
var1 etc...
//
|
_cons | 500 100 16.67 0.000 250 900
-----------------------------+----------------------------------------------------------------
/logs | .9123 .712 1.0
-----------------------------+----------------------------------------------------------------
level3var |
var(_cons)| .012 .03 .00001 1.40
-----------------------------+----------------------------------------------------------------
level3var>level2var |
var(_cons)| .7654 .30 .20 1.9
----------------------------------------------------------------------------------------------

I presumed the "/logs" output refers to the level 1 variance component, and denominator for ICC calculations would therefore be 0.9123 + 0.012 + 0.7654. Is this correct? If so, can anyone provide more information on calculating the 95% confidence intervals for the resulting ICCs.

Many thanks in advance,
Ben