On 16 Jan 2001 17:38:43 -0800, [EMAIL PROTECTED] (Rich Strauss)
wrote:
> I have what seems to be a straightforward question involving a conditional
> probability, but I must be missing something because I can't quite get a
> handle on it. Let's say I have treatment and control groups with
> individuals preassigned to each, with T individuals in the treatment group
> and C in the control group. I observe mortality after some period of time,
> with t of T dying in the treatment group and c of C in the control group.
> I would like a measure of the probability of death due to the treatment,
> over and above (in some sense) the probability of death in the control group.
>
> I know that P(x of T) is hypergeometric, assuming that the probabilities of
> death for treatment and control are identical, so I know how to determine
> whether (t of T) is significantly greater than (c of C). And I've just
> verified that this probability is the same as the chi-square probability
> for the 2 x 2 contingency table. But how do I measure this effect? As a
> simple difference between the probabilities for the two groups?
>
If you don't merely report the details, that "50% vs 30% survived,"
the usual effect size is in terms Odds Ratio. For 2x2 table,
(a,b; c;d), this is the number OR= ad/bc.
If it is a good description of the model (underlying logistic) (and
its success is why it is popular these days), various estimates will
be consistent.
The Relative Risk for two groups is also familiar, Risk1/Risk2, but it
becomes intractable to useful statistics (and misleading, to boot)
when the Risks are not small.
> I initially guessed that the value I wanted was just P(death | treatment),
> but of course this turns out to be just the ratio t/T, which contains no
> information about the control group. I'm sure this must be commonly done,
> as, for example, in estimating the additional probability of death at a
> particular age due to smoking, but I've scanned the resources (texts,
> personnel, etc.) I have available and can't find the relevant information.
> Can someone point me in the right direction?
Check textbooks or online sources on epidemiology. And Odds Ratio.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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