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## Competing-risks regression

Competing-risks survival regression provides a useful alternative to Cox regression in the presence of one or more competing risks. For example, say that you are studying the time from initial treatment for cancer to recurrence of cancer in relation to the type of treatment administered and demographic factors. Death is a competing event: the person under treatment may die, impeding the occurence of the event of interest, recurrence of cancer. Unlike censoring, which merely obstructs you from viewing the event, a competing event prevents the event of interest from occurring altogether, and your analysis should adjust accordingly.

Stata’s stcrreg implements competing-risks regression based on Fine and Gray’s proportional subhazards model. In Cox regression, you focus on the survivor function, which indicates the probability of surviving beyond a given time. In competing-risks regression, you instead focus on the cumulative incidence function, which indicates the probability of the event of interest happening before a given time. Competing-risks regression is semiparametric in that the baseline subhazard of the event of interest is left unspecified, and the effects of covariates are assumed to be proportional. Time-varying covariates and coefficients are allowed.

Here we fit a model for cervical cancer patients, where the event of interest is a relapse of cancer located in the pelvis. A competing event is the occurrence of cancer in another part of the body.

. stcrreg ifp tumsize pelnode, compete(failtype == 2) nolog

failure _d:  failtype == 1
analysis time _t:  dftime

Competing-risks regression                        No. of obs       =       109
No. of subjects  =       109
Failure event  : failtype == 1                    No. failed       =        33
Competing event: failtype == 2                    No. competing    =        17
No. censored     =        59

Wald chi2(3)     =     33.21
Log pseudolikelihood =  -138.5308                 Prob > chi2      =    0.0000

Robust

_t          SHR   Std. Err.      z    P>|z|     [95% Conf. Interval]

ifp     1.033206   .0178938     1.89   0.059     .9987231    1.068879

tumsize     1.297332   .1271191     2.66   0.008     1.070646    1.572013

pelnode     .4588123   .1972067    -1.81   0.070     .1975931    1.065365



Stata’s stcurve allows us to examine the cumulative incidence function:

. stcurve, cif at1(ifp=5 pelnode=0) at2(ifp=20 pelnode=0)


View a complete list of survival analysis features.