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From |
"moleps islon" <moleps2@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: R: st: R: probability question |

Date |
Thu, 12 Jun 2008 14:02:58 +0200 |

Thx a lot everyone. This certainly helped me out quite a bit. Moleps On Thu, Jun 12, 2008 at 9:30 AM, Carlo Lazzaro <carlo.lazzaro@tin.it> wrote: > Dear Richard e Svend, > thanks a lot for your further clarifications on this classic > classwork-issue. > By the way I was wondering whether it may be interesting to add to the Stata > bookshelf a tutorial-based textbook on probability (let's say from basics to > Bayesian probability distributions) issues related to biostatistics, > epidemiology, social sciences and alike (with alike I mean all the research > fields which are unknown for me) which can be tackled with Stata routines. > > (This is not an advertising stunt to promote myself as an author: this idea > is indeed the offspring of my hard times in dealing with the quantitative > world!) > > Kind Regards, > > Carlo > -----Messaggio originale----- > Da: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Svend Juul > Inviato: giovedì 12 giugno 2008 8.51 > A: statalist@hsphsun2.harvard.edu > Oggetto: Re: st: R: probability question > > > Moleps asked, and Carlo and Richard commented: > > 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. > > ==================== > > Carlo: > > 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) > > ====================== > > Richard: > > That might be more accurate than what I calculated before, but luckily > it gives pretty much the same result. For one person, the probability of > NOT getting cancer over 15 years is > > p(0) = 1 - (1 - exp(-rt)) = exp(-rt) = exp(-15/100000 * 15), i.e. > > . di exp(-15/100000 * 15) > .99775253 > > The probability that all 99 people should be so lucky is > > . di exp(-15/100000 * 15) ^ 99 > .8003149 > > Hence, the probability that at least one is not so lucky is > > . di 1 - (exp(-15/100000 * 15) ^ 99) > .1996851 > > Which is pretty close to my earlier calculation, which was > > . di 1 - ((1 - 15/100000 )^15^99) > .19969847 > > The difference is .00001337! > > I imagine there might be some other complications in these calculations. > The rate may not be constant across time; or people may die from > something else before they get kidney cancer. But for the problem as > stated, it sounds like there is a 20% chance of at least one person > getting kidney cancer. > > ====================================================================== > > To get the expected proportion over 15 years, 15*15/100000 = 0.00225 > is almost right with a rare event, but as Carlo pointed out, the > correct conversion from a rate to a proportion says: > > . display 1-exp(-15/100000 * 15) > .00224747 > > Now, the official -bitest- command does the rest of the job: > > . bitesti 99 1 0.00224747 > > N Observed k Expected k Assumed p Observed p > ------------------------------------------------------------ > 99 1 .2224995 0.00225 0.01010 > > Pr(k >= 1) = 0.199685 (one-sided test) > Pr(k <= 1) = 0.978786 (one-sided test) > Pr(k >= 1) = 0.199685 (two-sided test) > > note: lower tail of two-sided p-value is empty > > Pr(k >= 1) = 0.199685 > > Svend > > __________________________________________ > 1 > Svend Juul > Institut for Folkesundhed, Afdeling for Epidemiologi > (Institute of Public Health, Department of Epidemiology) > Vennelyst Boulevard 6 > DK-8000 Aarhus C, Denmark > Phone: +45 8942 6090 > Home: +45 8693 7796 > Email: sj@soci.au.dk > __________________________________________ > > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > > > > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: R: probability question***From:*Svend Juul <SJ@SOCI.AU.DK>

**R: st: R: probability question***From:*"Carlo Lazzaro" <carlo.lazzaro@tin.it>

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