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Re: How to generate continuous variable corresponding to Odds Ratio X
Posted:
Nov 6, 2006 12:59 PM


CORRECTED FOR THE UNFORGIVEABLE SIN OF TOPPOSTING!
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(1x)/[1P(1x)] = [P1/(1P1)]*exp{K*(xM)/s},
where M = (m1+m2)/2 and K = (m1m2)/s (Known in radar target detection and classification fields as the "The Kfactor"). 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



