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Re: st: Re: Interpretation of the Coefficients obtained via -stcox-
From
Yuval Arbel <[email protected]>
To
[email protected]
Subject
Re: st: Re: Interpretation of the Coefficients obtained via -stcox-
Date
Sun, 9 Sep 2012 22:05:04 +0300
Steve, thank you for the answer. We indeed get this solution of exp(b)
if we run -stcox- without -nohr-
BTW: I believe there is a gap between the mathematical and actual
solution. This emanates from the fact that the mathematical solution
is correct for a very small (infitisimal) change
On Sun, Sep 9, 2012 at 9:17 PM, Steve Samuels <[email protected]> wrote:
> You are not correct. Although your calculus is right, the approximation
> to the percentage change will be poor in general. Moreover it isn't
> necessary to approximate as the exact result is available.
>
> Suppose the model is:
> (*) log h(t|x) = a(t) + b x
>
> h(t|x) = exp(a(t) +b x)
>
> Increase x by 1 unit: h(t|x+1) = exp(a(t) +b x +b)
>
> hazard ratio ht(t|x+1)/h(t|x) = exp(b)
>
> Percentage change
>
> 100* (h(t|x+1) - h(t|x))/h(t|x) = 100* (exp(b) -1)
>
> Only if b is close to zero is this ~ 100*b
>
> Your results: For b = .0382773, exp(b)-1 = 0.0390 so the approximation is not
> bad. On the other hand, the coefficient for "appreciation" is about +11, but
> exp(11)-1 is ~60,000! The approximation is bad even for b = 0.51, the coefficient
> of your fourth predictor, as exp(0.51)-1 = 0.665.
>
>
> Steve
>
>
> On Sep 9, 2012, at 9:18 AM, Yuval Arbel wrote:
>
> 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 <[email protected]> wrote:
>> Dear statalisters,
>>
>> I appreciate very much your answer to this question.
>>
>> 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
>> diff_stdmadadarea permanentincomeestimate82 diff_mortgage
>> 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 <[email protected]> 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
>>> School of Business
>>> Carmel Academic Center
>>> 4 Shaar Palmer Street,
>>> Haifa 33031, Israel
>>> e-mail1: [email protected]
>>> e-mail2: [email protected]
>>
>>
>>
>> --
>> 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/
>
>
>
> --
> 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/
>
>
> *
> * 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/