# RE: st: RRR with CI from logit model

 From Leonelo Bautista To statalist@hsphsun2.harvard.edu Subject RE: st: RRR with CI from logit model Date Tue, 02 Nov 2004 09:05:55 -0600

```I think Ronan Conroy's advice in this case is very sound. What you are
observing may just pertain to the nature of the examples you are using. It
may happen with other examples, but you need to use subject matter to judge

On the other hand, I fail to see why you want to calculate relative risks
from a logistic model. Isn't the odds ratio from the logistic model a
reasonable estimate of the relative risk? If that's the case, as Joseph
Coveney suggested, you can use -glm- fam(bin) link(log), or -binreg-. That
should allow you to calculate absolute and relative risks with their
confidence intervals for any values of your independent variable.

I'm not familiar with -nlcom-, but I'd feel inclined to compare the results
from -logit- plus -nlcom- with those from -binreg- plus -lincom- and see if
they differ.

Leonelo Bautista

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Michael Ingre
Sent: Tuesday, November 02, 2004 5:47 AM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RRR with CI from logit model

On 2004-11-02, at 11.35, Ronán Conroy wrote:
> Take a step back here. Have you *graphed* your outcome against your
> predictor variable?

Thanks for your advice. Yes I have graphed it. And there is a squared
component that kicks in at about 7 on the scale were probabilities
starts to rise dramatically. The graphed probabilities looks fine and
are according to theory.

The problem is the standard errors in the predicted RRR using -nlcom-.
There seem to be a paradoxical relation here: the more extreme the RRR
the LESS significant they are.

The paradox described above can be found in auto.dta also. Consider a
logit model where the probability of a car being foreign is modelled as
a function of length. Length is negatively associated with foreign
(-.0797353). Using -nlcom- a significant (p<.001) ratio of 1.3 between
the predicted probabilities are fond for length=1 vs length=10. When
length=1 is compared to length=100 the ratio increase to 764 but is no
longer significant (p=.606). Code is listed below:

sysuse auto
logit foreign length

// RRR for length=1 vs length=10
nlcom (exp(1   * _b[length] + _cons) / (1+ exp(1   * _b[length] +
_cons))) /  ///
(exp(10  * _b[length] + _cons) / (1+ exp(10  * _b[length] +
_cons)))     //

// RRR for length=1 vs length=100
nlcom (exp(1   * _b[length] + _cons) / (1+ exp(1   * _b[length] +
_cons))) / ///
(exp(100 * _b[length] + _cons) / (1+ exp(100 * _b[length] +
_cons)))    //

I might be doing something I shouldn't and I'm happy for any advice on
how to calculate RRRs with CI from the logit model above using
auto.dta.

Michael

On 2004-11-02, at 11.35, Ronán Conroy wrote:

> Michael Ingre wrote:
>
>> A follow up on statistical power.
>>
>> I have calculated a few RRRs and an interesting pattern is emerging.
>> Extreme comparisons give insignificant p-values but others don't.
>>
>> RRR for 9.5 vs 1, p=.669
>> RRR for 9.5 vs 9, p=.030
>> RRR for  2  vs 1, p=.049
>>
>> Predicted absolute probabilities are: 9.5=.33 , 9=.14, 2=.000020 &
>> 1=.000015
>>
>> What is going on here? Am I doing something wrong? I appreciate any
>> suggestion because this makes no sense to me.
>
> Take a step back here. Have you *graphed* your outcome against your
> predictor variable? Use a smoother to have a look at the shape of the
> relationship. I sometimes use -autosmoo-, but usually do this sort of
> thing in JMP, where you can vary the smoothness of a spline
> interactively. It is handy to know if there is a threshold effect
> (above a critical value, risk begins to rise) or even a 'normal
> region' phenomenon, whereby risk is lowest in some normal region, and
> rises at the high and low extremes (weight and health is a classic
> example).
> You may also be the victim of small numbers in some of the categories.
>
> But relative risk ratios are a way of measuring a phenomenon. The
> first thing to do is to inspect the phenomenon personally, using the
> Mk I intra-ocular traumatic test.
>
> Ronan M Conroy (rconroy@rcsi.ie) Senior Lecturer in Biostatistics
> Royal College of Surgeons Dublin 2, Ireland +353 1 402 2431 (fax 2764)
> -------------------- Just say no to drug reps
> http://www.nofreelunch.org/
>
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>
>
------------------------------------------------
Michael Ingre , PhD student & Research Associate
Department of Psychology, Stockholm University &
National Institute for Psychosocial Medicine IPM
Box 230, 171 77 Stockholm, Sweden

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