c-Index for GLIMMIX model

[Haris]

Looking for ideas on how to calculate a c-index for a mixed GLIMMIX model--binary outcome with random effects.

The best I've found so far was to use a weighted average of c-indices from each level of the random variable.  Any other leads?

Thanks,

Haris

[SteveDenham]

This is an area where the literature isn't really settled yet.  The weighted average at least overcomes the non-additivity of c (at least for the most part). Are you applying the same number of bins to each level of the random variable?  If not, then the weight should also reflect that unequal replication.

Steve Denham

[Haris]

Here's at least something published on the matter: http://www.statistics.gov.hk/wsc/CPS031-P5-S.pdf.

I am not sure what you mean by "bins to each level of the random variable," can you elaborate?  The outcome is binary so there are only two bins at each level (as long as there are some events and non-events).  Otherwise, the predictors are all the same.

[SteveDenham]

Maybe I mis-interpreted what you meant by c-index.  I was thinking of c as the area under the ROC, and for that, you need to vary the cutpoint to generate values, and then add them up via the trapezoidal rule (if you are doing it the SAS way).  The key is that if you calculate the within cluster ROC values (as per Rahman et al.), you need to be sure that the same number of cutpoints are applied.  This is a real problem if the number of 'events' is small within a cluster, and worse if the total number of instances is much smaller in some clusters than in others, so that estimation of the ROC and its associated std error are inexact (see comments on page 5 of Rahman et al.).

Steve Denham