Standard error for the Breslow estimator of the cumulative hazard.

[Andrea Discacciati]

stcox's postestimation command predict allows the calculation of the Breslow estimates for the cumulative hazard (basechazard option), but not that of its standard error.

I am wondering if someone has written some code to calculate it and, if so, if he or she is willing to share it.

[Marcos Almeida]

Hello Andrea,

I wonder whether this option (based on the FAQ from the site http://www.stata.com/support/faqs/st...seline-hazard/ ) applies to your neeeds:

. stset studytime, failure(died)

     failure event:  died != 0 & died < .
obs. time interval:  (0, studytime]
 exit on or before:  failure

------------------------------------------------------------------------------
         48  total observations
          0  exclusions
------------------------------------------------------------------------------
         48  observations remaining, representing
         31  failures in single-record/single-failure data
        744  total analysis time at risk and under observation
                                                at risk from t =         0
                                     earliest observed entry t =         0
                                          last observed exit t =        39

. stcox drug age, nolog

         failure _d:  died
   analysis time _t:  studytime

Cox regression -- Breslow method for ties

No. of subjects =           48                  Number of obs    =          48
No. of failures =           31
Time at risk    =          744
                                                LR chi2(2)       =       36.29
Log likelihood  =   -81.765061                  Prob > chi2      =      0.0000

------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        drug |   .2153648   .0676904    -4.89   0.000     .1163154    .3987605
         age |   1.116351   .0403379     3.05   0.002     1.040025    1.198279
------------------------------------------------------------------------------

. predict hc0, basehc
(17 missing values generated)

. sum hc0

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
         hc0 |         31    .0069686    .0114544   .0004073   .0551102

. tabstat hc0, statistics( mean sd semean )

    variable |      mean        sd  se(mean)
-------------+------------------------------
         hc0 |  .0069686  .0114544  .0020573
--------------------------------------------

. predict mybasech, basechazard

. sum mybasech

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
    mybasech |         48    .0349674    .0446204   .0006713   .1463072

. tabstat mybasech, statistics( mean sd semean )

    variable |      mean        sd  se(mean)
-------------+------------------------------
    mybasech |  .0349674  .0446204  .0064404
--------------------------------------------

Best,

Marcos

[Andrea Discacciati]

Thank you Marcos for your reply. Unfortunately, things are not that simple.

I want to calculate the SE of the Breslow estimator of the cumulative hazard function. Formulas are presented for example here: http://support.sas.com/documentation..._details54.htm or in Therneau, Terry M., and Patricia M. Grambsch. Modeling survival data: extending the Cox model. Springer Science & Business Media, 2000 (page 267), in case you're interested.

However, can you perhaps help me identify which ado-file implements the basechazard option of the predict command? I tried to trace back the ado file starting from stcox_p.ado but I got nowhere. Is it implemented in the built-in command cox, maybe? That would be really helpful to help me write the necessary code for the calculation of the SE without reinventing the wheel.

[Marcos Almeida]

Hello Andrea,

This being so, it goes beyond my level of expertise. That said, after some browsing on the net, I found interesting stuff.

By clicking on the links below, I gather you may eventually find what you are looking for:

http://pauldickman.com/survival/strs.pdf

http://www.pauldickman.com/rsmodel/stata_colon/

http://www.pauldickman.com/rsmodel/s...ard_errors.pdf

Hopefully that helps!

Best,

Marcos