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Re: st: RE: Command "margin" after Cox Regression
From
Yuval Arbel <[email protected]>
To
[email protected]
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 <[email protected]> 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
> [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, Israel
e-mail: [email protected]
*
* For searches and help try:
* http://www.stata.com/help.cgi?search
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