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Topic: How to generate continuous variable corresponding to Odds Ratio X
Replies: 3   Last Post: Nov 7, 2006 5:58 PM

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 Greg Heath Posts: 6,387 Registered: 12/7/04
Re: How to generate continuous variable corresponding to Odds Ratio X
Posted: Nov 6, 2006 12:59 PM

CORRECTED FOR THE UNFORGIVEABLE SIN OF TOP-POSTING!

Haris wrote:
> Greg Heath wrote:
> > Haris wrote:
> > > I am looking to generate a continuous normally distributed random
> > > variable with a given MEAN and SD for two groups. Is there a
> > > systematic way to generate two such groups with N number of cases so
> > > that their odds ratio in a logistic regression would be predictable?
> > > In my case I am looking for OR=1.5 but any other number would do.
> > >
> > > Two normally distributed groups is the idealized case. If there are
> > > other distributions that I can use to solve this problem I would love
> > > to hear about them as well.

> >
> > I'm probably missing something. Why won't two normal distributions
> > with the same standard deviation and priors P1 = 2/5, P2 = 3/5
> > do the trick?

Sorry.

That's the answer to a different question. I was thinking of a 2
component univariate Gaussian mixture classification scenario
and misinterpreted the term odds ratio to be the odds (ratio of
the posterior probabilities). When s2=s1=s,

P(1|x)/[1-P(1|x)] = [P1/(1-P1)]*exp{K*(x-M)/s},

where M = (m1+m2)/2 and K = (m1-m2)/s (Known in radar target
detection and classification fields as the "The K-factor"). Choosing
a threshold at x = M then yields odds of at least 3/2 when P1 = 3/5.

> The problem I am trying to simulate has to do with two equal
> populations: those with events and without. I need to relate
> differences in the normally distributed properties of those populations
> to the presence of event. The simulation is for power calculations and
> those are normally based on 1SD difference between the two means. What
> you are proposing may work, I need to look into this. However, I am
> not sure how I would be able to link the mean difference and OR.

As stated above, I was thinking about a different problem.

Hope this helps.

Greg

Date Subject Author
11/6/06 Greg Heath
11/7/06 Ray Koopman
11/7/06 Ray Koopman