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RE: st: Survival analysis


From   "Kieran McCaul" <Kieran.McCaul@uwa.edu.au>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Survival analysis
Date   Wed, 2 Sep 2009 06:08:38 +0800

...

There isn't anything counterintuitive here: look at the K-M graph.

The failures in icp=0 occur in greater number then those in icp=1.  They also occur more quickly.  In icp=1 the failures take longer to accrue.  So overall, icp looks good, but if you start conditioning on some initial period of survival, icp is going to start to look "bad".  That's because the flat region in the survival curve for those on icp=0 occurs earlier than it does for those on icp=1.  So if you condition on about 2 days of survival, you are in the flat region of icdp=0 (essential no more failures occurring after this), but there are still failure occurring in icp=1.  So icp=1 starts to look "bad".

It isn't: icp is doing two things.  First, it's reducing the risk of failure overall and second, it's delaying failure in those who do ultimately fail. 

If this were a disease, I would say that without icp people most people survive, but those who don't succumb quickly. It's like cholera: most people survive, but those who die, die quickly.  So, people have an ability to fight off the disease.  With icp, more people survive and those who eventually fail take longer to fail.  So, if this were cholera, icp would be like a treatment that tended to reduce the severity of the cholera symptoms and increased the ability of people to fight off the disease.


______________________________________________
Kieran McCaul MPH PhD
WA Centre for Health & Ageing (M573)
University of Western Australia
Level 6, Ainslie House
48 Murray St
Perth 6000
Phone: (08) 9224-2701
Fax: (08) 9224 8009
email: Kieran.McCaul@uwa.edu.au
http://myprofile.cos.com/mccaul 
http://www.researcherid.com/rid/B-8751-2008
______________________________________________
If you live to be one hundred, you've got it made.
Very few people die past that age - George Burns


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of moleps islon
Sent: Wednesday, 2 September 2009 2:55 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: Survival analysis

Dear Marten and other listers,
Somehow that looks contraintuitive looking at the graphs (and from
what i understand I cannot post graphs or links here). But if you look
at the following output you`ll see that from patients surviving >.2
,.5,1 and 4 days the logrank test points in the direction of a
beneficial effect first, but detrimental effect afterwards. The PH
assumtion is not fulfilled initially, but later. Isn't this suggestive
of a breakpoint somewhere around 1 day ??



Regards,
M


patients surviving >.2 days

         failure _d:  dod
   analysis time _t:  cox

Iteration 0:   log likelihood =  -2393.672
Iteration 1:   log likelihood = -2374.6741
Iteration 2:   log likelihood = -2374.4875
Iteration 3:   log likelihood = -2374.4874
Refining estimates:
Iteration 0:   log likelihood = -2374.4874

Cox regression -- Breslow method for ties

No. of subjects =          971                     Number of obs   =       971
No. of failures =          357
Time at risk    =     248731.5
                                                   LR chi2(1)      =     38.37
Log likelihood  =   -2374.4874                     Prob > chi2     =    0.0000

------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         icp |   .4842698   .0598328    -5.87   0.000     .3801186     .616958
------------------------------------------------------------------------------

      Test of proportional-hazards assumption

      Time:  Time
      ----------------------------------------------------------------
                  |                      chi2       df       Prob>chi2
      ------------+---------------------------------------------------
      global test |                     25.20        1         0.0000
      ----------------------------------------------------------------

         failure _d:  dod
   analysis time _t:  cox


Log-rank test for equality of survivor functions

      |   Events         Events
icp   |  observed       expected
------+-------------------------
0     |       270         214.69
1     |        87         142.31
------+-------------------------
Total |       357         357.00

            chi2(1) =      38.71
            Pr>chi2 =     0.0000
patients surviving >.5 days

         failure _d:  dod
   analysis time _t:  cox

Iteration 0:   log likelihood = -1506.3678
Iteration 1:   log likelihood = -1505.0847
Iteration 2:   log likelihood = -1505.0842
Refining estimates:
Iteration 0:   log likelihood = -1505.0842

Cox regression -- Breslow method for ties

No. of subjects =          842                     Number of obs   =       842
No. of failures =          228
Time at risk    =       248667
                                                   LR chi2(1)      =      2.57
Log likelihood  =   -1505.0842                     Prob > chi2     =    0.1091

------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         icp |   .8043308   .1102187    -1.59   0.112      .614884    1.052146
------------------------------------------------------------------------------

      Test of proportional-hazards assumption

      Time:  Time
      ----------------------------------------------------------------
                  |                      chi2       df       Prob>chi2
      ------------+---------------------------------------------------
      global test |                     10.23        1         0.0014
      ----------------------------------------------------------------

         failure _d:  dod
   analysis time _t:  cox


Log-rank test for equality of survivor functions

      |   Events         Events
icp   |  observed       expected
------+-------------------------
0     |       143         131.12
1     |        85          96.88
------+-------------------------
Total |       228         228.00

            chi2(1) =       2.64
            Pr>chi2 =     0.1044
patients surviving >1 days

         failure _d:  dod
   analysis time _t:  cox

Iteration 0:   log likelihood = -994.44857
Iteration 1:   log likelihood = -992.59906
Iteration 2:   log likelihood = -992.59879
Refining estimates:
Iteration 0:   log likelihood = -992.59879

Cox regression -- Breslow method for ties

No. of subjects =          766                     Number of obs   =       766
No. of failures =          152
Time at risk    =       248591
                                                   LR chi2(1)      =      3.70
Log likelihood  =   -992.59879                     Prob > chi2     =    0.0544

------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         icp |   1.366676   .2218148     1.92   0.054     .9942913    1.878528
------------------------------------------------------------------------------

      Test of proportional-hazards assumption

      Time:  Time
      ----------------------------------------------------------------
                  |                      chi2       df       Prob>chi2
      ------------+---------------------------------------------------
      global test |                      2.66        1         0.1032
      ----------------------------------------------------------------

         failure _d:  dod
   analysis time _t:  cox


Log-rank test for equality of survivor functions

      |   Events         Events
icp   |  observed       expected
------+-------------------------
0     |        74          85.81
1     |        78          66.19
------+-------------------------
Total |       152         152.00

            chi2(1) =       3.79
            Pr>chi2 =     0.0516
patients surviving >2 days

         failure _d:  dod
   analysis time _t:  cox

Iteration 0:   log likelihood = -788.57192
Iteration 1:   log likelihood = -783.00942
Iteration 2:   log likelihood = -783.00902
Refining estimates:
Iteration 0:   log likelihood = -783.00902

Cox regression -- Breslow method for ties

No. of subjects =          735                     Number of obs   =       735
No. of failures =          121
Time at risk    =       248529
                                                   LR chi2(1)      =     11.13
Log likelihood  =   -783.00902                     Prob > chi2     =    0.0009

------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         icp |   1.840018   .3397673     3.30   0.001      1.28128     2.64241
------------------------------------------------------------------------------

      Test of proportional-hazards assumption

      Time:  Time
      ----------------------------------------------------------------
                  |                      chi2       df       Prob>chi2
      ------------+---------------------------------------------------
      global test |                      0.65        1         0.4187
      ----------------------------------------------------------------

         failure _d:  dod
   analysis time _t:  cox


Log-rank test for equality of survivor functions

      |   Events         Events
icp   |  observed       expected
------+-------------------------
0     |        50          68.29
1     |        71          52.71
------+-------------------------
Total |       121         121.00

            chi2(1) =      11.33
            Pr>chi2 =     0.0008
patients surviving >4 days

         failure _d:  dod
   analysis time _t:  cox

Iteration 0:   log likelihood = -669.88384
Iteration 1:   log likelihood = -661.82737
Iteration 2:   log likelihood = -661.82737
Refining estimates:
Iteration 0:   log likelihood = -661.82737

Cox regression -- Breslow method for ties

No. of subjects =          717                     Number of obs   =       717
No. of failures =          103
Time at risk    =       248467
                                                   LR chi2(1)      =     16.11
Log likelihood  =   -661.82737                     Prob > chi2     =    0.0001

------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         icp |   2.229562   .4553754     3.93   0.000     1.494055    3.327152
------------------------------------------------------------------------------

      Test of proportional-hazards assumption

      Time:  Time
      ----------------------------------------------------------------
                  |                      chi2       df       Prob>chi2
      ------------+---------------------------------------------------
      global test |                      0.09        1         0.7633
      ----------------------------------------------------------------

         failure _d:  dod
   analysis time _t:  cox


Log-rank test for equality of survivor functions

      |   Events         Events
icp   |  observed       expected
------+-------------------------
0     |        38          58.28
1     |        65          44.72
------+-------------------------
Total |       103         103.00

            chi2(1) =      16.37
            Pr>chi2 =     0.0001

.
end of do-file

.


On Mon, Aug 31, 2009 at 11:52 AM, Maarten buis<maartenbuis@yahoo.co.uk> wrote:
> -----------------------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
> http://www.maartenbuis.nl
> -----------------------------------------
>
>
> --- moleps islon  wrote:
>> > This is the ouput I´m getting using your approach:
>> >
>> > n=896, failures=292
>> >
>> > stcox var,tvc(var) texp((_t>1)_t)
>> >
>> > rh
>> >
>> > var HR 0.64, p=0.005, CI 0.47-0.87
>> >
>> > t
>> > var HR 1.01,p=0.001,CI 1.01-1.03
>> >
>> > So as far as I understand this the interpretation is
>> > that the -var- is protective within the first 24hrs,
>> > but detrimental afterwards ??
>
> --- On Mon, 31/8/09, Maarten buis wrote:
>> No, the coefficient in the t equation is an interaction
>> effect. So from t =0 to t=1 the hazard ratio increased
>> with 1%. So at t=0 the hazard ratio for var is
>> 0.64/1.01=0.62. In other words, in the first 24hrs var
>> was even more protective than afterwards (but only very
>> little, so I doubt whether that has any practical
>> relevance).
>
> Sorry, I did not see that you turned around the inquality
> sign (from < to >). So, in your case you assume that the
> PH assumption holds in the first 24hrs, and that
> afterwards the log hazard ratio changes linearly with time.
> So, from t=0 to t=1 the hazard ratio of var is .64, and
> after t=1 the hazard ratio increases by 1% every day. At
> t=2 the hazard ratio of var is 1.01*.64=.646, at t=3
> 1.01^2*.64=.653, at t=4 1.01^3*.64=.659, etc.
>
> To get the interpretation I gave in my previous post you
> have to replace
> stcox var,tvc(var) texp((_t>1)_t)
>
> with
> stcox var,tvc(var) texp((_t<1)_t)
>
> Hope this helps,
> Maarten
>
>
>
>
>
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