Optimism correction for hazard ratio?

I’m using bootstrap internal validation to correct a Cox proportional hazards model that uses principal component scores extracted from gene expression data as the predictor (X) variables.

Among other reasons, one reason I am correcting for optimism is so that I can compare our approach to a few other gene expression scores that were externally validated. We will use other approaches but for the comparison, we have determined a threshold and classified into high and low risk groups and are calculating the hazard ratio (HR) for the risk groups. (we are aware of the problems with this and are pursuing other approaches for our own work, but have been criticized for not comparing to established gene expression scores that have H/L risk groups so we’re doing this for comparison sake only).

I am adjusting the c index for optimism and this makes sense, but here are my questions:

  1. is it reasonable to use the same optimism correction algorithm to correct the HR?
  2. if yes, do I just subtract the optimism from the HR from the all original data model (the unadjusted HR)? or are there other methods or considerations for how to adjust?
  3. if no, does anyone have suggestions for reporting the HRs from the new, internally validated measure so they can be compared to the externally validated measures?

thanks in advance for your time, advice and explanations.

The high and low risk score approach is so defective that the entire project should be abandoned. There are better projects out there to be sure.

@f2harrell, we agree but when we tried to publish a paper without comparison to established gene expression signatures, it was criticized and rejected.

It’s fine to compare with published gene expression signatures as long as those signatures are not defective themselves, i.e., as long as you use the continuous form of the signature. High:low hazard ratios do not transport to other populations as they are functions of all the individual subject risks in the original data.

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thanks, that’s our approach and we’re continuing with it (other than this comparison where I don’t think that’s possible due to the nature of their signatures).

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