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<[email protected]> 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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