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I am using coxph with weights to represent sampling fraction of subjects.
Our simulation results show that the robust SE of beta systematically
under-estimate the empirical SD of beta.
Does anyone know how the robust SE are estimated in coxph using weights?
Is there any analytical formula for the ???weighted??? robust SE?
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The formal reference is Binder, D.A. (1992).
Fitting Cox's proportional hazards models from survey data.
Biometrika {\bf 79}, 139-47.
I am not aware of a systematic study of how well this estimator does, but there
could well be papers in the literature.
Let D = matrix of dfbeta residuals = residual(fit, type='dfbeta',
weighted=F),
one row per observation and one column per variable. Then for a simple weighted
model
var = D' W^2 D
where W = diagonal matrix of weights. Note that the dfbetas are the derivatives
of beta with respect to the weights; if all the weights are doubled the dfbetas
go down by half.
Terry Therneau