From: Michael Dewey <info_at_aghmed.fsnet.co.uk>

Date: Mon 29 Jan 2007 - 09:44:08 GMT

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Mon Jan 29 22:19:49 2007

Date: Mon 29 Jan 2007 - 09:44:08 GMT

At 21:13 28/01/2007, Bob Green wrote:

>Michael,

*>
**>Thanks. Yes, clearly the volume number for the Schanda paper I cited is wrong.
**>
**>Where things are a bit perplexing, is that I used the same method as
**>Peter suggested on two papers by Eronen (referenced below). I can
**>reproduce in R a similar odds ratio to the first published paper e.g
**>OR = 9.7 (CI= 7.4-12.6) whereas I obtained quite different results
**>from the second published paper (Eronen 2) of OR = 10.0 (8.1-12.5).
**>One reason why I wanted to work out the calculations was so I could
**>analyse data from studies using the same method, for confirmation.
**>
**>Now the additional issue, is that Woodward, who is also the author
**>of an epidemiological text, says in a review that Eronen used
**>wrong formula in a 1995 paper and indicates that this comment
**>applies also to later studies - he stated the "they use methods
**>designed for use with binomial data when they really have Poisson
**>data. Consequently, they quote odds ratios when they really have
**>relative rates and their confidence intervals are
**>inaccurate". Eronen1 cites the formula that was used for OR.
**>Schanda sets out his table for odds ratio the same as Eronen1
*

There do seem to be difficulties in what they are doing as they have not observed all the non-homicides, they estimate how many they are and then estimate the number of people with a given diagnosis using prevalence estimates from another study. I think you are moving towards writing an article criticising the statistical methods used in this whole field which I think is going beyond the resources of R-help.

>For the present purpose, my primary question is: as you have now

*>seen the Schanda paper, would you consider Schanda calculated odds
**>or relative risk?
**>
**>Also, when I tried the formula suggested by Peter (below) I obtained
**>an error - do you know what M might be or the source of the error?
**>
**>exp(log(41*2936210/920/20068)+qnorm(c(.025,.975))*sqrt(sum(1/M)))
**>Error in sum(1/M) : object "M" not found
**>
**>
**> > eronen1 <- as.table(matrix(c(58,852,13600-58,1947000-13600-852),
**> ncol = 2 , dimnames = list(group=c("scz", "nonscz"), who=
**> c("sample", "population"))))
**> > fisher.test(eronen1)
**>
**>
**>p-value < 2.2e-16
**>alternative hypothesis: true odds ratio is not equal to 1
**>95 percent confidence interval:
**> 7.309717 12.690087
**>sample estimates:
**>odds ratio
**> 9.713458
**>
**> > eronen2
**> <- as.table(matrix(c(86,1302,13530-86,1933000-13530-1302), ncol =
**> 2 , dimnames = list(group=c("scz", "nonscz"), who= c("sample", "population"))))
**> > fisher.test(eronen2)
**>
**>p-value < 2.2e-16
**>alternative hypothesis: true odds ratio is not equal to 1
**>95 percent confidence interval:
**> 7.481272 11.734136
**>sample estimates:
**>odds ratio
**> 9.42561
**>
**>References
**>
**>Eronen, M. et al. (1996 - 1) Mental disorders and homicidal behavior
**>in Finland. Archives of General Psychiatry, 53, 497-501
**>
**>Eronen, M et al (1996 - 2). Schizophrenia & homicidal
**>behavior. Schizophrenia Bulletin, 22, 83-89
**>
**>Woodward, Mental disorder & homicide. Epidemiologia E Psichiatria
**>Sociale, 9, 171-189
**>
**>Any comments are welcomed,
**>
**>Bob
**>
**>At 01:57 PM 28/01/2007 +0000, Michael Dewey wrote:
**>>At 22:01 26/01/2007, Peter Dalgaard wrote:
**>>>Bob Green wrote:
**>>>>Peetr & Michael,
**>>>>
**>>>>I now see my description may have confused the issue. I do want
**>>>>to compare odds ratios across studies - in the sense that I want
**>>>>to create a table with the respective odds ratio for each study.
**>>>>I do not need to statistically test two sets of odds ratios.
**>>>>
**>>>>What I want to do is ensure the method I use to compute an odds
**>>>>ratio is accurate and intended to check my method against published sources.
**>>>>
**>>>>The paper I selected by Schanda et al (2004). Homicide and major
**>>>>mental disorders. Acta Psychiatr Scand, 11:98-107 reports a total
**>>>>sample of 1087. Odds ratios are reported separately for men and
**>>>>women. There were 961 men all of whom were convicted of homicide.
**>>>>Of these 961 men, 41 were diagnosed with schizophrenia. The
**>>>>unadjusted odds ratio is for this group of 41 is cited as
**>>>>6.52 (4.70-9.00). They also report the general population aged
**>>>>over 15 with schizophrenia =20,109 and the total population =2,957,239.
**>>
**>>Looking at the paper (which is in volume 110 by the way) suggests
**>>that Peter's reading of the situation is correct and that is what
**>>the authors have done.
**>>
**>>>>Any further clarification is much appreciated,
**>>>A fisher.test on the following matrix seems about right:
**>>> > matrix(c(41,920,20109-41,2957239-20109-920),2)
**>>>
**>>> [,1] [,2]
**>>>[1,] 41 20068
**>>>[2,] 920 2936210
**>>>
**>>> > fisher.test(matrix(c(41,920,20109-41,2957239-20109-920),2))
**>>>
**>>> Fisher's Exact Test for Count Data
**>>>
**>>>data: matrix(c(41, 920, 20109 - 41, 2957239 - 20109 - 920), 2)
**>>>p-value < 2.2e-16
**>>>alternative hypothesis: true odds ratio is not equal to 1
**>>>95 percent confidence interval:
**>>>4.645663 8.918425
**>>>sample estimates:
**>>>odds ratio
**>>> 6.520379
**>>>
**>>>The c.i. is not precisely the same as your source. This could be
**>>>down to a different approximation (R's is based on the noncentral
**>>>hypergeometric distribution), but the classical asymptotic formula gives
**>>>
**>>> > exp(log(41*2936210/920/20068)+qnorm(c(.025,.975))*sqrt(sum(1/M)))
**>>>[1] 4.767384 8.918216
**>>>
**>>>which is closer, but still a bit narrower.
**>>
**>>Michael Dewey
**>>http://www.aghmed.fsnet.co.uk
**>
*

Michael Dewey

http://www.aghmed.fsnet.co.uk

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