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Re: st: Modelling Relative Risks with -fracpoly-


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Modelling Relative Risks with -fracpoly-
Date   Wed, 20 Mar 2013 16:40:38 +0000

I would look at nonlinear regression texts for bestiaries of functions e.g.

http://www.amazon.com/Ecological-Models-Data-Benjamin-Bolker/dp/0691125228

Nick

On Wed, Mar 20, 2013 at 4:15 PM, Colin Angus <c.r.angus@sheffield.ac.uk> wrote:
> Thanks Nick,
>
> In this scenario an exposure of 0 is plausible and attainable
> (exposure is alcohol consumption, so 0 represents abstention).
> Essentially I am trying to pool a variety of RR estimates at different
> levels of exposure (all estimated wrt people with 0 exposure) to fit a
> dose-response curve. By definition this curve must go through the
> point RR=1 at exposure=0, but I can't figure out how to fit a curve
> conditional on this.
>
> Colin Angus
> Research Assistant
> Health Economics and Decision Science
>
> School of Health and Related Research (ScHARR)
> University of Sheffield
> Regent's Court
> 30 Regent Street
> Sheffield
> S1 4DA
>
>
> On 20 March 2013 15:12, Nick Cox <njcoxstata@gmail.com> wrote:
>> Sorry, that was too hasty. You said much more than I noticed in a
>> brisk reading.
>>
>> However, forcing through the origin here still seems more problematic
>> than usual.
>>
>> In the easiest applications, (0, 0) is unattainable but a sensible
>> limit on physical (biological, economic, ...) grounds. (Mundane
>> example: length and area of objects.) In the best applications,
>> forcing a function through the origin is also consistent with the data
>> say.
>>
>> Here it seems that RR < 1 and RR > 1 could be something you observe
>> even for exposure at or near 0, just as a matter of empirical
>> fluctuation. If they are about equally common, your curve should
>> reflect that any way. If they aren't equally common, force is not
>> nice.
>>
>> Nick
>>
>> On Wed, Mar 20, 2013 at 3:03 PM, Nick Cox <njcoxstata@gmail.com> wrote:
>>> What is the origin here?
>>>
>>> Normally something we should all have been able to answer at age 13 or
>>> so, but please bear with me.
>>>
>>> If logRR = 0 then RR = 1.
>>>
>>> If RR = 0 then logRR is indeterminate.
>>>
>>> Do you want either limiting behaviour?
>>>
>>> If so, why? If not, what else?
>>>
>>> Either way, you could try choosing a set of powers that had the
>>> behaviour you want, but that might get in the way of -fracpoly-'s
>>> scope for adjusting to the data.
>>>
>>> Nick
>>>
>>> On Wed, Mar 20, 2013 at 2:52 PM, Colin Angus <c.r.angus@sheffield.ac.uk> wrote:
>>>
>>>> I'm using the -fracpoly- command to model the log relative risk of an
>>>> event as a function of a single continuous exposure variable, where
>>>> the reference category for my relative risk is those with an exposure
>>>> of 0 (i.e. my log RR at 0 exposure is 0). So my command is:
>>>>
>>>> -fracpoly: regress logRR exposure [weight=weight]-
>>>>
>>>> I cannot see how to force the fitted fractional polynomial function
>>>> through the origin. Even if I use the -nocon- command to supress the
>>>> constant term, the transformations of the exposure variable mean that
>>>> the fitted value at 0 isn't 0.
>>>>
>>>> Can anybody help me?
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