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# Re: st: higher occurrence of disease X in rare disease Y

 From Doug Hemken To statalist@hsphsun2.harvard.edu Subject Re: st: higher occurrence of disease X in rare disease Y Date Thu, 05 Dec 2013 12:16:28 -0600

```Thanks, Nick. I see Mata is more R-like than I had appreciated!

On 12/05/13, Nick Cox  wrote:
> Doug's code is fine and suits the purpose perfectly.
>
> A footnote is to underline that Mata can be used to the same "smart
> calculator" end, e.g.
>
> . mata
> : X = (0..6)'
> : binomialp(6,X,1/36)
> 1
> +---------------+
> 1 | .8444875698 |
> 2 | .1447692977 |
> 3 | .0103406641 |
> 4 | .0003939301 |
> 5 | 8.44136e-06 |
> 6 | 9.64727e-08 |
> 7 | 4.59394e-10 |
> +---------------+
> : binomialp(6,(0..6)',1/36)
> 1
> +---------------+
> 1 | .8444875698 |
> 2 | .1447692977 |
> 3 | .0103406641 |
> 4 | .0003939301 |
> 5 | 8.44136e-06 |
> 6 | 9.64727e-08 |
> 7 | 4.59394e-10 |
> +---------------+
>
>
> Nick
> njcoxstata@gmail.com
>
>
> On 5 December 2013 14:42, Doug Hemken <dehemken@wisc.edu> wrote:
> > Here is a script that illustrates the probabilities using Stata, it is such a small problem that you can illustrate statistical power by trail-and-error:
> >
> > set obs 7
> > gen X = _n - 1
> > gen prob = binomialp(6,X,1/36)
> > gen prob10 = binomialp(10,X,1/36)
> > gen prob12 = binomialp(12,2*X,1/36)
> >
> >
> > On 12/05/13, Doug Hemken wrote:
> >> If your sample size is literally six cases, then your unconditional probability of seeing disease X is 0.145. If there is no relation between Y and X, it wouldn't be too unusual to see 1 case of X crop up in 6 cases of Y. This is from a binomial distribution.
> >>
> >> On 12/05/13, "tiong21@netzero.net" wrote:
> >> > The prevalence of disease (X) is 1 in 36 in the general population. In a sample population with a very rare disease (Y) of unknown etiology, the prevalence of disease X is 1 in 6 ( ie: 1 case of X was found in the sample population of 6 rare cases of disease Y. How do I show statistically that this higher occurrence of disease X in rare disease Y is not due to chance? And as a corollary suggest that disease X may be a contributory factor in the etiology of disease Y (an issue of causality). Furthermore, should a Poisson distribution be used to calculate the probabilities? A sample Stata script will be much appreciated.
> >> >
> >> >
> >> > Tiong The
> >> > tiong21@netzero.net
> >> >
> >> > *
> >> > * For searches and help try:
> >> > * http://www.stata.com/help.cgi?search
> >> > * http://www.stata.com/support/faqs/resources/statalist-faq/
> >> > * http://www.ats.ucla.edu/stat/stata/
> >>
> >> --
> >> Doug Hemken
> >> 4226I Social Science Bldg.
> >>
> >> dehemken@wisc.edu
> >> 262-4327
> >> *
> >> * For searches and help try:
> >> * http://www.stata.com/help.cgi?search
> >> * http://www.stata.com/support/faqs/resources/statalist-faq/
> >> * http://www.ats.ucla.edu/stat/stata/
> >
> > --
> > Doug Hemken
> > 4226I Social Science Bldg.
> >
> > dehemken@wisc.edu
> > 262-4327
> >
> > To make a consulting appointment send me an email, or use the on-line scheduler:
> > https://calendar.wisc.edu/scheduling-assistant/public/profiles/PlRxCykH.html
> > *
> > * For searches and help try:
> > * http://www.stata.com/help.cgi?search
> > * http://www.stata.com/support/faqs/resources/statalist-faq/
> > * http://www.ats.ucla.edu/stat/stata/
>
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/faqs/resources/statalist-faq/
> * http://www.ats.ucla.edu/stat/stata/

--
Doug Hemken
4226I Social Science Bldg.

dehemken@wisc.edu
262-4327

To make a consulting appointment send me an email, or use the on-line scheduler:
https://calendar.wisc.edu/scheduling-assistant/public/profiles/PlRxCykH.html
*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/faqs/resources/statalist-faq/
*   http://www.ats.ucla.edu/stat/stata/
```