# [R] binomial simulation

Moshe Olshansky m_olshansky at yahoo.com
Tue Aug 14 02:06:43 CEST 2007

```As I understand this,
P(T+ | D-)=1-P(T+ | D+)=0.05
is the probability not to detect desease for a person
at ICU who has the desease. Correct?

What I asked was whether it is possible to mistakenly
detect the desease for a person who does not have it?

Assuming that this is impossible the formula is below:

If there are N patients, each has a probability p to
have the desease (p=0.6 in your case) and q is the
probability to detect the desease for a person who has
it (q = 0.95 for ICU and q = 0.8 for a regular unit),
then

P(k have the desease AND m are detected) =
P(k have the desease)*P(m are detected / k have the
desease) =
C(N,k)*p^k*(1-p)^(N-k)*C(k,m)*q^m*(1-q)^(k-m)
where C(a,b) is the Binomial coefficient "a above b" -
the number of ways to choose b items out of a (when
the order does not matter). You of course must assume
that N >= k >= m >= 0 (otherwise the probability is
0).

To generate such pairs (k infected and m detected) you
can do the following:

k <- rbinom(N,1,p)
m <- rbinom(k,1,q)

Regards,

Moshe.

--- sigalit mangut-leiba <smangut at gmail.com> wrote:

> Hi,
> The probability of false detection is: P(T+ |
> D-)=1-P(T+ | D+)=0.05.
> and I want to find the joint probability
> P(T+,D+)=P(T+|D+)*P(D+)
> Sigalit.
>
>
> On 8/13/07, Moshe Olshansky <m_olshansky at yahoo.com>
> wrote:
> >
> > Hi Sigalit,
> >
> > Do you want to find the probability P(T+ = t AND
> D+ =
> > d) for all the combinations of t and d (for ICU
> and
> > Reg.)?
> > Is the probability of false detection (when there
> is
> > no disease) always 0?
> >
> > Regards,
> >
> > Moshe.
> >
> > --- sigalit mangut-leiba <smangut at gmail.com>
> wrote:
> >
> > > hello,
> but
> > > still i can't get what i
> > > need.
> > > I have 2 units: icu and regular. from icu I want
> to
> > > take 200 observations
> > > from binomial distribution, when probability for
> > > disease is: p=0.6.
> > > from regular I want to take 300 observation with
> the
> > > same probability: p=0.6
> > > .
> > > the distribution to detect disease when disease
> > > occurred- *for someone from
> > > icu* - is: p(T+ | D+)=0.95.
> > > the distribution to detect disease when disease
> > > occurred- *for someone from
> > > reg.unit* - is: p(T+ | D+)=0.8.
> > > I want to compute the joint distribution for
> each
> > > unit: p(T+,D+) for icu,
> > > and the same for reg.
> > > I tried:
> > >
> > > pdeti <- 0
> > >
> > > pdetr <- 0
> > >
> > > picu <- pdeti*.6
> > >
> > > preg <- pdetr*.6
> > >
> > > dept <- c("icu","reg")
> > >
> > > icu <- rbinom(200, 1, .6)
> > >
> > > reg <- rbinom(300, 1, .6)
> > >
> > > for(i in 1:300) {
> > >
> > > if(dept=="icu") pdeti==0.95
> > >
> > > if (dept=="reg") pdetr==0.80
> > >
> > > }
> > >
> > > print(picu)
> > >
> > > print(preg)
> > >
> > > and got 50 warnings:
> > >
> > > the condition has length > 1 and only the first
> > > element will be used in: if
> > > (dept == "icu") pdeti == 0.95
> > > the condition has length > 1 and only the first
> > > element will be used in: if
> > > (dept == "reg") pdetr == 0.8
> > >
> > > I would appreciate any suggestions,
> > >
> > > thank you,
> > >
> > > Sigalit.
> > >
> > >       [[alternative HTML version deleted]]
> > >
> > > ______________________________________________
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> > > reproducible code.
> > >
> >
> >
>
> 	[[alternative HTML version deleted]]
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