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I have a left truncated, right censored cox model:

coxph(Surv(start, stop, censor) ~ x + y, mydata)

I would like to know how much of the observed variance (as a number
between 0 and 1) is explained by each variable. How could I do that?

Adding terms sequentially and then using anova(mod1, mod2) tells me
whether I get a significant improvement of the fit, but does not tell me
how much variance I actually explain? 

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There is not a "variance explained" in a Cox model, since it does not
try to predict the actual survival time.  There are several proposals in
the literature for an "approximate" R^2.  If you use summary(fit) it
will print one of the older ideas, which unfortuantely was shown by
later literature to not be a very good approach (replacing this is
another item on my long list of "someday fix").  At present your best
choice is to use the c-statistic, which is also printed out by summary.

Terry Therneau

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