Interpreting COX regression model

[Jeffrey Hing]

I am new to survival analysis
the following is my stata output for stcox i.OPtype age i.Grade i.pT_stg i.pN_stg i.profile_grp i.adjuvantCTx i.adjuvantRTx i.adjuvantHTx

Does the model have good fit ? Can we interpret Grade, pT_stg pN_stg and adjuvantCTx are predictive factors for event?

Why does grade 1 , pT_stg 2 and 3 return empty ?
Cox regression with no ties

No. of subjects = 496 Number of obs = 496
No. of failures = 11
Time at risk = 41,547.4334
LR chi2(14) = 27.97
Log likelihood = -49.900141 Prob > chi2 = 0.0144

----------------------------------------------------------------------------------
_t | Haz. ratio Std. err. z P>|z| [95% conf. interval]
-----------------+----------------------------------------------------------------
OPtype |
Oncoplastic BCS | .6868941 .5714724 -0.45 0.652 .1344991 3.508006
age | 1.00784 .0337547 0.23 0.816 .9438062 1.076217
|
Grade |
1 | 4.58e+08 . . . . .
2 | 2.26e+08 1.83e+08 23.68 0.000 4.60e+07 1.11e+09
3 | 1.77e+08 2.31e+08 14.57 0.000 1.38e+07 2.28e+09
|
pT_stg |
1 | 1.57e+08 1.98e+08 14.97 0.000 1.33e+07 1.86e+09
2 | 5.94e+07 . . . . .
3 | 9.59e-10 . . . . .
|
pN_stg |
1 | 2.596447 3.103781 0.80 0.425 .2493773 27.03348
2 | 47.70519 72.07748 2.56 0.011 2.468825 921.809
3 | 101.268 161.3288 2.90 0.004 4.461004 2298.855
|
profile_grp |
HR+ Her- | .036285 .0767722 -1.57 0.117 .0005738 2.294609
HR+ Her2+ | 4.89e-21 . . . . .
HR- Her2- | .1837431 .3253954 -0.96 0.339 .0057121 5.910521
HR- Her2+ | .4165586 .8317754 -0.44 0.661 .0083179 20.86111
|
adjuvantCTx |
Yes | .0623398 .0685511 -2.52 0.012 .0072236 .5379938
|
adjuvantRTx |
Yes | .951613 1.114361 -0.04 0.966 .0958701 9.445777
|
adjuvantHTx |
Yes | .7045474 .7733386 -0.32 0.750 .0819593 6.056505
----------------------------------------------------------------------------------

[Maarten Buis]

You are probably overfitting your data. With only 11 failures there just isn't a lot of information in your data. Simplifying your model is probably unavoidable. We don't like that, but statistical technique can only reveal information that is already present in the data. If the information is not in the data, than no statistical technique can save us. (On the other hand, since this seems to be medical data, the patients and their families will be quite happy there are so few failures...). One way to simplify your model is to reduce the number of categories in your categorical variables. A good candidate will be Grade. In your reference category (0) it only has 4 observations. That is one of the reasons of the ridiculous effect sizes. So that has to go, maybe merge categories 0 and 1. That is probably not enough, you will need to drop more variables.

[Jeffrey Hing]

Thank you. I shall try to collapse and remove variables.

1) I am trying to show difference in outcomes in the OPtype if any.. . any suggestion how this can be done better? given the events are between 10 to 40 , and total n = 490
when i use stcox i.OPtype, p=0.71 -> i think this is good evidence that the OPtype does not have any predictive value.... but how do i show that it remains so after adjusting for other covariates?

Cox regression with no ties

No. of subjects = 538 Number of obs = 538
No. of failures = 11
Time at risk = 45,002.2667
LR chi2(1) = 0.14
Log likelihood = -64.648001 Prob > chi2 = 0.7068

----------------------------------------------------------------------------------
_t | Haz. ratio Std. err. z P>|z| [95% conf. interval]
-----------------+----------------------------------------------------------------
OPtype |
Oncoplastic BCS | .7786501 .5273234 -0.37 0.712 .2064834 2.936294
----------------------------------------------------------------------------------



2) can i clarify
stcox var1 = univariate analysis
stcox var1 var2 var 3.... means a multivariate analysis

so i have done all the univariate analysis on the individual variables -> only adjuvantCTx has been shown to be significant in univariate 0.03

i see some paper using a higher p cut off to decide to be put in the multivariate like 0.1 . what is the highest p cut off recommended to form part of the multivariate ? 0.2 ? 0.3?

3) so in this case i decide to fit adjuvantCTx into a multivariate analysis with others .... how important is the Prob > chi2 value to be <0.05 when i fit the multiple covariates?

Do I have to show the Prob > chi2 value in the final results of multivariate analysis ? Some studies seem to omit it... is that bad statistics reporting?

[Jeffrey Hing]

I have collapsed and reduced the variables to binary groups as clinically sound as it can be

Do you think this model is a better fit ?

Can i draw some hypothesis that Nodal involvement and adjuvant CTx were significant preditive factors from the multivariate analysis?

Adjusted model for IBDFS -> N stage, HR+ , no adjuvantCTx – predictive
Cox regression with no ties

No. of subjects = 496 Number of obs = 496
No. of failures = 11
Time at risk = 41,547.4334
LR chi2(8) = 15.49
Log likelihood = -56.140712 Prob > chi2 = 0.0503

----------------------------------------------------------------------------------
_t | Haz. ratio Std. err. z P>|z| [95% conf. interval]
-----------------+----------------------------------------------------------------
OPtype |
Oncoplastic BCS | 1.004597 .707045 0.01 0.995 .252876 3.990945
age | 1.000331 .0289541 0.01 0.991 .9451615 1.05872
1.Grade_b | .9460382 .8408483 -0.06 0.950 .1657113 5.400889
1.pT_stg_b | .3051431 .3492425 -1.04 0.300 .0323807 2.875551
1.pN_stg_b | 6.277062 5.011925 2.30 0.021 1.312544 30.01919
1.HR_gp | .226595 .154796 -2.17 0.030 .0593965 .8644494
|
adjuvantCTx |
Yes | .093439 .076913 -2.88 0.004 .0186154 .4690112
|
adjuvantRTx |
Yes | 1.078709 .982753 0.08 0.934 .1808927 6.432616
----------------------------------------------------------------------------------