[R-sig-Epi] R-sig-Epi Digest, Vol 18, Issue 1

[Ian Fellows]

-----Original Message-----
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Sent: Thursday, October 04, 2007 3:00 AM
To: r-sig-epi at stat.math.ethz.ch
Subject: R-sig-Epi Digest, Vol 18, Issue 1


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Today's Topics:

   1. Probability of falling incidence (Ralf Finne)
   2. Re: Probability of falling incidence (Kevin Viel)


----------------------------------------------------------------------

Message: 1
Date: Wed, 03 Oct 2007 17:24:28 +0300
From: "Ralf Finne" <Ralf.Finne at syh.fi>
Subject: [R-sig-Epi] Probability of falling incidence
To: <r-sig-epi at stat.math.ethz.ch>
Message-ID: <4703D04D020000EE00004826 at valhall.syh.fi>
Content-Type: text/plain; charset=UTF-8

Hi everybody.

Below are the incidence numbers for  end-stage renal disease in the
Helsinki region for the past five years.

The following question has arisen:

What is the probability  that the decreased  incidence for 2006
is due to random variablilty and not caused by any systematic effect?

2002   75
2003   73
2004   69
2005   65
2006   28

Are there any solutions available in R?

Very thankful for your answers

Ralf Finne
Svenska yrkesh?skolan
Vasa Finland



------------------------------

Message: 2
Date: Wed, 03 Oct 2007 09:38:54 -0500
From: Kevin Viel <kviel at sfbrgenetics.org>
Subject: Re: [R-sig-Epi] Probability of falling incidence
To: r-sig-epi at stat.math.ethz.ch
Message-ID: <001b01c805cb$1fa7f4e0$723a7cce at win.sfbrgenetics.org>
Content-Type: text/plain; charset=us-ascii


> -----Original Message-----
> From: r-sig-epi-bounces at stat.math.ethz.ch
> [mailto:r-sig-epi-bounces at stat.math.ethz.ch] On Behalf Of Ralf Finne
> Sent: Wednesday, October 03, 2007 9:24 AM
> To: r-sig-epi at stat.math.ethz.ch
> Subject: [R-sig-Epi] Probability of falling incidence
>
> Hi everybody.
>
> Below are the incidence numbers for  end-stage renal disease
> in the Helsinki region for the past five years.
>
> The following question has arisen:
>
> What is the probability  that the decreased  incidence for
> 2006 is due to random variablilty and not caused by any
> systematic effect?
>
> 2002   75
> 2003   73
> 2004   69
> 2005   65
> 2006   28
>
> Are there any solutions available in R?
>
> Very thankful for your answers

Ralf,

  This is not enough data for us to be able to suggest a test.  We would
need to know the study design, with particular emphasis on the statistical
sampling strategy (stratified, simple random sampling, etc.).  28 cases out
of 1000 p-y is much different from 280 cases out of 10000 p-y, for instance.

  Unfortunately, I am only lurker on this list and cannot suggest a
procedure in R.


HTH,

Kevin


Kevin Viel, PhD
Post-doctoral fellow
Department of Genetics
Southwest Foundation for Biomedical Research
San Antonio, TX 78227



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End of R-sig-Epi Digest, Vol 18, Issue 1
****************************************


Hello Ralf,

My first instinct is to assume that your data is from a poisson
distribution. If you have information on renal failure on a finer timescale,
I'd look to see if this assumption holds.

We can test the equality of two poisson rates using the binomial
distribution. Under the null hypothesis that the rate of the first 4 data
points is the same as the last, the distribution of the last rate,
conditional upon the five year rate (23+75+73+69+65) is:
y5 - binomial(n=23+75+73+69+65,p=1/(1+4))

so using an exact binomial test we have:
> sum(dbinom(0:23,23+75+73+69+65,1/(1+4)))*2
[1] 2.626615e-09

so, if there was no difference in 2006, the probability that we would see a
rate as extreme as 23 is VERY small <.0000001.

With so few years, the poisson assumption, though reasonable, is impossible
to check. I would be interested in other opinions on this.

Ian