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# Re: st: Survival Analysis estat phtest with very large sample size--need help

 From Peter Rymkiewicz To statalist@hsphsun2.harvard.edu Subject Re: st: Survival Analysis estat phtest with very large sample size--need help Date Fri, 06 Dec 2013 11:34:07 -0700

```Thanks Adam,

This is very useful. I appreciate your help.

Peter

Peter

On 13-12-06 11:08 AM, Adam Olszewski wrote:
```
```To answer your other question through the list:
The estat phtest is basically a statistical test for the zero slope of
residuals graph. As you can imagine, even a very very tiny slope will
be "statistically significant" once the dataset is large enough. You
can try to plot the residuals with a confidence interval band (twoway
lfitci) and see for yourself, and perhaps this is the way to go if you
want to just arbitrarily decide what is proportional and what is not.
But if you see a noticeable slope, then of course the hazard is not
proportional. You have to realize that the PH assumption is a
mathematical approximation of the world that is not true in a "real"
sense anyway. It actually just cannot be: if you observe your
population for survival long enough, everyone will die and what is the
hazard ratio at that time? The question is - does it matter for the
purpose of what you are studying?
AO

On Fri, Dec 6, 2013 at 12:55 PM, Peter Rymkiewicz
<peter.rymkiewicz@gmail.com> wrote:
```
```Hi Adam,

Thanks for your response. I agree with all that you have said... part of the
issue is that this work is towards a thesis and I need to reference
literature or statistics materials. Will try to use the TVC option with the
original model and look to see what the resulting effect is on the HR of
each of the covariates in  the model.

I am also running an alternative model which actually captures time
dependance. as you predicted the AIC is higher but this model actually
includes information past baseline.

Thanks,
Peter

On 13-12-05 7:41 PM, Adam Olszewski wrote:
```
```Hi Peter,
As with any statistical test that uses a null hypothesis, the p-value
for the phtest is dependent on the sample size. These tests were not
developed for such large datasets. In population-based survival
analyses violations of PH assumptions are universal, just as linearity
assumptions are. One way to deal with it on a practical level is to
see how much inclusion of a time-varying effect would affect your main
effect HR. If the difference is null, then the PH violation is
practically of no significance. This helps if you are only interested
in one coefficient (more of a problem if your variable of interest
violates the PH, in which you should rethink your interpretation).
Other ways of dealing with it are: 1) relying on the graphical
interpretation of residuals alone, as you did, 2) using AIC as a
measure of model fit: does the inclusion of time-varying effects (or
stratification in Cox model) significantly alter model fit? More often
than no the AIC will actually increase.
I cannot quote you literature on this off the top of my head though.
Best,
AO

On Thu, Dec 5, 2013 at 9:26 PM, prymkiewicz <peter.rymkiewicz@gmail.com>
wrote:
```
```Hi,

I need a bit of help.

I am doing a survival analysis on a large population ~435732 people.  I
have
been testing the PH assumption using estat phtest and schoenfled
residuals.
I believe that the large sample size is causing the phtest indicate
evidence
against the PH assumption while the schoenfeld plot would indicate that
the
model variables adheres to the PH assumption. I have included the global
and
individual variable tests, as well as the plot for one of our variables
(mets). Could you let me know the cause of this and could you let me know
if
there are alternative methods or references in literature acknowledging
the
phtest and alternative methods for very large study populations.

Thanks,
Peter

. estat phtest, detail

Test of proportional-hazards assumption

Time:  Time
----------------------------------------------------------------
|       rho            chi2       df       Prob>chi2
------------+---------------------------------------------------
male        |      0.01247        11.18        1         0.0008
age         |      0.05331       252.06        1         0.0000
0b.urban    |            .            .        1             .
1.urban     |     -0.01640        19.44        1         0.0000
99.urban    |     -0.00225         0.36        1         0.5472
1b.quintile |            .            .        1             .
2.quintile  |     -0.00620         2.74        1         0.0976
3.quintile  |     -0.00745         3.98        1         0.0461
4.quintile  |     -0.00025         0.00        1         0.9457
5.quintile  |     -0.00311         0.70        1         0.4039
99.quintile |     -0.00119         0.10        1         0.7499
mi_1        |     -0.00795         4.63        1         0.0314
chf_1       |     -0.02492        47.01        1         0.0000
pvd_1       |      0.00206         0.32        1         0.5734
cevd_1      |     -0.02076        32.80        1         0.0000
dem_1       |      0.00630         3.05        1         0.0807
copd_1      |     -0.01545        17.10        1         0.0000
rheum_1     |     -0.00840         5.06        1         0.0245
pub_1       |     -0.00712         3.67        1         0.0553
mildld_1    |     -0.00959         6.59        1         0.0102
diab_uc_1   |     -0.02159        34.32        1         0.0000
diab_c_1    |      0.01731        21.99        1         0.0000
para_1      |     -0.01532        17.14        1         0.0000
rd_1        |     -0.03307        82.48        1         0.0000
cancer_1    |     -0.03237        72.39        1         0.0000
mlsd_1      |     -0.00246         0.43        1         0.5099
mets_1      |     -0.06236       272.50        1         0.0000
hiv_1       |     -0.00863         5.31        1         0.0213
------------+---------------------------------------------------
global test |                   1392.71       26         0.0000
----------------------------------------------------------------

<http://statalist.1588530.n2.nabble.com/file/n7580460/phtest_plot_mets_1.jpg>

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