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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 15:23:50 +0200
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:
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--
Dr. Yuval Arbel
School of Business
Carmel Academic Center
4 Shaar Palmer Street,
Haifa 33031, Israel
e-mail1: [email protected]
e-mail2: [email protected]
*
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