# Re: st: Survival analysis

 From moleps islon To statalist@hsphsun2.harvard.edu Subject Re: st: Survival analysis Date Tue, 1 Sep 2009 20:54:33 +0200

```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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>

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```