I can calculate a likelihood ratio statistic to measure how well my data fits either of two mutually exclusive models:

$\Lambda({data}) = \frac{ f( \theta_0 | {data} )}{f( \theta_1 | {data} )} $

Calculating this statistic is straightforward to me, but I'd like some measure of statistical confidence to be carried along with the likelihood ratio. Is there something analogous to a confidence interval for a likelihood ratio? Or is all of the information about the relative confidence of each model?