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From |
Steve Samuels <sjsamuels@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Re: Interpretation of the Coefficients obtained via -stcox- |

Date |
Sun, 9 Sep 2012 14:17:56 -0400 |

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/

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

**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>

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