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

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: RE: Command "margin" after Cox Regression |

Date |
Thu, 27 Oct 2011 06:31:04 +0200 |

Now I'm coming to the real problem that bothers me all along: I ran the experiment again, but this time I used "mean_reduct" instead of "max_red", where mean is obtained for mean_red=0, mean1 is obtained for mean_red=10 etc. What does not make sense here is that compared to "max_red" the projected survival rates begin from a lower point (.7347253 compared to .9951255) and deteriorate at a much quicklier pace with the same variation in the rumerical values of the variables. This is in spite of the fact that compared to a hazard rate of 1.1227 the hazard rate of "mean_reduct" is smaller (1.030668). Moreover, compared to "mean_red", the numerical values of "max_red" is higher (they range from 75 to 95, where mean_reduct range from 16.22278 to 73.81435). Assuming that the algorithm works fine, the only sensible explanation I could find for these outcomes is the following: Somehow (and unlike simple regression analysis) projected survival rates are influenced from the estimated MSE: note that the log-likelihood of "mean reduct" is higher (-75795.357 compared to -78351.631) and the calculated z-value of "mean_reduct" is much smaller (69.02 compared to 5.82). I wonder, what is your opinion on this matter. Here is the second output: . stcox mean_red6 failure _d: fail == 1 analysis time _t: time_index id: appt Iteration 0: log likelihood = -78368.249 Iteration 1: log likelihood = -75795.357 Iteration 2: log likelihood = -75795.357 Refining estimates: Iteration 0: log likelihood = -75795.357 Cox regression -- Breslow method for ties No. of subjects = 9547 Number of obs = 499393 No. of failures = 9547 Time at risk = 547035 LR chi2(1) = 5145.78 Log likelihood = -75795.357 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ _t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- mean_red6 | 1.030668 .0004511 69.02 0.000 1.029784 1.031553 ------------------------------------------------------------------------------ . predict mean6,basesurv (8405 missing values generated) . collapse (mean) mean_reduct mean mean1 mean2 mean3 mean4 mean5 mean6 if fail==1,by(time_index) . summ Variable | Obs Mean Std. Dev. Min Max -------------+-------------------------------------------------------- time_index | 103 63 29.87753 12 114 mean_reduct | 103 47.93156 20.28016 16.22278 73.81435 mean | 103 .7347253 .2201497 0 .9999749 mean1 | 103 .6749088 .2458189 0 .999966 mean2 | 103 .6084346 .2670347 0 .999954 -------------+-------------------------------------------------------- mean3 | 103 .5370196 .281635 0 .9999378 mean4 | 103 .4628317 .2892216 0 .9999159 mean5 | 103 .3884503 .2912637 0 .9998863 mean6 | 103 .3170086 .2900842 0 .9998462 . ttest mean==mean1 Paired t test ------------------------------------------------------------------------------ Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- mean | 103 .7347253 .021692 .2201497 .6916993 .7777513 mean1 | 103 .6749088 .0242213 .2458189 .626866 .7229515 ---------+-------------------------------------------------------------------- diff | 103 .0598165 .0032359 .0328403 .0533982 .0662348 ------------------------------------------------------------------------------ mean(diff) = mean(mean - mean1) t = 18.4856 Ho: mean(diff) = 0 degrees of freedom = 102 Ha: mean(diff) < 0 Ha: mean(diff) != 0 Ha: mean(diff) > 0 Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.0000 . ttest mean1==mean2 Paired t test ------------------------------------------------------------------------------ Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- mean1 | 103 .6749088 .0242213 .2458189 .626866 .7229515 mean2 | 103 .6084346 .0263117 .2670347 .5562455 .6606238 ---------+-------------------------------------------------------------------- diff | 103 .0664742 .0031302 .0317685 .0602653 .072683 ------------------------------------------------------------------------------ mean(diff) = mean(mean1 - mean2) t = 21.2361 Ho: mean(diff) = 0 degrees of freedom = 102 Ha: mean(diff) < 0 Ha: mean(diff) != 0 Ha: mean(diff) > 0 Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.0000 . ttest mean2==mean3 Paired t test ------------------------------------------------------------------------------ Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- mean2 | 103 .6084346 .0263117 .2670347 .5562455 .6606238 mean3 | 103 .5370196 .0277503 .281635 .481977 .5920622 ---------+-------------------------------------------------------------------- diff | 103 .071415 .0031549 .0320184 .0651573 .0776727 ------------------------------------------------------------------------------ mean(diff) = mean(mean2 - mean3) t = 22.6365 Ho: mean(diff) = 0 degrees of freedom = 102 Ha: mean(diff) < 0 Ha: mean(diff) != 0 Ha: mean(diff) > 0 Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.0000 . ttest mean3==mean4 Paired t test ------------------------------------------------------------------------------ Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- mean3 | 103 .5370196 .0277503 .281635 .481977 .5920622 mean4 | 103 .4628317 .0284979 .2892216 .4063064 .5193571 ---------+-------------------------------------------------------------------- diff | 103 .0741879 .0034517 .0350305 .0673415 .0810342 ------------------------------------------------------------------------------ mean(diff) = mean(mean3 - mean4) t = 21.4934 Ho: mean(diff) = 0 degrees of freedom = 102 Ha: mean(diff) < 0 Ha: mean(diff) != 0 Ha: mean(diff) > 0 Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.0000 . ttest mean4==mean5 Paired t test ------------------------------------------------------------------------------ Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- mean4 | 103 .4628317 .0284979 .2892216 .4063064 .5193571 mean5 | 103 .3884503 .0286991 .2912637 .3315259 .4453748 ---------+-------------------------------------------------------------------- diff | 103 .0743814 .0038889 .0394675 .0666679 .0820949 ------------------------------------------------------------------------------ mean(diff) = mean(mean4 - mean5) t = 19.1268 Ho: mean(diff) = 0 degrees of freedom = 102 Ha: mean(diff) < 0 Ha: mean(diff) != 0 Ha: mean(diff) > 0 Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.0000 . ttest mean5==mean6 Paired t test ------------------------------------------------------------------------------ Variable | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- mean5 | 103 .3884503 .0286991 .2912637 .3315259 .4453748 mean6 | 103 .3170086 .0285828 .2900842 .2603147 .3737025 ---------+-------------------------------------------------------------------- diff | 103 .0714417 .0042013 .042639 .0631084 .0797751 ------------------------------------------------------------------------------ mean(diff) = mean(mean5 - mean6) t = 17.0045 Ho: mean(diff) = 0 degrees of freedom = 102 Ha: mean(diff) < 0 Ha: mean(diff) != 0 Ha: mean(diff) > 0 Pr(T < t) = 1.0000 Pr(|T| > |t|) = 0.0000 Pr(T > t) = 0.0000 . end of do-file On Wed, Oct 26, 2011 at 6:49 PM, Weichle, Thomas <Thomas.Weichle@va.gov> wrote: > Hi Yuval, > The baseline survival is calculated for every observed event time in the > dataset for the reference group (those subjects with > all covariates=0). Based on your example, you calculated a baseline > survival for the model which included max_red1. Another baseline > survival is calculated for the model which included max_red2. These > baseline survivals are different because the reference group represents > something slightly different when you generated max_red1 and max_red2. > This variation in baseline survival, I believe, does modify the survival > rates. > > Tom Weichle > Math Statistician > Center for Management of Complex Chronic Care (CMC3) > Hines VA Hospital, Bldg 1, C202 > 708-202-8387 ext. 24261 > Thomas.Weichle@va.gov > > > * > * 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, Israel e-mail: 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/

**References**:**Re: st: RE: Command "margin" after Cox Regression***From:*"Weichle, Thomas" <Thomas.Weichle@va.gov>

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