> The lines that I hoped to be the survival probabilities for each edtrt-group
> adjusted for confounding by log(bili) are nearly identical to the KM-lines,
> and they certainly don't appear adjusted for the very strong confounding by
> log(bili). I'm not quite sure what they are, though.
Yes, survexp will fit direct adjusted curves (and also the Hakulinen and
conditional methods). For your example, I would expect that the ordinary
Kaplan-Meier curves for treatment 1 vs 2 should be almost identical to the
adjusted curves for treatment 1 vs 2. The PBC data is from a randomized trial,
the two treatment arms are (not surprisingly) very well balanced with respect
to bilirubin values, and so adjusting for imbalance makes no real change. This
is exactly what the survexp code that you gave does.
If you are expected the curves to change, then I guess I'm not sure what you
mean by "strong confounding". Bilirubin is perhaps the most important clinical
measure of severity for any of the cholestatic liver diseases, of which PBC is
one; but being a strong predictor of mortality does not necessarily imply
confounding.
Standard errors for the direct curve are daunting -- it is several pages of
code in a Gail and Benichou (?) paper. I need to create an example for doing
this with the bootstrap. One problem is the two sources of variation. The
original Cox model's curves have variance of course, but do we consider the
population of subjects being averaged over (for the DA curve) to be fixed or
random?
For a long explanation of expected survival I would refer you to chapter 10
of Therneau and Grambsch, "Modeling Survival Data". One of the more confusing
aspects is that things get re-discovered and renamed, the "direct adjusted
survival" curve for instance is Ederer's method (1961) brought forward to a
Cox model. The ideas are not hard, but it does take a whole chapter.
Terry Therneau
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