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

[Adam Olszewski <adam.olszewski@gmail.com>]

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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