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


From   Adam Olszewski <adam.olszewski@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Survival Analysis estat phtest with very large sample size--need help
Date   Fri, 6 Dec 2013 13:08:57 -0500

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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>>> http://statalist.1588530.n2.nabble.com/Survival-Analysis-estat-phtest-with-very-large-sample-size-need-help-tp7580460.html
>>> Sent from the Statalist mailing list archive at Nabble.com.
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