Hazard assumption not met in STATA

[Buyadaa Oyunchimeg]

Dear Statalist,

I have categorized participants into 4 groups based on two baseline parameters to compare the mortality among groups. I tested the proportional hazard assumption using estat phtest, detail command, but the PH assumption is not met.

Here is what I got:

         stptime, per(1000) by(gr)
 
         failure _d:  event == 1
   analysis time _t:  t_eventyears
                 id:  ID
 
 Group |  person-time    failures     rate             [95% Conf. Interval]
-----------+-----------------------------------------------------------
 GR_1 |    30375.285        150    4.9382252   [ 4.20795    5.795237]
 GR_2 |     12924.76         99    7.6597168     [6.29019    9.327423]
 GR_3 |    1523.6044        29    19.033812     [13.22701    27.38987]
 GR_4|    2167.1376          7     3.2300672     [1.539883    6.775409]
-----------+-----------------------------------------------------------
     total |    46990.787     285   6.0650186    [5.400218     6.81166]
 
. stcox i.gr, nolog
 
         failure _d:  event == 1
   analysis time _t:  t_eventyears
                 id:  ID
 
Cox regression -- Breslow method for ties
 
No. of subjects =       10,111                  Number of obs    =      10,111
No. of failures =          285
Time at risk    =  46990.78722
                                                LR chi2(3)       =       42.49
Log likelihood  =   -2509.9229                  Prob > chi2      =      0.0000
 
 
 
 
-------------------------------------------------------------------------------------------------------
              _t | Haz. Ratio     Std. Err.       Z      P>|z|            [95% Conf. Interval]
--------------------------------------+----------------------------------------------------------------
               gr |
        GR_2  |   1.553045   .2011129     3.40   0.001          [1.204917    2.001756]
        GR_3  |   3.885477   .7882809     6.69   0.000          [2.61068    5.782759]
        GR_4  |   .6511265   .2517825    -1.11   0.267          [.3051521    1.389359]
-------------------------------------------------------------------------------------------------------





                Test of proportional-hazards assumption
                Time:  Time
                ----------------------------------------------------------------
                                rho            chi2           df        Prob>chi2
                ------------+---------------------------------------------------
                1b.gr            .            .                  1             .
                2.gr      0.09032         2.33           1         0.1272
                3.gr      0.21086        12.71          1         0.0004
                4. gr     0.22599        14.52          1         0.0001
                ------------+---------------------------------------------------
            global test                   25.16          3         0.0000
                ---------------------------------------------------------------- 

What would you suggest?

Thank you in advance.

[Maarten Buis]

Your stcox model estimated that at every point in time the hazard in group 4 is 0.65 times the hazard in group 1, that is the hazard in group 4 is (0.65-1)*100%= - 35% smaller in group 4 than group 1. Notice that in interpreting I did not specify the time point at which I looked to compare group 1 and group 4. I don't have to, because stcox assumes that this ratio is always the same. That is an assumption, which could be wrong. You tested that assumption using estat phtest. If that assumption is not met, than you need to relax that assumption. In this case, that means allowing the effects of gr to change with time. To allow the effect of one variable to change with another variable, is adding an interaction effect. This interaction effect is best added using the tvc() and texp() options, in stcox.

[Buyadaa Oyunchimeg]

Thank for your answer.