# [R] replicating the odds ratio from a published study

Michael Dewey info at aghmed.fsnet.co.uk
Sun Jan 28 14:57:27 CET 2007

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