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# Re: st: Re: Interpretation of the Coefficients obtained via -stcox-

 From Yuval Arbel To statalist Subject Re: st: Re: Interpretation of the Coefficients obtained via -stcox- Date Sun, 9 Sep 2012 16:18:40 +0300

```Dear statalisters,

I ask this question because I noted that on one hand some scholars,
who applied the Cox Regression, seems to  avoid a direct
interpretation of the coefficients obtained via this procedure. It
occurred to me there might be a resemblance to -probit-, which does
not yield the coefficient in terms of marginal probabilities (as
opposed to
-dprobit-).

On the other hand, if we take a look at the model's specification
according to stata's manual:

h(t) = h0(t) exp( b1x1 +...  + bkxk)

and derive the term d(h(t))/d(xk), we get:

d(h(t))/d(xk)=h0(t) exp( b1x1 +...  + bkxk)bk=h(t)bk

and then: bk=[dh(t)/h(t)]/d(xk) implying a percent chance on the
hazard to survive in the numerator.

I wonder am I correct here?

On Sun, Sep 9, 2012 at 9:26 AM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
> Dear statalisters,
>
>
> I'm attaching below the estimation results of -stcox-.
>
> Do they imply that if we increase mean_reduct by 1 unit the hazard to
> survival increase by 3.83 percent?
>
> . stcox mean_reduct reductcurrent_mean_reduct rent_net8
> appreciation if nachut==0 & nachutspouse==0 & diff_per>=-5 &
> diff_per<=5,nohr
>
>          failure _d:  fail == 1
>    analysis time _t:  time_index
>                  id:  appt
>
> Iteration 0:   log likelihood = -56991.691
> Iteration 1:   log likelihood = -54168.973
> Iteration 2:   log likelihood = -53930.527
> Iteration 3:   log likelihood = -53916.083
> Iteration 4:   log likelihood = -53915.926
> Iteration 5:   log likelihood = -53915.926
> Refining estimates:
> Iteration 0:   log likelihood = -53915.926
>
> Cox regression -- Breslow method for ties
>
> No. of subjects =         7191                     Number of obs   =    324499
> No. of failures =         7191
> Time at risk    =       351446
>                                                    LR chi2(7)      =   6151.53
> Log likelihood  =   -53915.926                     Prob > chi2     =    0.0000
>
> ------------------------------------------------------------------------------
>           _t |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
> -------------+----------------------------------------------------------------
>  mean_reduct |   .0382773   .0006943    55.13   0.000     .0369165    .0396382
> reductcurr~t |   .0282488   .0007893    35.79   0.000     .0267018    .0297958
>    rent_net8 |   .0018389   .0001947     9.45   0.000     .0014573    .0022204
> diff_stdma~a |  -.5076186   .0579597    -8.76   0.000    -.6212176   -.3940197
> permanent~82 |  -.0005113   .0000862    -5.93   0.000    -.0006803   -.0003423
> diff_mortg~e |  -7.715171    1.23864    -6.23   0.000    -10.14286   -5.287481
> appreciation |   10.94379   3.632834     3.01   0.003     3.823562    18.06401
> ------------------------------------------------------------------------------
>
>
> On Tue, Aug 21, 2012 at 1:14 AM, Yuval Arbel <yuval.arbel@gmail.com> wrote:
>> Dear Statalisters,
>>
>> According to stata manual the command -stcox- estimates the following model:
>>
>> h(t) = h0(t) exp( b1x1 +...  + bkxk)
>>
>> where h(t) is the hazard to survival.
>>
>> Can I infer from this specification that bk in its original form
>> (nohr) measures the percent change of the hazard to survive with
>> respect to xk?
>>
>>
>> --
>> Dr. Yuval Arbel
>> 4 Shaar Palmer Street,
>> Haifa 33031, Israel
>> e-mail1: yuval.arbel@carmel.ac.il
>> e-mail2: yuval.arbel@gmail.com
>
>
>
> --
> Dr. Yuval Arbel
> 4 Shaar Palmer Street,
> Haifa 33031, Israel
> e-mail1: yuval.arbel@carmel.ac.il
> e-mail2: yuval.arbel@gmail.com
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--
Dr. Yuval Arbel