# Re: st: RRR with CI from logit model

 From Michael Ingre To statalist@hsphsun2.harvard.edu Subject Re: st: RRR with CI from logit model Date Tue, 2 Nov 2004 12:46:58 +0100

```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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