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Re: st: stcox in case the ph-assumption is rejected
From
Yuval Arbel <[email protected]>
To
[email protected]
Subject
Re: st: stcox in case the ph-assumption is rejected
Date
Fri, 6 Jan 2012 16:24:48 +0200
I'm refering to my following working paper published at SSRN:
http://ssrn.com/abstract=1973326
My intentions are only to supplement a footnote and present the
HP-assumption tests in an appendix and not to go further beyond that.
I provide these stratifications as an example. The question is whether
in your opinion this is sufficient - or should I modify all the
outcomes reported in the paper based on the -tvc- option.(On one hand,
I would like to make here a careful econometric work. On the other
hand, I consider whether it worth all the trouble or it might be
sufficient to show that at least one stratification does not reject
the PH-hypothesis)
On Fri, Jan 6, 2012 at 3:46 PM, Maarten Buis <[email protected]> wrote:
> 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 <[email protected]> wrote:
>>>> On Fri, Jan 6, 2012 at 10:06 AM, Yuval Arbel <[email protected]> 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: [email protected]
>> e-mail2: [email protected]
>>
>> *
>> * 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:
> * 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: [email protected]
e-mail2: [email protected]
*
* 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/