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Re: st: stcox in case the ph-assumption is rejected


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: stcox in case the ph-assumption is rejected
Date   Fri, 6 Jan 2012 14:46:55 +0100

You should use stratification only for those variables you do not care
about, as after stratification you can no longer include that variable
 in your model, and thus not show what the effect of that variable is.
I would not use stratification for (pseudo-)continuous variables,
because it is an idea that is based on a small set of well defined
groups (or at least a number of well defined groups with a sufficient
number of observations in each group). Splitting a pseudo-continuous
variable at the mean sounds a bit too ad hoc for my taste to classify
as two well defined groups.

Hope this helps,
Maarten (not Marteen)

On Fri, Jan 6, 2012 at 2:23 PM, Yuval Arbel wrote:
> Thanks Marteen - that seems to be very helpful.
>
> I also thought about a different solution I would like to consult with
> you about:
>
> For each of the explanatory variables in the regression model I
> defined a dummy variable which receives 1 for periods whose numerical
> values are above or equal the sample mean and 0 otherwise. This
> provides several possible stratifications. I then ran the Cox
> regression on these dummy variables, where, as mentioned above, each
> of which provides a different stratification, followed by the
> PH-assumption test. Now and as we can see from the outcomes below - I
> can say that the outcomes of the Cox regression is valid only for
> stratifications where the PH-assumption is valid.
>
> Here is the output:
>
> . stcox mean_reduct_dum1 reductcurrent_mean_reduct_dum1 rent_net8_dum
> diff_stdmadadarea_dum diff_mortgage_dum perma
>> nentincomeestimate82_dum appreciation_dum,nohr
>
>         failure _d:  fail == 1
>   analysis time _t:  time_index
>                 id:  appt
>
> Iteration 0:   log likelihood = -78368.249
> Iteration 1:   log likelihood = -75173.499
> Iteration 2:   log likelihood = -75117.414
> Iteration 3:   log likelihood = -75116.825
> Iteration 4:   log likelihood = -75116.825
> Refining estimates:
> Iteration 0:   log likelihood = -75116.825
>
> Cox regression -- Breslow method for ties
>
> No. of subjects =         9547                     Number of obs   =    499393
> No. of failures =         9547
> Time at risk    =       547035
>                                                   LR chi2(7)      =   6502.85
> Log likelihood  =   -75116.825                     Prob > chi2     =    0.0000
>
> ------------------------------------------------------------------------------
>          _t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
> mean_redu~m1 |   1.160556   .0260155    44.61   0.000     1.109567    1.211546
> reductcur~m1 |   1.332635   .0276246    48.24   0.000     1.278492    1.386779
> rent_net8_~m |   .2179676   .0216012    10.09   0.000       .17563    .2603052
> diff_stdma~m |   .8829475   .0920925     9.59   0.000     .7024495    1.063446
> diff_mortg~m |   .2271822   .0913231     2.49   0.013     .0481921    .4061722
> permanenti~m |  -.0774641   .0212722    -3.64   0.000    -.1191569   -.0357713
> appreciati~m |  -.1104136   .0475282    -2.32   0.020    -.2035672   -.0172601
> ------------------------------------------------------------------------------
>
> . estat phtest,detail
>
>      Test of proportional-hazards assumption
>
>      Time:  Time
>      ----------------------------------------------------------------
>                  |       rho            chi2       df       Prob>chi2
>      ------------+---------------------------------------------------
>      mean_redu~m1|     -0.29894       664.62        1         0.0000
>      reductcur~m1|     -0.01441         2.31        1         0.1283
>      rent_net8_~m|     -0.01523         2.21        1         0.1374
>      diff_stdma~m|     -0.01545         0.10        1         0.7516
>      diff_mortg~m|     -0.14583         6.94        1         0.0084
>      permanenti~m|      0.06388        39.67        1         0.0000
>      appreciati~m|      0.04365        17.29        1         0.0000
>      ------------+---------------------------------------------------
>      global test |                    758.70        7         0.0000
>      ----------------------------------------------------------------
>
> I wonder what is your opinion. We see here 3 stratifications, which
> makes the results of the Cox regression valid
>
> Thanks, Yuval
>
> On Fri, Jan 6, 2012 at 2:54 PM, Maarten Buis <maartenlbuis@gmail.com> wrote:
>>> On Fri, Jan 6, 2012 at 10:06 AM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>>>> My first question is whether this discussion [of the proportional hazard assumption, MB] is relevant if I am
>>>> applying the Cox model to describe the exercise of call (real) options
>>>> to purchase appartments.
>>>>
>>>> My second question is <snip>: is there any command to incorporate the -stcox- with
>>>> varying hazard level across time? I'm aware of the -strata()- option,
>>>> but I wonder whether I can somehow account for time-varying covariates
>>>> and incorporate it with -stcox-
>>
>> On Fri, Jan 6, 2012 at 9:33 AM, Yuval Arbel wrote:
>>> Note also that in the medical context, the treatment - is a binary
>>> variable, which equals 1 for the experimental treatment and 0
>>> otherwise.
>>> In our context - the variable of interest is the reduction rate in
>>> percentage points - where this variable is quantitative.
>>
>> The proportional hazard assumption is required for Cox regression
>> regardless of whether you are dealing with medical or economic data,
>> the variables are binary or (pseudo-)continuous, or you have
>> experimental or observational data.
>>
>> I gave an example on how to estimate and interpret a Cox model in
>> which you relax the proportional hazard assumption by allowing the
>> effect to change over time here:
>> <http://www.stata.com/statalist/archive/2011-06/msg00358.html>
>>
>> Hope this helps,
>> Maarten
>>
>> --------------------------
>> Maarten L. Buis
>> Institut fuer Soziologie
>> Universitaet Tuebingen
>> Wilhelmstrasse 36
>> 72074 Tuebingen
>> Germany
>>
>>
>> http://www.maartenbuis.nl
>> --------------------------
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/statalist/faq
>> *   http://www.ats.ucla.edu/stat/stata/
>
>
>
> --
> Dr. Yuval Arbel
> School of Business
> Carmel Academic Center
> 4 Shaar Palmer Street,
> Haifa 33031, Israel
> e-mail1: yuval.arbel@carmel.ac.il
> e-mail2: yuval.arbel@gmail.com
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/



-- 
--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany


http://www.maartenbuis.nl
--------------------------

*
*   For searches and help try:
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*   http://www.ats.ucla.edu/stat/stata/


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