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Re: st: stcox in case the ph-assumption is rejected
From
Yuval Arbel <[email protected]>
To
[email protected]
Subject
Re: st: stcox in case the ph-assumption is rejected
Date
Sat, 7 Jan 2012 17:54:41 +0200
Marteen,
I don't see why -stpm2- does not solve my problem. After all -stpm2-
somewhat relaxes the PH assumption. Lets say I take 9 knots: if I have
10 years, doesn't it mean the proportional hazard varies every year?
if I compare it to a simple time-series analysis: the -tvc- is an
interaction term between time and variables where the cubic spline is
similar to a fixed-effect model of panel data, isn't it? if this is
the case, in my view these are two different available tools, where
both can be used.
On Sat, Jan 7, 2012 at 5:26 PM, Maarten Buis <[email protected]> wrote:
> I hate to give bad news but you still haven't solved your problem: you
> just replaced one model that depends on the proportional hazard
> assumption with another model that relies on the proportional hazard
> assumption. You still need to model how the effects changes over time.
> In both -stcox- and -stpm2- that can be done by either using the
> -stratify()- or the -tvc()- options. The former is mainly useful for
> categorical variables that are only there as a control variable and is
> not of substantive interest, the latter can be used for any
> explanatory variable.
>
> -- Maarten
>
> On Sat, Jan 7, 2012 at 4:58 AM, Yuval Arbel <[email protected]> wrote:
>> Thanks very much Alex, By scaling to hazard, it worked fine. I'm very
>> satisfied with the results, which are robust to -stcox- and I
>> incorporated an additional footnote in the paper draft. I'm generally
>> familiar with the cubic-spline method, which allows time variations,
>> but also permits well-defined derivatives at the knots. Here is the
>> outputs:
>>
>> . doedit
>>
>> . do "D:\kingston\public_housing\robustness_PH_assumption.do"
>>
>> . clear
>>
>> . clear matrix
>>
>> . set memory 500m
>> (512000k)
>>
>> . set matsize 800
>>
>> . use "g:\public housing\test_sample_May_07_Bought.dta", clear
>>
>> .
>> .
>> . stpm2 mean_reduct reductcurrent_mean_reduct rent_net8
>> diff_stdmadadarea diff_mortgage permanentincomeestimate82 a
>>> ppreciation,df(4) scale(hazard)
>> note: delayed entry models are being fitted
>>
>> Iteration 0: log likelihood = -1512.9266
>> Iteration 1: log likelihood = -1378.564
>> Iteration 2: log likelihood = -1375.8226
>> Iteration 3: log likelihood = -1375.8201
>> Iteration 4: log likelihood = -1375.8201
>>
>> Log likelihood = -1375.8201 Number of obs = 499393
>>
>> ------------------------------------------------------------------------------
>> | Coef. Std. Err. z P>|z| [95% Conf. Interval]
>> -------------+----------------------------------------------------------------
>> xb |
>> mean_reduct | .0380149 .0005223 72.79 0.000 .0369912 .0390385
>> reductcurr.. | .0209263 .0004782 43.76 0.000 .019989 .0218637
>> rent_net8 | .0027275 .0001649 16.54 0.000 .0024043 .0030508
>> diff_stdma~a | -.2068624 .0283549 -7.30 0.000 -.262437 -.1512879
>> diff_mortg~e | -9.819042 .5364728 -18.30 0.000 -10.87051 -8.767574
>> permanent~82 | -.0005591 .0000685 -8.16 0.000 -.0006933 -.0004248
>> appreciation | 23.16299 2.165592 10.70 0.000 18.91851 27.40747
>> _rcs1 | 5.573527 .1047814 53.19 0.000 5.368159 5.778895
>> _rcs2 | 1.805992 .0491048 36.78 0.000 1.709749 1.902236
>> _rcs3 | -.34599 .0112847 -30.66 0.000 -.3681077 -.3238723
>> _rcs4 | -.076871 .0026999 -28.47 0.000 -.0821628 -.0715792
>> _cons | -5.34359 .1040326 -51.36 0.000 -5.54749 -5.13969
>> ------------------------------------------------------------------------------
>>
>> . test mean_reduct==reductcurrent_mean_reduct
>>
>> ( 1) [xb]mean_reduct - [xb]reductcurrent_mean_reduct = 0
>>
>> chi2( 1) = 947.55
>> Prob > chi2 = 0.0000
>>
>> . stcox mean_reduct reductcurrent_mean_reduct rent_net8
>> diff_stdmadadarea permanentincomeestimate82 diff_mortgage a
>>> ppreciation,nohr
>>
>> failure _d: fail == 1
>> analysis time _t: time_index
>> id: appt
>>
>> Iteration 0: log likelihood = -78368.249
>> Iteration 1: log likelihood = -74721.874
>> Iteration 2: log likelihood = -74566.501
>> Iteration 3: log likelihood = -74561.567
>> Iteration 4: log likelihood = -74561.555
>> Refining estimates:
>> Iteration 0: log likelihood = -74561.555
>>
>> Cox regression -- Breslow method for ties
>>
>> No. of subjects = 9547 Number of obs = 499393
>> No. of failures = 9547
>> Time at risk = 547035
>> LR chi2(7) = 7613.39
>> Log likelihood = -74561.555 Prob > chi2 = 0.0000
>>
>> ------------------------------------------------------------------------------
>> _t | Coef. Std. Err. z P>|z| [95% Conf. Interval]
>> -------------+----------------------------------------------------------------
>> mean_reduct | .0353358 .0005278 66.94 0.000 .0343012 .0363703
>> reductcurr.. | .0221957 .0005134 43.23 0.000 .0211894 .0232019
>> rent_net8 | .0025506 .0001655 15.41 0.000 .0022263 .0028749
>> diff_stdma~a | -.4642809 .0446886 -10.39 0.000 -.5518688 -.3766929
>> permanent~82 | -.0004675 .0000689 -6.79 0.000 -.0006025 -.0003325
>> diff_mortg~e | -6.430141 .8913818 -7.21 0.000 -8.177217 -4.683064
>> appreciation | 9.629971 3.161657 3.05 0.002 3.433237 15.8267
>> ------------------------------------------------------------------------------
>>
>> . test mean_reduct==reductcurrent_mean_reduct
>>
>> ( 1) mean_reduct - reductcurrent_mean_reduct = 0
>>
>> chi2( 1) = 450.86
>> Prob > chi2 = 0.0000
>>
>> . estat phtest,detail
>>
>> Test of proportional-hazards assumption
>>
>> Time: Time
>> ----------------------------------------------------------------
>> | rho chi2 df Prob>chi2
>> ------------+---------------------------------------------------
>> mean_reduct | -0.18814 220.31 1 0.0000
>> reductcurr..| -0.21984 436.16 1 0.0000
>> rent_net8 | -0.03327 10.10 1 0.0015
>> diff_stdma~a| 0.03801 0.38 1 0.5357
>> permanent~82| -0.01174 1.35 1 0.2459
>> diff_mortg~e| 0.21517 10.31 1 0.0013
>> appreciation| -0.05323 11.87 1 0.0006
>> ------------+---------------------------------------------------
>> global test | 543.71 7 0.0000
>> ----------------------------------------------------------------
>>
>>
>> On Fri, Jan 6, 2012 at 11:46 PM, Alex Gamma <[email protected]> wrote:
>>> Yuval,
>>>
>>> provided that you -stset- your data correctly (i.e. as containing delyed entries), stpm2 obviously requires you to specifiy the scale option in order to estimate such models. Apart from the command's help-file, there is also a paper from The Stata Journal that explains the use of stpm2 in detail.
>>>
>>> Paul C. Lambert & Patrick Royston
>>> Further development of flexible parametric models for survival analysis
>>> The Stata Journal (2009) 9, Number 2, pp. 265–290
>>>
>>> Alex
>>>
>>>
>>>
>>>> Thanks, that sounds great.
>>>>
>>>> I tried this and got the following error command:
>>>>
>>>> . stpm2 mean_reduct reductcurrent_mean_reduct rent_net8
>>>> diff_stdmadadarea diff_mortgage permanentincomeestimate82 a
>>>>> ppreciation,df(4)
>>>> note: delayed entry models are being fitted
>>>> The scale must be specified
>>>>
>>>> Note that in my sample - tenants start to exercise at t=13. Is this
>>>> fact has something to do with this error message?
>>>>
>>>> On Fri, Jan 6, 2012 at 5:14 PM, Alex Gamma <[email protected]> wrote:
>>>>> Hi Yuval,
>>>>>
>>>>> I prefer the user-written command STPM2 for these kinds of situation. It makes it easy to model variables that violate the PH-assumption as time-dependent effects using cubic splines.
>>>>>
>>>>> - ssc describe stpm2 -
>>>>> - ssc install stpm2 -
>>>>>
>>>>> Alex
>>>>>
>>>>>
>>>>> Am 06.01.2012 um 09:06 schrieb Yuval Arbel:
>>>>>
>>>>>> Dear Statalist Participants,
>>>>>>
>>>>>> I'm working with stata 11.2. Having read carefully stata's manual
>>>>>> under the title "stcox PH-assumption tests" I have two questions
>>>>>> (which seems to be relevant to Marteen's answer in another thread):
>>>>>>
>>>>>> The manual shows very nicely the following situation related to
>>>>>> medical experiments: if we take two groups of cancer patients, where
>>>>>> one group is exposed to a standard treatment and the other to a
>>>>>> special treatment - and we would like to show that the experimental
>>>>>> treatment is more efficient, we anticipate a paralel upward shift of
>>>>>> the projected survival rates compared to the actual ones. If this is
>>>>>> the case - the PH-assumption, namely the assumption that the hazard to
>>>>>> survival is constant over the sample period, is supported
>>>>>> statistically.
>>>>>>
>>>>>> My first question is whether this discussion is relevant if I am
>>>>>> applying the Cox model to describe the exercise of call (real) options
>>>>>> to purchase appartments.
>>>>>>
>>>>>> My second question is the following: suppose that the PH-assumption
>>>>>> does not hold in the sample and the above discussion is relevant. The
>>>>>> stata manual says the following: "If the assumption fails, alternative
>>>>>> modeling choices would be more appropriate (e.g. , a stratified Cox
>>>>>> model, time-varying covariates)."
>>>>>>
>>>>>> The question is: is there any command to incorporate the -stcox- with
>>>>>> varying hazard level across time? I'm aware of the -strata()- option,
>>>>>> but I wonder whether I can somehow account for time-varying covariates
>>>>>> and incorporate it with -stcox-
>>>>>>
>>>>>> --
>>>>>> Dr. Yuval Arbel
>>>>>> School of Business
>>>>>> Carmel Academic Center
>>>>>> 4 Shaar Palmer Street,
>>>>>> Haifa 33031, Israel
>>>>>> e-mail1: [email protected]
>>>>>> e-mail2: [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/
>>>>>
>>>>>
>>>>> *
>>>>> * 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 33031, Israel
>>>> e-mail1: [email protected]
>>>> e-mail2: [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/
>>>
>>>
>>> *
>>> * 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 33031, Israel
>> e-mail1: [email protected]
>> e-mail2: [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/
>
>
>
> --
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
>
> http://www.maartenbuis.nl
> --------------------------
>
> *
> * 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 33031, Israel
e-mail1: [email protected]
e-mail2: [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/