I have a survival model with patients nested in hospitals that includes a random-effect for the hospitals. The random effect is gamma-distributed, and I am trying to report the 'relevance' of this term on a scale that is easily understood.

I have found the following references which use the Median Hazard Ratio (a bit like the Median Odds Ratio), and calculated this.

[Bengtsson T, Dribe M: Historical Methods 43:15, 2010](http://www.tandfonline.com/doi/abs/10.1080/01615440903270299")

However, now I wish to report the uncertainty associated with this estimate using the bootstrap. The data is survival data, and hence there are multiple observations per patient, and multiple patients per hospital. It seems obvious that I need to cluster the patient observations when re-sampling. But I don't know if I should cluster the hospitals too (i.e. resample hospitals, rather than patients?

I am wondering if the answer depends on the parameter of interest, and so would be different if the target was something that was relevant at the patient level rather than the hospital level?

I have listed the stata code below in case that helps.
    
    cap program drop est_mhr
    program define est_mhr, rclass
	stcox patient_var1 patient_var2 ///
		, shared(hospital) ///
		noshow
	local twoinvtheta2 = 2 / (e(theta)^2)
	local mhr = exp(sqrt(2*e(theta))*invF(`twoinvtheta2',`twoinvtheta2',0.75))
	return scalar mhr = `mhr'
    end

    bootstrap r(mhr), reps(50) cluster(hospital): est_mhr