0
$\begingroup$

I am conducting survival analysis, investigating the association between a binary factor (TRUE/FALSE) and all cause mortality. I use the rms package:

 > m <- cph(dead ~ factor, data=dta)
 >
 > summary(m)
 ...                  Low High ... Effect
 factor - TRUE:FALSE  1   2        0.14

In my interpretation, this means a HR of exp(0.14)=1.15 for those with factor == T.

Predict(m) gives me the estimates of the log Relative Hazard - and I would have assumed that it would be 0 for FALSE and 0.14 for TRUE - but this is not the case:

 > Predict(m)
 ...                   yhat
factor.1    FALSE   -0.0014
factor.2    TRUE     0.14

I have to admit that I don't understand this. If this is the relative hazard, what is it relative to? There are no missing data or values other than TRUE or FALSE.

Improve this question
$\endgroup$
2
  • 1
    $\begingroup$ Why did you assume it would be 0? $\endgroup$
    – Tim
    Commented Mar 15, 2022 at 13:39
  • $\begingroup$ As it is log(relative hazard) - shouldn't the reference be 1? $\endgroup$
    – Gux
    Commented Mar 15, 2022 at 13:46

1 Answer 1

Reset to default
1
$\begingroup$

This has to do with what is taken to be the reference baseline hazard/survival curve for a Cox survival model.

A regression coefficient for a binary predictor in a Cox model, as in your first display, represents the log of the relative hazard between the 2 values of that predictor. That relative hazard is independent of the particular choice of baseline hazard, under the proportional hazards assumption.

The 2 values reported in your second display are for differences for each predictor from the baseline hazard at some reference condition. The choice of reference condition is software-specific. In the R survival package the default baseline hazard in the basehaz() function is at a "mean" value that makes no sense with a categorical predictor (as the help page acknowledges) but can make some internal calculations more reliable. Something like that seems to be going on here.

When you do full survival-curve predictions or predictions of differences between specified combinations of predictor values, the choice of baseline hazard cancels out. There is nothing to be concerned about from your second display.

Improve this answer
$\endgroup$
2
  • $\begingroup$ Thank you! So the big question is really what reference is used and whether it can be changed. $\endgroup$
    – Gux
    Commented Mar 15, 2022 at 19:03
  • 1
    $\begingroup$ @Gux one trick is always to specify desired combination(s) of all predictor values if you don't know or don't accept the defaults. The software will then combine its own choice of reference with your choice of predictor values to give the correct corresponding survival curve(s) or differences in hazards among sets of predictor values. The help pages for the rms Predict() and survplot() functions show several examples of how to do that, as do Harrells' course notes and book. $\endgroup$
    – EdM
    Commented Mar 15, 2022 at 19:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.