Re: st: Modelling Relative Risks with -fracpoly-

[Nick Cox <njcoxstata@gmail.com>]

I alerted Patrick Royston to this thread. (Patrick is not a member of
Statalist, but one of the progenitors of fractional polynomials.)

He wrote:

"Sounds to me potentially like a "spike at zero" problem, which occurs
when the exposure is semi-continuous (e;g. cigarettes smoked per day)
and you wish to model a "probability spike" at zero exposure and a
continuous function for positive exposures. The topic -- sometimes
cryptically known as the "Robertson problem" due to an early paper on
this by said author -- is discussed in our 2008 book (Royston &
Sauerbrei, "Multivariable model-building", Wiley, Chichester) and
treated in detail in a paper in press with the Biometrical Journal
(Becher, Lorenz, Royston, Sauerbrei, 2013).

Actually, -fracpoly- has undocumented options -zero- and -catzero-
that are designed for this problem. Curiously, similar options are
available with -mfp- that are documented.

Colin may wish to investigate this avenue. He could indeed use -mfp-
instead of -fracpoly- if he wished."

Nick

On Wed, Mar 20, 2013 at 4:40 PM, Nick Cox <njcoxstata@gmail.com> wrote:
> 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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