What makes you think that if you sum two distributions the median is the weighted average of the median of the two distributions? It isn't.
Consider a trivial example. 2/3 are on SOC and most all event within 1 month. While 1/3 get a magic cure and live for 10 years. The median is under 1 month.
OK, your numbers will be reasonably close for this type example. But you can not blindly assert they are "right" so it is fair for somebody to ask what you are doing.
In practice trying to do this type stuff via pure math is almost impossible given the curve shapes. That is why most who do this use a random simulation model Leprecon did this quite well if you want to look up his work (and he had a "long" view, so I am not pushing a short thesis).
Oohh i was guessing that as you're a statistician that you were using R.
I didn't notice any testing or estimation in your model. For the testing did you use the log rank stat? some version of weighted log rank stat? RMST? A combo test? Or some kind of other bootstrapped permutation test?
For the estimation was it PH Cox or some kind of piecewise cox? RMST? Milestones?
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