Comparing median times to OS between two crossing IPTW-adjusted KM curves

Hi all,

I m doing IPTW-adjusted survival analyses to compare two treatments with Stata 13.
I ve generated IPTW-adjusted KM curves for treatment A and B by using the following commands:

stset DX_LASTCONTACT_DEATH [pweight = iptw], failure (VITAL_STATUS==0)
sts graph, by (TREATMENT)

My problem is that the curves are crossing only one time at 18 months of follow-up.
I can calculate the median times to OS (IQR) in each weighted treatment groups by using

stsum, by (TREATMENT)

But I can't get the appropriate p value to compare these two median times, as Stata only allows to run a Cox regression based test after the weighting by using:

sts test TREATMENT

This test (like the log-rank test) is only valid when the PH assumption is not rejected, which is not the case when I run

stcox TREATMENT
estat phtest

as the p value from the PH test is significant (P<0.001)

I ve decided to calculate two different HRs (with their corresponding 95% CI and p values) before and after the crossing by using a time varying covariate approach:

stcox TREATMENT, tvc(TREATMENT) texp((_t>18))
nlcom (exp(_b[main:TREATMENT] + _b[tvc:TREATMENT] ))

But I still need an overall p value for the comparison of median times to OS between the two treatment groups.

My questions are:
1. Which test is powered enough to compare median times to OS between two treatment groups in the present and controversial situation where the IPTW-adjusted KM curves cross and the PH assumption is rejected?
2. Which codes should I use to run this test in the weighted population?

Thanks for your help
Thomas