Competing risk regression without a control group?

[Tim Anderson]

Hello,

I am trying to graph the cumulative hazard of running out of new medications (nonpersistence) within one year for a cohort of patients, accounting for the competing risk of death. In this example, the date the patient is censored is represented by the variable latest_fill_trunc and reason for censoring is represented by the variable persistent_end which = 2 if the patient died and =1 if the patient ran out of medications but did not die.

Using competing risk regressions, as shown below, I can plot the comparison of patients who received one type of new medication vs another (intensification_type variable).

. stset latest_fill_trunc, failure (persistent_end2==1)

     failure event:  persistent_end2 == 1
obs. time interval:  (0, latest_fill_trunc]
 exit on or before:  failure

------------------------------------------------------------------------------
       2691  total observations
          0  exclusions
------------------------------------------------------------------------------
       2691  observations remaining, representing
       1153  failures in single-record/single-failure data
     630707  total analysis time at risk and under observation
                                                at risk from t =         0
                                     earliest observed entry t =         0
                                          last observed exit t =       365

. stcrreg intensification_type, compete(persistent_end2==2)

         failure _d:  persistent_end2 == 1
   analysis time _t:  latest_fill_trunc

Iteration 0:   log pseudolikelihood = -8818.6153  
Iteration 1:   log pseudolikelihood = -8818.6129  
Iteration 2:   log pseudolikelihood = -8818.6129  

Competing-risks regression                       No. of obs       =      2,691
                                                 No. of subjects  =      2,691
Failure event  : persiste~2 == 1                 No. failed       =      1,153
Competing event: persiste~2 == 2                 No. competing    =        266
                                                 No. censored     =      1,272

                                                 Wald chi2(1)     =      47.38
Log pseudolikelihood = -8818.6129                Prob > chi2      =     0.0000

--------------------------------------------------------------------------------------
                     |               Robust
                  _t |        SHR   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------+----------------------------------------------------------------
intensification_type |      1.630      0.116     6.88   0.000        1.419       1.874
--------------------------------------------------------------------------------------

stcurve, cumhaz at1(intensification_type=0) at2(intensification_type=1) ///
xtitle(Days Following Medication Start) ///
ylabel(0(0.2)1) yscale(range(0 1)) ytitle(Cumulative Incidence of Nonpersistnce) ///

However, I also want to generate a graph for the entire population, not stratified by type of medication. I do not understand how to do this competing risk regressions, as they require a stratifying variable and if I attempt the same code without a stratifying variable I get errors.

. stcrreg, compete(persistent_end2==2)

         failure _d:  persistent_end2 == 1
   analysis time _t:  latest_fill_trunc

Competing-risks regression                       No. of obs       =      2,691
                                                 No. of subjects  =      2,691
Failure event  : persiste~2 == 1                 No. failed       =      1,153
Competing event: persiste~2 == 2                 No. competing    =        266
                                                 No. censored     =      1,272

                                                 Wald chi2(0)     =       0.00
Log pseudolikelihood = -8842.3574                Prob > chi2      =          .

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

stcurve, cumhaz ///
xtitle(Days Following Medication Start) ///
ylabel(0(0.2)1) yscale(range(0 1)) ytitle(Cumulative Incidence of Nonpersistnce) ///

prediction not valid after fitting null model
r(498);

I also tried including a variable that represents the entire cohort (all observations cohort==1) but it is dropped from the model due to collinearity

. stcrreg cohort, compete(persistent_end2==2)
note: cohort omitted because of collinearity

         failure _d:  persistent_end2 == 1
   analysis time _t:  latest_fill_trunc

redundant or inconsistent constraints

Is there another way to graph cumulative hazards for an entire population, accounting for competing risks, similar to what can be done with a regular stcox which does not account for competing risks

stset latest_fill_trunc, failure (persistent_end)
sts graph, xtitle(Days) ytitle(% Persistence) title(Medication Level Persistence)

Appreciate your insight

[Nicoletta Riva]

Hello,

If you have not solved your problem yet, you could try

stcurve, cif

Kind regards,

Nicoletta

[Ceri Richards]

Probably too late to be helpful, but I had a similar issue and used:

webuse hypoxia, clear
stset dftime, failure(failtype==1)
gen dummy=1
stcrreg dummy, compete(failtype==2)

Interestingly it works fine on STATA 16 I have on one computer, but crashes on STATA 15. So version might be the issue.