Thanks go out to both Kieran and Marten for providing immense help.
In doing a multivariate survival analysis with several time-varying
covariates (found using estat phtest,det and graphs after "regular"
stcox) i fitted the model
(1) xi:stcox a b c d e i.g, tvc(b d e i.g)
after first having done univariate modeling with
(2) stcox a, tvc(a) etc
finding significant interaction with time for b d e & i.g (hence the tvc var).
-How do I know from this that (1) fulfills the PH assumption and that
(_t) is the "correct" form of interaction with time (instead of ln _t
etc)?
-When the time interaction is significant in the univariate model, but
not in the multivariate model-how do I determine the reason for this ?
Appreciate your time and efforts,
M
On Wed, Sep 2, 2009 at 12:08 AM, Kieran McCaul<[email protected]> wrote:
> ...
>
> 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: [email protected]
> 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: [email protected] [mailto:[email protected]] On Behalf Of moleps islon
> Sent: Wednesday, 2 September 2009 2:55 AM
> To: [email protected]
> 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<[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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