[R] coxph - weights- robust SE

[Terry Therneau]

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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