[R] How to obtain restricted estimates from coxph()?

Andrews, Chris chrisaa at med.umich.edu
Thu Oct 17 14:05:37 CEST 2013

Consider the function f(x) = x on the open interval (0,1).  It does not have a maximum.
That is what your likelihood function will look like.  The MLE does not exist.
Chris

(Although if everything is continuous and you are okay with limits there is an extension that gets you to Terry's original answer.)

-----Original Message-----
From: Y [mailto:yuhanusa at gmail.com]
Sent: Wednesday, October 16, 2013 7:08 PM
To: Göran Broström
Cc: r-help at r-project.org
Subject: Re: [R] How to obtain restricted estimates from coxph()?

Thanks very much for your help, Terry and G?ran!

As pointed out by G?ran, the difficult part is that it's an open set. How
to obtain a valid MLE in this case?

Thanks,
YH

On Wed, Oct 16, 2013 at 9:55 AM, G?ran Brostr?m <goran.brostrom at umu.se>wrote:

>
>
> On 2013-10-16 14:33, Terry Therneau wrote:
>
>>
>>
>> On 10/16/2013 05:00 AM, r-help-request at r-project.org wrote:
>>
>>> Hello,
>>>
>>> I'm trying to use coxph() function to fit a very simple Cox proportional
>>> hazards regression model (only one covariate) but the parameter space is
>>> restricted to an open set (0, 1). Can I still obtain a valid estimate by
>>> using coxph function in this scenario? If yes, how? Any suggestion would
>>> be
>>> greatly appreciated. Thanks!!!
>>>
>>
>> Easily:
>>      1.  Fit the unrestricted model.  If the solution is in 0-1 you are
>> done.
>>      2.  If it is outside, fix the coefficient.  Say that the solution is
>> 1.73, then the
>> optimal solution under contraint is 1.
>>
>
> OK, except for the small annoyance that 1 is not a member of the open set
> (interval) (0, 1). Maybe the answer is "No" in this case? Depends on what
> lies in the word 'valid'. If 'MLE', the answer is No.
>
>           Redo the fit adding the paramters  "init=1, iter=0".  This
>> forces the program to
>> give the loglik and etc for the fixed coefficient of 1.0.
>>
>> Terry Therneau
>>
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>> and provide commented, minimal, self-contained, reproducible code.
>>
>>
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>

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