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st: R: probability question


From   "Carlo Lazzaro" <carlo.lazzaro@tin.it>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: R: probability question
Date   Wed, 11 Jun 2008 10:28:51 +0200

-----Original message-----
On 2008 June 10 moleps islon wrote:

Dear statalisters, can someone help me out with this basic question?


I need to calculate the probability of the following event:

That at least one patient out of 99 suffers from kidneycancer
(incidence 15/100000 pr year) over a time period of 15 years.


Dear Moleps,

searching the literature (Briggs A, Sculpher M, Claxton K. Decision
Modelling for Health Economic Evaluation. Oxford: Oxford University Press,
2006:51) I have found out a formula for converting rate into probabilities:

p=1-exp(-rt)

where:

p=probability;
r= instantaneous rate, provided that it is constant over the period of
interest (t)

Hence, your 15-year probability would be:

Display 1-exp(-15/100000*15) 
.00224747

and your 1-year probability would be:

display 1-exp(-15/100000*1) 
.00014999 // that is, around 15 new cases per year.

Eventually, I have tried to sketch a temptative answer to your question,
referring to the 1-year probability that at least one patient convert to
kidney cancer:

Display
1/100000+1/99999+1/99998+1/99997+1/99996+1/99995+1/99994+1/99993+1/99992+1/9
9991+1/99990+1/99989+1/99988+1/99987+1/99986
.00015001

I do hope that my last try will not mislead you. Probably, Stata gurus on
the list can support you with a better solution.

HTH and Kind Regards,

Carlo
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