The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* »

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
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
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


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?


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.


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.