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From |
Yuval Arbel <yuval.arbel@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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 <sjsamuels@gmail.com> 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 <yuval.arbel@gmail.com> 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 <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 >>> 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 >> >> >> >> -- >> 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/ > > > > -- > 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/ > > > * > * 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/

**Follow-Ups**:**st: Calculate average elements matrix (below the diagonal )***From:*John Antonakis <John.Antonakis@unil.ch>

**References**:**st: Re: Interpretation of the Coefficients obtained via -stcox-***From:*Yuval Arbel <yuval.arbel@gmail.com>

**Re: st: Re: Interpretation of the Coefficients obtained via -stcox-***From:*Yuval Arbel <yuval.arbel@gmail.com>

**Re: st: Re: Interpretation of the Coefficients obtained via -stcox-***From:*Steve Samuels <sjsamuels@gmail.com>

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