Scott: I don't think that you can equate 50% prior with CI ranging from
1-99%. As the matter of fact, information theory has been developed to
measure uncertainty and provides the link between uncertainty and
probabilities. As you might know, the measure that quantifies this
uncertainty is called entropy and in fact it relates to availability of our
(say, management) choices. When the probabilities of all choices are equal
(e.g. to treat vs. no treat, to assign treatment A vs. treatment B in RCT,
etc) the entropy is maximal. Alternatively, if the probability of available
options (choices) is not equal, 50% prior might not relate to high degree of
uncertainty (your second example).
Several years ago we published a theoretical piece on the relationship
between treatment threshold and diagnostic entropy (Med Hypotheses
1995;45:503-509), but unfortunately never have had time to further develop
it.
hope this helps
ben
Benjamin Djulbegovic, MD
Associate Professor of Medicine
H. Lee Moffitt Cancer Center & Research Institute
at the University of South Florida
Division of Blood and Bone Marrow Transplant
12902 Magnolia Drive
Tampa, FL 33612
Editor: Evidence-based Oncology
e-mail:[log in to unmask]
http://www.hsc.usf.edu/~bdjulbeg/
phone:(813)979-7202
fax:(813)979-3071
> -----Original Message-----
> From: Dr. Scott Richardson [SMTP:[log in to unmask]]
> Sent: Monday, November 22, 1999 5:18 PM
> To: EBH
> Subject: "P(D+) = 50%" - Huh?
>
> Howdy, colleagues.
>
> I would like your help in understanding something about prior probability
> values of 50%. I have come across 2 fairly different notions about the
> meaning of this:
>
> 1. "P(D+) of 50% means we have no idea." I hear this explanation often,
> e.g.
> in conversations that center around the Bayesian interpretation of trials
> (ahem), but also in presentations about interpreting diagnostic tests.
> This
> may seem sensible at first glance, when one is estimating the probability
> of
> only one event, that will either happen or not happen. With no
> information,
> one might be tempted to think that it'll be equally likely that the event
> will happen and the event will not happen, leading to the guess of P(D+) =
> 50%.
> My discomfort arises because "have no idea" sounds like our
> knowledge is
> imprecise, which I would have thought would be better expressed in one or
> more statements about the precision, such as the confidence interval,
> rather
> than the point estimate. If folks use P(D+) = 50% this way, wouldn't this
> really mean something like "a confidence interval around our prior
> probability ranges from <1 to >99%"? Wouldn't saying it as "=50%" hide
> this
> imprecision? Does no information about the probability of an event really
> mean that it is just as likely to happen as to not happen?
>
> 2. "P(D+) of 50% means this event is pretty likely." I hear this
> explanation
> when discussions about differential diagnosis turn numerate. Often such
> conversations include a demonstration of how P(D+) = 50% for a condition
> is
> well above our threshold for testing, and possibly above our threshold for
> initial treatment while awaiting confirmatory testing. For busy,
> experienced
> clinicians, a P(D+) of 50% may be the estimate for a patient's working
> diagnosis.
> Thus, this explanation seems to surface in situations where
> probabilities
> are being estimated for more than one event (in this example, diagnoses).
> Yet why wouldn't the same principle might apply for one event, e.g. a
> trial
> of a single event, for which a Bayesian interpretation is planned?
>
> Thus, how is an event with prior probability of 50% (prior odds 1:1) to be
> understood? As an event with an uncertain point estimate but a very wide
> confidence interval (explanation #1), or as an event that is fairly likely
> (#2)?
>
> I would welcome vigorous and respectful discussion of both points of view
> [and others, if they're out there]. I will try to summarize what I learn
> for
> the list.
>
> Cheers!
> WSR
>
> W. Scott Richardson, M.D.
> Audie L. Murphy Memorial Veterans Hospital *******************
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