Checking proportional hazard assumption

[David Meldon]

Dear Statalist Community,

I am sorry if this post has an obvious solution, but it is something I am not 100% convinced about and that is why I decided to post it here. Thank you very much in advance.

I am doing a survival analysis study from a cohort of patients, looking if they have a stroke with the aim of finding risk factors. I explained this in detail in some of my previous posts. The time variable is age, to standardise for it.

One of the important factors, from its clinical relevance, is gender.

The Kaplan Meyer curve and survival function looks like the following.

sts list, by(sex)

         failure _d:  stroketotallong_ == 1
   analysis time _t:  meanageass_
  enter on or after:  time==.
  exit on or before:  stroketotallong_==2
                 id:  id

             At           Net    Survivor      Std.
  Time     Risk   Fail   Lost    Function     Error     [95% Conf. Int.]
------------------------------------------------------------------------
Male 
    17        0      0     -2      1.0000         .          .         .
    18        2      0     -2      1.0000         .          .         .
    19        4      0     -3      1.0000         .          .         .
    20        7      0     -4      1.0000         .          .         .
    21       11      0     -4      1.0000         .          .         .
    22       15      0     -1      1.0000         .          .         .
    23       16      0      2      1.0000         .          .         .
    24       14      0     -1      1.0000         .          .         .
    25       15      0     -2      1.0000         .          .         .
    26       17      1      4      0.9412    0.0571     0.6502    0.9915
    27       12      0      2      0.9412    0.0571     0.6502    0.9915
    29       10      0      1      0.9412    0.0571     0.6502    0.9915
    30        9      0     -1      0.9412    0.0571     0.6502    0.9915
    31       10      0      1      0.9412    0.0571     0.6502    0.9915
    32        9      0     -1      0.9412    0.0571     0.6502    0.9915
    33       10      0     -2      0.9412    0.0571     0.6502    0.9915
    34       12      0      3      0.9412    0.0571     0.6502    0.9915
    35        9      0     -4      0.9412    0.0571     0.6502    0.9915
    36       13      2     -6      0.7964    0.1058     0.4893    0.9300
    37       17      0      1      0.7964    0.1058     0.4893    0.9300
    38       16      1      0      0.7466    0.1103     0.4551    0.8972
    39       15      0      1      0.7466    0.1103     0.4551    0.8972
    40       14      0      1      0.7466    0.1103     0.4551    0.8972
    41       13      2      1      0.6317    0.1196     0.3570    0.8148
    42       10      1     -5      0.5686    0.1232     0.3019    0.7663
    43       14      2     -3      0.4873    0.1182     0.2484    0.6901
    45       15      1      0      0.4549    0.1147     0.2287    0.6566
    46       14      1     -4      0.4224    0.1110     0.2087    0.6225
    47       17      1     -2      0.3975    0.1072     0.1947    0.5945
    48       18      0      3      0.3975    0.1072     0.1947    0.5945
    49       15      1     -5      0.3710    0.1033     0.1792    0.5645
    50       19      2     -4      0.3320    0.0961     0.1581    0.5172
    51       21      1      1      0.3162    0.0928     0.1500    0.4972
    52       19      1      3      0.2995    0.0894     0.1411    0.4761
    53       15      2     -1      0.2596    0.0818     0.1186    0.4261
    54       14      0     -1      0.2596    0.0818     0.1186    0.4261
    55       15      0      1      0.2596    0.0818     0.1186    0.4261
    57       14      0     -2      0.2596    0.0818     0.1186    0.4261
    58       16      1     -3      0.2434    0.0783     0.1100    0.4047
    59       18      2     -1      0.2163    0.0719     0.0961    0.3677
    60       17      0      2      0.2163    0.0719     0.0961    0.3677
    61       15      1     -7      0.2019    0.0685     0.0885    0.3479
    62       21      0      1      0.2019    0.0685     0.0885    0.3479
    63       20      2      0      0.1817    0.0631     0.0787    0.3186
    64       18      1      0      0.1716    0.0604     0.0737    0.3038
    65       17      0     -2      0.1716    0.0604     0.0737    0.3038
    66       19      0      5      0.1716    0.0604     0.0737    0.3038
    68       14      1      0      0.1594    0.0573     0.0674    0.2862
    69       13      1      2      0.1471    0.0542     0.0612    0.2685
    70       10      0      2      0.1471    0.0542     0.0612    0.2685
    72        8      1      1      0.1287    0.0505     0.0507    0.2443
    73        6      0     -1      0.1287    0.0505     0.0507    0.2443
    74        7      0      2      0.1287    0.0505     0.0507    0.2443
    75        5      0     -2      0.1287    0.0505     0.0507    0.2443
    76        7      2     -2      0.0919    0.0422     0.0308    0.1946
    77        7      2      0      0.0657    0.0340     0.0192    0.1532
    78        5      1      3      0.0525    0.0296     0.0137    0.1320
    79        1      0      1      0.0525    0.0296     0.0137    0.1320
    81        0      0     -1      0.0525    0.0296     0.0137    0.1320
    87        1      0      1      0.0525    0.0296     0.0137    0.1320
Female 
    17        3      0     -8      1.0000         .          .         .
    18       11      0     -5      1.0000         .          .         .
    19       16      0     -2      1.0000         .          .         .
    21       18      0     -3      1.0000         .          .         .
    22       21      0     -4      1.0000         .          .         .
    23       25      0      4      1.0000         .          .         .
    24       21      0      2      1.0000         .          .         .
    25       19      0     -2      1.0000         .          .         .
    26       21      0      1      1.0000         .          .         .
    27       20      0     -5      1.0000         .          .         .
    29       25      0      3      1.0000         .          .         .
    30       22      0      1      1.0000         .          .         .
    31       21      1     -2      0.9524    0.0465     0.7072    0.9932
    32       22      0     -3      0.9524    0.0465     0.7072    0.9932
    33       25      1      6      0.9143    0.0582     0.6975    0.9780
    34       18      0      2      0.9143    0.0582     0.6975    0.9780
    35       16      0     -7      0.9143    0.0582     0.6975    0.9780
    36       23      0     -1      0.9143    0.0582     0.6975    0.9780
    37       24      0      1      0.9143    0.0582     0.6975    0.9780
    38       23      1     -5      0.8745    0.0679     0.6590    0.9578
    39       27      1      2      0.8421    0.0727     0.6314    0.9378
    40       24      1     -5      0.8071    0.0777     0.5965    0.9149
    41       28      1     -2      0.7782    0.0801     0.5710    0.8939
    42       29      1      0      0.7514    0.0817     0.5476    0.8732
    43       28      0      4      0.7514    0.0817     0.5476    0.8732
    44       24      0     -2      0.7514    0.0817     0.5476    0.8732
    45       26      0     -1      0.7514    0.0817     0.5476    0.8732
    46       27      2     -6      0.6957    0.0846     0.4968    0.8285
    47       31      0      7      0.6957    0.0846     0.4968    0.8285
    48       24      1     -1      0.6667    0.0859     0.4697    0.8046
    50       24      0      1      0.6667    0.0859     0.4697    0.8046
    51       23      0     -1      0.6667    0.0859     0.4697    0.8046
    52       24      3     -9      0.5834    0.0876     0.3944    0.7319
    53       30      2     -5      0.5445    0.0860     0.3638    0.6939
    54       33      1      2      0.5280    0.0849     0.3513    0.6772
    55       30      1      0      0.5104    0.0839     0.3376    0.6593
    56       29      1      0      0.4928    0.0828     0.3240    0.6413
    57       28      0      5      0.4928    0.0828     0.3240    0.6413
    58       23      1     -2      0.4714    0.0820     0.3063    0.6200
    59       24      2      2      0.4321    0.0797     0.2750    0.5796
    61       20      1      0      0.4105    0.0786     0.2574    0.5575
    62       19      1     -1      0.3889    0.0774     0.2400    0.5352
    64       19      1      3      0.3684    0.0759     0.2239    0.5136
    65       15      0      1      0.3684    0.0759     0.2239    0.5136
    66       14      1      0      0.3421    0.0749     0.2018    0.4873
    67       13      1      3      0.3158    0.0737     0.1802    0.4606
    69        9      1     -3      0.2807    0.0734     0.1494    0.4279
    70       11      3     -4      0.2041    0.0653     0.0946    0.3428
    71       12      1     -1      0.1871    0.0621     0.0846    0.3207
    72       12      0     -1      0.1871    0.0621     0.0846    0.3207
    73       13      1      0      0.1727    0.0589     0.0766    0.3012
    74       12      1     -1      0.1583    0.0557     0.0686    0.2816
    75       12      2     -1      0.1320    0.0495     0.0544    0.2444
    76       11      0      2      0.1320    0.0495     0.0544    0.2444
    77        9      1      0      0.1173    0.0461     0.0464    0.2240
    78        8      1      0      0.1026    0.0426     0.0386    0.2034
    79        7      0      2      0.1026    0.0426     0.0386    0.2034
    83        5      2     -1      0.0616    0.0340     0.0164    0.1511
    84        4      0      2      0.0616    0.0340     0.0164    0.1511
    86        2      0      1      0.0616    0.0340     0.0164    0.1511
    87        1      0      1      0.0616    0.0340     0.0164    0.1511
------------------------------------------------------------------------

From these results, it seems that males have a higher risk than females at a younger age, and this gets reversed as patients get older.

This made me think that the variable gender violets the PH assumption, hence, I should stratify for it in the Cox regression, instead of running the regression with sex as a covariable. However, if I run a stcox with sex and test for its PH assumption, I get the results that state that the PH assumption is not violated.

 stcox sex 

         failure _d:  stroketotallong_ == 1
   analysis time _t:  meanageass_
  enter on or after:  time==.
  exit on or before:  stroketotallong_==2
                 id:  id

Iteration 0:   log likelihood = -250.79081
Iteration 1:   log likelihood = -250.04182
Iteration 2:   log likelihood = -250.04144
Refining estimates:
Iteration 0:   log likelihood = -250.04144

Cox regression -- Breslow method for ties

No. of subjects =          380                  Number of obs    =       1,849
No. of failures =           73
Time at risk    =         2093
                                                LR chi2(1)       =        1.50
Log likelihood  =   -250.04144                  Prob > chi2      =      0.2209

------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         sex |   .7456718   .1779156    -1.23   0.219     .4671464    1.190262
------------------------------------------------------------------------------

. estat phtest

      Test of proportional-hazards assumption

      Time:  Time
      ----------------------------------------------------------------
                  |                      chi2       df       Prob>chi2
      ------------+---------------------------------------------------
      global test |                      2.45        1         0.1172
      ----------------------------------------------------------------

Given this, I thought about using sex as a covariable...but every day that goes by makes me feel a bit more insecure about that decision.

I would be really grateful if you could advise me on this issue.

Thank you very much.

David.

[Carlo Lazzaro]

David:
I find strange that -gender- can be the only predictor for a stroke occurrence.
Untreated high BP, previous strokes and high BMI are the first other independent variables that spring to an amateur's mind,
That said, I would take a look at the tons of literature on this topic and reconsider the right-hand side of my regression equation accordingly.

[David Meldon]

Dear Carlo,

Thank you very much for your reply.

Indeed, those risk factors you listed are critical in the general population. In my study, we look at the risk of stroke in a rare genetic condition (which is treatable) that affects differently to males than females; hence, the interest in knowing if the risk of stroke was different between them. However, I also have cardiovascular risk factors (diabetes, hypertension, smoking...) as well as other important factors of the disease (heart problems...) My idea was:

1. Look at the univariate analysis and KM curves
2. Adjust each possible risk factor by gender and genetic alteration stratifying by no treatment status (this will be done through a stcox regression with gender + genetic alteration + the other risk factor)
3. Multivariate stcox regression with all the risk factors that are significant in step 2.

This is why it is so important to me to know if I can put gender in the stcox regression or stratify by it, as it will appear in all the regressions. I hope this clarifies my previous post.

Once again, thank you very much for your help.

Best regards,

David.

[Carlo Lazzaro]

David:
1) despite its wide presence in high standing clinical journal, I'm not a big fan of univariate analyses, as the predictors are more informative when they're adjusted by each other. Notwithstanding, sometimes univariate analyses highlight some unexpected predictor as relevant (admittedly, I do not think this is your case, as stroke predictors have been well studied);
2) I would follow your point 2) and see what happens;
3) just a sidelight from the pedantry corner: you have a multivariate regression when you have more than one regressand (see for instance -help mvreg-). In your case you have a multiple -stcox-, since you will end up with for than one predictors.

[David Meldon]

Dear Carlo,

Thank you very much for your reply.

I will follow your advice and thank you very much for clarifying the multivariate/multiple stcox. It will be really important when the time to write the paper comes.

Best regards,

David.

[Carlo Lazzaro]

David:
yes, it is, just like all the trivial mistakes that can unleash reviewers' (bad) reaction to our papers !