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


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

*
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